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SYSTEMATICS OF ALPHA-RADIOACTIVE ISOTOPES
I. Perlman, A. Ghiorso, and G. T. Seaborg*)
INTRODUCTION
Interest in the systematics of the properties of alpha-radioactive substances goes back to the early investigations of natural radioactivity, which showed that there is a direct dependence between the energy, or velocity, of $\alpha$-particles and the decay constant[^1]. Since then many attempts have been made to connect empirically the various data on alpha decay and, what is still more important, quantum mechanics has been successfully used to elucidate the nature of $\alpha$-decay[^2].
The importance of establishing the regularities of alpha decay is determined by a number of reasons. The discovery of artificial radioactivity and the continuous improvement of methods for obtaining unstable nuclei have made it possible to investigate the properties of an ever increasing number of different types of nuclei. In the case of the heavy elements, for which alpha radioactivity is predominant, it is extremely important to be able to predict, at least roughly, the radioactive properties of unknown nuclei, since the range of half-life periods that may occur here is extraordinarily large. At present such predictions can be made quite reliably, and this circumstance has substantially aided the production and identification of new types of nuclei in the region of the heavy elements. Although this is perhaps obvious, it should nevertheless be noted here that, since the creation and study of new isotopes is under consideration, along with the characteristics of alpha decay it is also necessary to consider the question of the beta stability of the isotopes.
Another important reason for the interest shown in alpha decay is due to the possibilities these data provide for elucidating the internal structure of the atomic nuclei of heavy elements. Alpha-decay energies can be measured quite accurately, and it is generally considered that they give unambiguous values
*) Physical Review 77, 26 (1950).
for the total decay energy. Since the heaviest elements are connected with the lead isotopes by continuous decay series, by making several substantial approximations it proves possible to connect, on an energy basis, the majority of nuclei in this region with one another. In short, it becomes possible to distinguish regions of greater nuclear stability from neighboring regions in which the nucleons are more weakly bound. Finally, additional information on the structure of the nucleus can be obtained by considering the dependence of the decay constant on the factors which, according to the quantum-mechanical interpretation of the alpha-decay process, determine the decay constants; in this way it is possible to determine to what extent the theory of alpha decay is capable of explaining all the new data.
The amount of available data has increased so greatly in recent years that a revision of the regularities of alpha decay has become necessary. Approximately 10 years ago only 24 alpha emitters were known, and all of them belonged to the naturally radioactive families. During the following 5 years reports were published on only 5 new emitters, one of which had been produced artificially, while the others were discovered as a result of a more careful investigation of radioactive substances occurring under natural conditions. At the present time about 100 types of alpha-active nuclei are known. The majority of the new isotopes may be divided into groups according to their position among the elements and according to the methods of their preparation. Work on the transuranium elements led to the discovery of 16 alpha emitters in this region[^4]. The production of appreciable quantities of \(U^{233}\) added another 7 alpha emitters, which are products of its decay and members of the radioactive family \(4n+1\)[^5,^6]. Correspondingly, 4 new types were discovered as a result of the discovery of the parallel series \(U^{237}\), and 18 isotopes in five new short-lived parallel series[^8]. Another group of 18 alpha emitters was obtained as a result of the formation, by neutron-deficient isotopes, of bismuth, polonium, astatine, emanation, and francium[^9].
The importance of the new alpha emitters discovered in recent years is determined by the fact that they increase the number of types of nuclei in which alpha decay is observed and, in addition, some of them fill the gaps between already known isotopes. The most important new regions for which data are available are the transuranium elements and isotopes with a deficiency of neutrons relative to beta-stable nuclei. The band of nuclei emitting alpha particles has thus expanded both vertically and horizontally.
Regularities in the properties of alpha-radioactive isotopes have now been established with sufficient accuracy for such a number of nuclei that it has become possible to make substantial
predictions for all nuclei, from bismuth to the elements lying beyond curium. Most of the values of alpha-particle energies and part of the data on half-lives have already been reported in several recent publications^10.
ALPHA-DECAY ENERGIES
General regularities
There are, obviously, many different ways of revealing energy regularities in alpha decay. The most complete would be the construction of an energy surface, from which one could determine the degree of instability of nuclei of any type. However, the direct graphical representation of alpha-decay energies is simpler and, moreover, it permits an enlargement of the scale. In graphs of this type one obtains a family of curves whose form depends on the choice of the argument and on the parameter chosen for joining the points.
One of the first methods of treating the data was proposed by Fфrner^11, who plotted the velocity of the alpha particle as a function of mass number and showed that, when the isotopes of each element are joined, parallel straight lines are obtained, with the exception of several notable deviations. Schintlmeister^12 constructed a similar graph, but in addition joined also the points with the same “neutron excess” \((A - 2Z = N - Z)\)*. It is evident that the members of a radioactive series directly connected with one another by alpha decay will all have the same “neutron excess.” A more complete treatment and interpretation of the available data was carried out by Berthelot^13 and, more recently, by Karlik^14, who used methods similar to those described above.
Another method of correlating alpha-decay data, applied recently by Wapstra^15 and Glückauf^16, consists in indicating the magnitude of the mass defect or of the alpha-decay energy at the point corresponding to the given nucleus on a graph of \(A\) as a function of \(A - 2Z\), or of \(Z\) as a function of \(N = A - Z\). Lines drawn through points of equal instability then serve to represent the regularities of this property.
The value of any method for representing the properties of alpha decay is determined above all by the accuracy with which it is possible to predict the properties of previously unknown alpha emitters. The latter, in turn, depends on how often new data fit into the adopted scheme. For general purposes, perhaps none of these methods has an advantage over the others, since the uncertainties due to extrapola—
* \(A\) — mass number, \(Z\) — number of protons; \(N\) — number of neutrons.
...inherent in all methods, and the latter make it possible with equal success to draw conclusions about the properties of nuclei.
At the present time, for almost all elements between bismuth and curium there are data indicating that the regularities in the properties of alpha decay can be well represented on a graph giving the dependence of the alpha-decay energy on the mass number, if the points corresponding to the isotopes of a given element are connected with one another. Such a representation of the available data is given in Fig. 1. Along the ordinate is plotted the alpha-decay energy*) for transitions between ground states, including the energy of the $\gamma$ rays in those cases where it is known that the most energetic alpha particles are accompanied by $\gamma$ radiation. If attention is concentrated on the heavy elements, leaving aside for the time being astatine and the lighter elements, then the most characteristic feature of the alpha energies is the circumstance that all the isotopes of one element can be joined by a relatively straight line, showing an increase of the energy with decreasing mass number. The general course is rectilinear, and the fact that in some places the line deviates somewhat from a straight line should not cause surprise. Possible reasons for this fact will be discussed below.
The general course of the increase of alpha energy with decreasing mass number can be explained quite satisfactorily by considering sections of the energy surface at constant mass number.
A number of such sections in idealized form is shown in Fig. 2 for $A$, $A - 2$, $A - 4$, etc. The parabolic form of these sections at constant $A$ was derived by Bethe and Bacher$^{17}$ from their semiempirical mass equation, which was transformed into a more convenient form by Bohr and Wheeler$^{18}$, who also determined the values of the parameters. These Bohr and Wheeler parabolas give, consequently, the relation between the energies of isobars. The abscissae in Fig. 2 are not continuous. This was done in order to separate the parabolas, and on each of them $Z$ indicates the position of the same atomic number.
As is known, in going from lead to uranium, in order to attain approximately equivalent configurations with respect to beta stability, on the average two neutrons are added for each additional proton. Therefore, if the element $Z$ lies at the vertex of the parabola corresponding to the mass number $A - 2$, as is shown in Fig. 2, then the element $Z - 2$ will lie approximately at the vertex of the parabola $A - 8$. It is further assumed that the coeffi-
*) In the present article the total energy of the transition between ground states will be called the “alpha-decay energy” or simply the “alpha energy,” while the kinetic energy of the alpha particle will be called the “alpha-particle energy.”
Fig. 1. Dependence of the energy of alpha decay of heavy nuclei on mass number.
...packing coefficient changes regularly in this region, and therefore, if the ordinates of Fig. 2 are functions of the mass defect or of the packing factor, then the parabolas will go precisely as shown. Identical parabolas arranged in this way have the property that the vertical projections of alpha-decay lines drawn between points of two parabolas (for example, from \(A, Z\) to \(A - 4, Z - 2\)) increase as \(A\) decreases.
Until the sections of the energy surface at constant \(A\) are approximately identical parabolas without sharp breaks, and so long as the slope of the surface is comparatively constant, a decrease in the mass number of each element must be accompanied by an increase in alpha energy. Koman \(^{19}\), deriving from the Bohr-Wheeler mass equation \(^{18}\) an expression for the alpha energy, obtained analytically the same results as we obtained graphically, provided that equivalent assumptions are made concerning the shape of the energy surface. It should be noted that the section of the energy surface at constant \(A\) is determined by a single parabola only if \(A\) is odd; but the same reasoning is applicable also to the case of “even \(A\),” when doubly odd nuclei lie on a parabola of higher energy than doubly even nuclei, since alpha decay is a transition between nuclei of the same type.
Fig. 2. Parabolic sections of the energy surface showing an increase in alpha energy with decreasing mass number.
The explanation given above with the aid of Fig. 2 assumes that the parabolic sections of the energy surface are identical and are shifted uniformly along the energy axis. Obviously, neither of these assumptions corresponds to reality, and further conclusions about the shape of the surface can be made only on the basis of a more detailed study of alpha-decay data. To do this, it is useful to construct a visual representation of exactly which regions of the energy ...
surfaces are considered. The corresponding portion of the surface is shown schematically in Fig. 3; along the vertical axis some mass function is plotted, for example the mass defect, and along the other axes are plotted the atomic number and the mass number. The surface has been idealized in the sense that it shows no irregularities due to even and odd relationships, but the latter do not enter into the consideration of alpha decay, since alpha transitions occur between nuclei of the same type. Several lines of constant \(Z\) and constant \(A\), as well as several reference points, are shown. In the lower part of Fig. 3 one may note certain sharp irregularities of the relief, which will be discussed below. For the present it will suffice to determine what information can be obtained from alpha-decay data in the region of mass numbers exceeding 216.
Fig. 3. Energy surface in the region of heavy elements.
Fig. 3 shows the line \(a—b\), drawn along the bottom of the valley; this line is sometimes called the line of beta stability. One may also imagine other curves, parallel to this line of stability, which will connect nuclei of the same degree of beta stability. From the alpha-decay energies one can obtain information on the slope of these curves and, consequently, on the slope of the surface itself. The alpha-decay energies indicate slopes not in the direction of the curves, but in a direction making a certain angle with them, as shown by the arrow \(\alpha\) in Fig. 3. Keeping this limitation of interpretation in mind, one may nevertheless note a quite definite trend in this region, consisting, first, in a strong slope of the bottom of the valley at masses above 216 and in a tendency toward the formation of a plateau between 224 and 236, after which there follows an increase of the slope at still higher mass numbers. These figures should not be regarded as precise, since no sharp breaks in the slope are observed,
and it is possible that other effects are superimposed in a direction not parallel to the valley.
The grounds for these conclusions can be clarified with the aid of Fig. 4. It shows the alpha-decay energy as a function of mass number, with nuclei of constant \(Z\) connected (by thin lines)
Fig. 4. Regularities of the alpha-energy of heavy elements. (Heavy solid lines connect nuclei with the same beta stability; dashed lines connect nuclei belonging to the same alpha-decay chain.)
to one another as in Fig. 1. The thick lines in Fig. 4 should represent regions of the same degree of beta stability. Thus, the line \(XY\) connects points lying on the line of stability \(a—b\), Fig. 3; the lower lines connect points of Bohr–Wheeler parabolas with \(Z\) values smaller than the \(Z\) corresponding to greatest stability, while the lines above \(XY\) pass through points with larger values of \(Z\) than the \(Z\) of greatest stability. The ordinate, i.e. the alpha energy, for each of the curves passes through a minimum, thereby indicating the existence of a minimum slope toward the energy surface
in this region. The reason for the vertical displacement of the curves in Fig. 4 can best be understood by referring to the model in Fig. 3. Since alpha decay occurs in a direction forming a certain angle with the valley, the values of the alpha energies corresponding to points situated on the left slope of the valley will progressively increase as one moves up along the slope, and will decrease as one moves upward along the other slope.
One may also consider the alpha-decay curves connecting points of one alpha-decay sequence with one another. Some of these lines are shown by dashed curves in Fig. 4; minima are also found in them. Here, however, the minima are due to at least two effects: first, the plateau in the direction of the valley and, second, the transition from one slope of the valley to the other.
It is impossible to connect this plateau with the structure of the nucleus in the same spirit as, for example, is possible in interpreting certain sharp irregularities in the lead region (see the discussion below). The practical significance of the existence of this region is that the half-lives of certain $\alpha$-radioactive nuclei in the region of beta stability consequently prove to be sufficiently long for their existence under natural conditions.
Let us consider what would result in the case of a somewhat greater inclination of the energy surface. Then $U^{238}$, which is regarded as beta-stable, could have a half-life 10 or 20 times shorter and would have practically all decayed. In $U^{240}$ the lifetime with respect to alpha decay would be longer, but, being beta-unstable, it would be transformed into $Pu^{240}$, for which again the alpha-decay period would be too small. It may be asserted that the conditions for the preservation in nature of some isotope are that this isotope be the heaviest beta-stable isotope of the given element, i.e. that it lie on the corresponding side of the valley, and also that it lie on this plateau. Apparently only two nuclei, $Th^{232}$ and $U^{238}$, satisfy these conditions. Another nucleus with a long lifetime, $U^{235}$, exists in nature for another reason, connected with an abnormally large decay-energy period. This will become clearer when half-lives are discussed.
Returning to Fig. 1, one may note that the smooth course of the energy curves as functions of mass number, beginning with the lightest and ending with the heaviest isotope of each element lying between emanation and curium, is not valid for the elements below emanation. At present even isotopes of emanation and francium have been identified which do not fit into this sequence. Here, for the heaviest isotopes of each element, the increase of alpha energy with decreasing mass number is clearly visible, but then a point of sharp break is reached,
after which the alpha energy decreases as the mass number decreases. At still lower mass numbers a minimum occurs in the curve, and the original trend again resumes.
The bismuth isotopes are especially interesting in that their alpha activity disappears over a wide interval of mass numbers and then reappears again at very low masses. The condition for an increase of alpha energy with decreasing mass number is fulfilled from Bi\(^{214}\) to Bi\(^{211}\), whereas for Bi\(^{210}\) the alpha energy is considerably smaller, and for Bi\(^{209}\) (stable bismuth) the alpha energy, judging from the absence of visible alpha activity, must be less than 4 Mev. Several bismuth isotopes are known \(^{3,20}\) in the interval Bi\(^{202}\)—Bi\(^{207}\)*), but alpha activity has not been found in any of them. At still lower mass numbers, however (Bi\(^{201}\) and below), alpha activity reappears. A similar behavior, but at higher energies, is observed for polonium and astatine, and also, probably, for higher elements.
This behavior can be explained by sharp irregularities of the energy surface of the type indicated in the lower part of the model shown in Fig. 3. It is easy to see that the Bohr–Wheeler “parabolas” at constant \(A\) have an appreciable dip, which represents a deviation from the general trend, and with its aid, by a method similar to that used in Fig. 2, one can explain the observed inversion of alpha energies.
Another method that can be used consists in considering lines on the energy surface at constant \(Z\). This has been done schematically in Fig. 5 for \(Z = 84\) and \(Z = 82\). The lengths of the arrows represent the alpha energies of polonium isotopes having the indicated mass numbers, and in this way one can trace the increase of the alpha energy from Po\(^{220}\) to Po\(^{212}\), followed by its sharp decrease, and then a gradual increase with further decrease of the mass number. One should not attach great significance to the exact form of these contours, apart from the fact that they will have a similar form if the irregularities of the energy surface are located along some line corresponding to a constant number of neutrons, as shown in Fig. 3. The changes in the slope of the curves in Fig. 5 have been chosen so that they correspond to the experimental data on alpha decay. It should be noted that the contours are drawn only through even-even nuclei. This was done so as not to complicate the picture with even-odd alternations. In essence, the inversion in alpha energy noted in this region is due to the anomalous magnitude
*) Bi\(^{203}\) and Bi\(^{205}\) decay by electron capture; the corresponding half-lives are 2 hours and 14 days (D. C. Karraker and D. H. Templeton, unpublished). Bi\(^{203}\) decays by electron capture with a period of 12 hours (H. M. Neuman and T. Perlman, unpublished).
nuclear binding corresponding to the presence of 126 neutrons, and will be discussed below.
The preceding sections were devoted to elucidating the general regularities of alpha decay. It is now proposed to discuss the data presented in Fig. 1, and to note certain conclusions that can be drawn concerning the properties of a number of individual nuclei.
Fig. 5. Schematic section of the energy surface for \(Z = 84\) and \(Z = 82\), illustrating the regularities of the alpha energies of polonium isotopes. (The arrows indicate the mass numbers of the polonium isotopes; the length of the arrows is proportional to the alpha energies.)
Evaluation of the data
Most of the methods used for determining alpha energies are characterized by a very high accuracy of the values obtained. Errors in the determination of the energies almost never exceed 100 kev, and most values are known with substantially greater accuracy. As will be seen in the last part of the present article, there is hope of calculating nuclear radii on the basis of alpha-decay data, and an uncertainty in alpha energies of the order of 10 kev would already be significant and undesirable. However, for establishing general regularities and for clarifying the principal errors of interpretation, which have a different origin, such accuracy is not required. In several cases there are doubts concerning the value of the mass number; in Fig. 1 such cases are marked by a question mark printed after the mass number. In no case were the adopted values of the mass numbers chosen completely arbitrarily; thus, for example, four alpha emitters of bismuth having a neutron deficiency were arranged in agreement with the data for the excitation function, and the mass numbers of some of them were chosen on the basis of considering their genetic connection with the decay products of lead and thallium arising as a result of successive decay by means of the capture of atomic electrons.
For some other data given in Fig. 1, the question mark is placed before the symbol, as in the case of \(\mathrm{Pu}^{232}\), which
indicates the uncertainty of the energy value, due in this case to the absence of resolution of this group from others formed simultaneously during irradiation. In all cases where the energies were calculated or estimated, this was indicated accordingly in the figure.
In addition to the uncertainties already mentioned, it must be emphasized that it is the total decay energy that should be considered, and essentially we have made the implicit assumption that the indicated alpha energies correspond to transitions to the ground state. In those cases where it is known that this is not so, corrections were introduced by adding the energy of the $\gamma$ rays, as in the case of $\mathrm{U}^{235}$ and $\mathrm{Am}^{241}$ (see details in the appendix). There are weighty grounds for thinking that in many cases, not yet proved, the observed alpha particles do not correspond to transitions to the ground level. As an example, we note that $\mathrm{Pu}^{239}$ and $\mathrm{U}^{233}$, which clearly do not fall on a straight line, are associated with considerable gamma radiation$^{3}$; the latter may mean that the group of alpha particles observed here does not correspond to a transition to the ground level. Further considerations in favor of the existence of such a phenomenon will be given in discussing the question of the dependence of half-life periods on energy.
The alpha energies of three other nuclei—$\mathrm{Bi}^{210}$ (RaE), $\mathrm{Pu}^{241}$, and $\mathrm{Am}^{242}$—were calculated from closed decay cycles, since it was impossible to measure the energy of the $\alpha$ particle directly. In all three cases the process of alpha decay could be recognized from the appearance of the daughter isotope. Broda and Feather$^{22}$ identified 4-minute thallium as a decay product of RaE and, using the beta-decay energy of these two isotopes and the alpha energy of $\mathrm{Po}^{210}$, it was possible to calculate the alpha energy of RaE. The following schemes
\[ \begin{array}{ccc} & \mathrm{Am}^{241} & \\ \alpha,\ 5.63 \swarrow & & \nwarrow\ \beta^{-}<0.02 \\ \mathrm{Np}^{237} & & \mathrm{Pu}^{241} \\ \beta^{-},\gamma\ 0.5 \searrow & & \swarrow\ \alpha\ 5.1\ (\mathrm{calc.}) \\ & \mathrm{U}^{237} & \end{array} \qquad \begin{array}{ccc} & \mathrm{Cm}^{242} & \\ \alpha\ 6.18 \swarrow & & \nwarrow\ \beta^{-}\ 0.6 \\ \mathrm{Pu}^{238} & & \mathrm{Am}^{242} \\ \beta^{-},\gamma\ 1.4 \searrow & & \swarrow\ \alpha\ 5.4\ (\mathrm{calc.}) \\ & \mathrm{Np}^{238} & \end{array} \]
show the data used for calculating the alpha energies of $\mathrm{Pu}^{241}$ and $\mathrm{Am}^{242}$ (for further discussion see the appendix).
Bismuth and neighboring elements. Effect of 126 neutrons.
The recent discovery of alpha radioactivity in bismuth isotopes, extremely neutron-deficient (Fig. 1), is interesting in that it signifies a “secondary appearance” of alpha radioactivity of bismuth with a considerable difference in mass number from that of
for natural alpha emitters. A possible explanation of this has already been put forward; namely, one may suppose that the course of the alpha energies for these light isotopes of bismuth, polonium, and astatine essentially resumes the same course that is characteristic of the heavy isotopes, i.e., an increase in alpha energy with decreasing mass number. This resumption of the general regularity occurs after a certain interruption caused by the presence of a region of anomalously large nuclear binding.
From the available data it is easy to see why alpha activity was not detected in such previously known isotopes as Bi$^{205}$ and Bi$^{204}$. Extrapolating the curves in Fig. 1 for bismuth, one may estimate that the alpha energy of these isotopes should be of the order of, or less than, 4 MeV. The alpha-decay period corresponding to this energy would probably be greater than $10^8$ years, and therefore it would be impossible to detect alpha particles. As will be seen below, it would be desirable to know that part of the decay constant of the electron-capturing bismuth isotopes which pertains to alpha emission, since the relation between the half-life and the energy gives additional information about the nuclear radius and, consequently, about the binding energy of the nucleus.
The alpha emitter with an energy of 5.15 MeV which is identified with Bi$^{201}$ has a measured half-life of one hour, whereas even a rough estimate of its alpha-decay period gives a value of 50 years, i.e., a very small alpha branch.
The secondary appearance of large alpha energies, making it possible to detect isotopes of bismuth, polonium, and astatine very poor in neutrons, suggests that elements of still lower atomic number may also possess alpha activity. This question was considered in greater detail by Koman$^{19}$. Recently in our laboratory$^{23}$ a number of short-lived alpha emitters were observed in this region; these emitters were obtained by irradiating gold with high-energy deuterons, and two of them are tentatively assigned to isotopes of gold and mercury. On the other hand, similar experiments did not detect alpha activity in lead. This circumstance may mean that the region of stability leading to a decrease in alpha energy and to an anomalous increase in lifetime in the localized region for astatine, polonium, and bismuth extends near lead and, possibly, thallium, as a result of which alpha activity is not observed. After passage through this region, the alpha energies and the alpha-decay constants again become sufficiently large, especially for isotopes relatively poor in neutrons.
In considering the cause of the inversion of the alpha energies of bismuth, polonium, and astatine, one must postulate the existence
region of anomalously stable nuclear binding. There is every reason to believe that, for each element, in passing from large to small mass numbers this effect begins at some definite number of neutrons, as indicated in Fig. 3. Thus, the maximum values of the alpha energy of bismuth and polonium occur for the isotopes Bi\(^{211}\) and Po\(^{212}\), and for astatine probably for At\(^{213}\) (see the following section). All these isotopes decay by emitting alpha particles and turn into nuclei with 126 neutrons; it is quite probable that this number of neutrons corresponds to a particularly stable nuclear structure as compared with nuclei with a larger number of neutrons\(^{25,26}\). It should be noted that, since the alpha-decay energy is taken as the main criterion, there is no sharp jump in nuclear binding at a number of neutrons less than 126, in contrast to what is observed for a number of neutrons exceeding this value.
Neither Fig. 1 nor theory makes it possible to predict quantitatively in which elements beyond astatine this effect of 126 neutrons will appear. As can be seen in Fig. 3, the decline of the energy surface due to the configuration with 126 neutrons extends all the way to element 88, i.e. to radium. It may also be noted that for each subsequent element the minima of alpha energy caused by this lowering of the surface should occur at progressively increasing alpha energies. For the isotopes Bi, Po, and At having 126 neutrons, the alpha energies are respectively: \(<4\) Mev, \(5.3\) Mev, and \(5.9\) Mev. Since the differences for the subsequent elements apparently decrease, it is difficult to extrapolate to the next nucleus with 126 neutrons—Em\(^{212}\), but it is reasonable to suppose that its alpha energy will be less than \(6.4\) Mev. As will be seen below, for nuclei with 126 or fewer neutrons alpha decay is strongly forbidden and, judging from the curves of Fig. 9, depending on the energy, for Em\(^{212}\) one may expect a lifetime in the interval from several minutes to an hour. Owing to the configuration of 126 neutrons it is possible that the nucleus Em\(^{212}\) is sufficiently stable to be beta-stable. As a result, one may expect that at least this light isotope of emanation should be observable. In short, since the matter concerns predictions, there is every reason to think that the curve for the isotopes of emanation (element 86) in Fig. 1 will reach a maximum at Em\(^{214}\), and at smaller mass numbers will descend into a region in which the alpha energies of the nuclei will be of the order of \(6\) Mev.
Quite recently, in our laboratory, attempts were made to obtain isotopes of emanation and francium with low mass number by bombarding thorium with high-energy protons. Alpha emitters were discovered in the predicted energy region; they must be assigned to nuclei with a smaller mass number,
than in any nuclei of these elements known up to now. In particular, to two of these activities the following characteristics were assigned: \(\mathrm{Em}^{212}\), period 23 minutes, particle energy \(6.17\) MeV; \(\mathrm{Fr}^{212}\), period 19 minutes, alpha-particle energy \(6.25\) MeV.
This same effect may possibly occur also in the higher elements, but it must be less sharply expressed and should be more difficult to observe, since not only will the lifetimes for alpha decay in the heavy elements be shorter because of the larger alpha energies, but also, at a constant number of neutrons, the neutron deficiency of the corresponding nuclei will progressively increase, and these nuclei will therefore have short periods for transformation by electron capture.
PREDICTION OF NUCLEAR PROPERTIES
Methods and examples
It is obvious that, with the aid of the regularities presented in Fig. 1, one can predict the alpha energies of many nuclei without resorting to the extensive experimental material already available; and this path has indeed been used by a number of investigators. In addition, one can use the dependence of half-period on energy to predict alpha-decay periods; these correlations will be considered in the present article somewhat below. We shall not attempt to compile a list of predicted properties of nuclei at present unknown, or of their modes of decay. However, there are several important generalizations that can be obtained either on the basis of existing data or on the basis of predictions, and these should be discussed. One of them, concerning the comparatively long-lived alpha-active isotopes of emanation and francium of small mass number, has already been discussed. It will perhaps not be superfluous briefly to recall the basic premises and the methods used.
The first consideration is that all nuclei in the region under consideration are, according to energy data, alpha-unstable, and almost all of them, whether natural isotopes or artificially produced, would have measurable alpha activity if alpha decay were the only type of instability. Alpha decay, however, may fail to be observed in beta-unstable nuclei if the ratio of the beta half-period to the alpha half-period is very small. Similarly, a beta-unstable nucleus may practically fail to exhibit this instability if the alpha half-period is relatively very small.
For a number of reasons it is desirable to know whether a nucleus is stable or unstable with respect to beta decay, independently of its alpha-decay properties. Beta-stable nuclei in this region are quite ana-
analogous to stable nuclei in lower parts of the periodic system, and their structure gives information about the structure of the nucleus in general. An example of such a case will be given in one of the following sections; there the possibility is discussed of the absence of beta-stable isotopes in astatine (element 85), which apparently also occurs for two other elements: technetium (element 43) and promethium (element 61). An entirely different use of the knowledge of beta-stability is connected with obtaining certain types of nuclei by means of the beta-decay process. Thus, for example, it is quite legitimate to doubt the correctness of difficult measurements indicating that astatine isotopes arise in the rare branching of the “A-products” (polonium isotopes) of the natural radioactive series, since it can be shown quite convincingly that these “A-products” are beta-stable. In general, the question of beta-stability is very important, and in Table I an attempt has been made to compile the corresponding list of heavy nuclei.
In addition to predicting the type of decay, it is very important to be able to predict also its probability. The prediction of the magnitudes of alpha-radiation periods constitutes the main content of the present article. The precise prediction of alpha-decay lifetimes, together with analogous predictions for beta-stability, is the principal condition determining the method of best production and identification of new unknown isotope species. Such predictions were exceptionally valuable in the successive production of transuranium and transplutonium elements and are guiding factors in experiments on obtaining still higher elements. Thus, along with predictions concerning alpha-decay, it is often important to estimate the energies of beta-decay and electron-capture transformations and, further, by means of the Sargent diagram, to estimate also the half-lives.
These predictions can be made by methods differing both in their essence and in their reliability. Alpha-energies can be determined by the corresponding interpolation or extrapolation on a graph similar to that given in Fig. 1; in doing so, however, it is necessary to keep in mind the sharp changes that occur in nuclei with configurations close to the configurations corresponding to closed shells. For example, it can be said with sufficient confidence that the alpha-energy of Em\(^{221}\) should lie between the energies for Em\(^{220}\) and Em\(^{222}\) and is equal to \(6.0 \pm 0.1\) MeV; on the other hand, it would be erroneous to assign to At\(^{213}\) an alpha-energy lying between At\(^{214}\) and At\(^{212}\), since, judging from other regularities, one may conclude that the energy of At\(^{213}\) should be higher than that of At\(^{214}\) (as shown in Fig. 1), similarly to what occurs for the pairs Bi\(^{211}\)—Bi\(^{212}\) and Po\(^{212}\)—Po\(^{213}\).
Having information on certain decay energies, it often turns out—
can be calculated from decay cycles; the simplest type of such a cycle is the following.
\[ \begin{array}{ccccc} && (Z+1)^A && \\ & \alpha \swarrow && \searrow \beta^- & \\ (Z-1)^{A-4} && \text{electron capture} && Z^A \\ & \searrow \beta^- && \swarrow \alpha & \\ && (Z-2)^{A-4} && \end{array} \]
Any three members uniquely determine the fourth. Sometimes, with very little experimental material, one can make estimates which in turn lead to very important conclusions. Thus, one may use alpha-decay energies to judge nuclear spins near closed neutron and proton shells. For example, the problem is to obtain data concerning the spin of \( \mathrm{Pb}^{209} \), which has one more neutron than the number of neutrons in the “closed shell” (126), and also to determine the spin of \( \mathrm{Po}^{209} \), which has one neutron fewer than 126. The known data are shown in the following scheme (dotted lines denote decay modes not yet observed).
\[ \begin{array}{ccccc} && \mathrm{Po}^{209} && \\ & \swarrow \alpha && \dashrightarrow\ \text{electron capture (?) } & \\ \begin{array}{c} 5.00\,\mathrm{MeV}\\ 200\,\gamma\\ \mathrm{Pb}^{205} \end{array} &&&& \mathrm{Bi}^{209} \\ & \dashrightarrow\ \text{electron capture} && \dashleftarrow\alpha & \uparrow\ \beta;\,0.01\,\mathrm{MeV} \\ && \mathrm{Tl}^{205} && \mathrm{Pb}^{209} \end{array} \]
Proceeding from the absence of alpha activity in natural bismuth (minimum half-life \(\sim 10^{12}\) years) and using the relations considered below between half-life and energy, one can say almost with certainty that the alpha-decay energy of \( \mathrm{Bi}^{209} \) is less than \(4\,\mathrm{MeV}\), and possibly considerably less than this value, say of the order of \(3\,\mathrm{MeV}\). Since \( \mathrm{Pb}^{205} \) must be heavier than \( \mathrm{Tl}^{205} \), it can at once be said that \( \mathrm{Po}^{209} \) is heavier than \( \mathrm{Bi}^{209} \) by at least \(1\,\mathrm{MeV}\), and probably by considerably more. In preparations of \( \mathrm{Po}^{209} \) with appreciable alpha activity, the upper limit for the electron-capture process, as determined from the intensity of X-radiation, is 10 percent, which leads for this mode of decay to a minimum half-life of 2000 years.\(^{24}\) Considering that this value is a minimum for the half-life and that the decay energy in any case is not less than \(1\,\mathrm{MeV}\),
and possibly considerably greater, we come to the conclusion that this decay process is strongly forbidden in comparison with many others, for which the half-life for this energy is of the order of 100 minutes.^29 It is known that the spin of \(\mathrm{Bi}^{209}\) is \(9/2\), and since it is necessary to postulate a large change of spin in the transition \(\mathrm{Po}^{209}—\mathrm{Bi}^{209}\), \(\mathrm{Po}^{209}\) must be assigned a small spin, say \(1/2\).
Another isobar transforming into \(\mathrm{Bi}^{209}\) is \(\mathrm{Pb}^{209}\) from the \(\mathrm{U}^{233}\) family. Its half-life is 3.3 hours and the decay energy is \(0.7\) Mev. This half-life and energy correspond to an allowed transition, which Fezer and Richardson^30 associate with a change of spin by \(-1\). Already on this basis one would have to assign to \(\mathrm{Pb}^{209}\) the enormous spin \(11/2\), but in any case it should be approximately equal to the value of the spin for \(\mathrm{Bi}^{209}\), i.e. it should be large. The main point that should be noted is that \(\mathrm{Pb}^{209}\), having 127 neutrons, possesses one excess neutron in comparison with the configuration with 126 neutrons and, according to Mayer,^31 this excess neutron should in fact be located on the \(7i\) level with spin term \(i_{11/2}\). Turning now to \(\mathrm{Po}^{209}\), we see that it has 125 neutrons, one neutron fewer than the number in a closed shell. According to Mayer’s term scheme, the last filled levels in the shell have the spin term \(i_{13/2}\), but, as was noted for the preceding shells, these levels with high spin number are filled only in pairs, and there is an intersection with a level of smaller spin number. In this case the 125th neutron would have the spin term \(4p_{1/2}\), which, according to Mayer, is the nearest level to the first \(i\)-levels. As can be seen, this is in good agreement with the properties of \(K\)-capture in \(\mathrm{Po}^{209}\) considered above. It should be noted that the analogous nucleus should be \(\mathrm{Pb}^{207}\) (125 neutrons), and Nordheim,^32 Mayer^31 and Finberg and Gammak^33 assign the odd neutron to the \(4p\) state with spin \(1/2\).
For a further illustration of the use of alpha-decay data for predicting nuclear properties, let us consider the case of two astatine isotopes.
First of all we shall touch on the question of the alpha energy of \(\mathrm{At}^{213}\), equal, according to Fig. 19, to 2 Mev; this value is predicted. It may be noted that \(\mathrm{At}^{214}\) has almost the same alpha energy as \(\mathrm{ThC}'\) (\(\mathrm{Po}^{212}\)), which is the most energetic of all alpha emitters known up to now. It is therefore of some interest to determine whether \(\mathrm{At}^{213}\) has an even higher decay energy. The uncertainty in the present case is due to the absence of data on the beta stability of \(\mathrm{Po}^{213}\), if such stability exists, and on the energy of \(K\)-capture of \(\mathrm{At}^{213}\). Although this cannot be asserted with certainty, it is nevertheless very probable that \(\mathrm{Po}^{213}\) is either \(\beta^{-}\)-stable or only very little
unstable with respect to At\(^{213}\). The beta-stability of Po\(^{213}\) will be discussed below in the section on beta-stability. Assuming that the energy of the beta decay Po\(^{213}\)—At\(^{213}\) is zero, that the total decay energy for the beta transition Pb\(^{209}\) is equal to 0.70 MeV, and, finally, knowing the alpha energy of Po\(^{213}\), equal to 8.5 MeV, one can calculate that the alpha energy of At\(^{213}\) will be equal to 9.2 MeV. This energy would correspond to the hypothesis that the largest alpha energy in this region corresponds to that isotope of each given element which transforms into a nucleus with 126 neutrons; in the present case this will be the transformation At\(^{213}\) → Bi\(^{209}\). To this estimate of the decay energy of At\(^{213}\) it is necessary to add the electron-capture energy of At\(^{213}\), or to subtract the \(\beta^-\)-energy of Po\(^{213}\), depending on what actually takes place.
According to Karlik and Bernert\(^{34}\), At\(^{216}\) arises in the thorium family through a \(\beta^-\)-branching of the decay of ThA (Po\(^{216}\)). These authors observed a weak alpha group with energy 7.57 MeV and a half-period equal to the period of the separated thoron (Em\(^{220}\)); they therefore attributed this group to a branching of the transformation ThA (\(\sim 0.01\%\)), in agreement with the scheme
flowchart LR
A["ThA(Po²¹⁶)"] -- "β⁻(0.01%)" --> B["At²¹⁶"]
B -- "α" --> C["ThB(Pb²¹²)"]
A -- "α(99.99%)" --> D["ThB(Pb²¹²)"]
E["Tn(Em²²⁰)<br/>α(55 sec)"] --> A
Karlik and Bernert drew attention to a serious difficulty connected with this interpretation. Namely: summation of the decay energies of the closed cycle leads to the conclusion that At\(^{216}\) (if one uses the values of the alpha energy of At\(^{216}\) obtained by these authors) is in fact unstable with respect to ThA by 0.15 MeV, whereas the observed \(\beta^-\)-branching of ThA would require an energy of 1 MeV with the opposite sign, so that a discrepancy of 1.15 MeV is obtained. Retaining their assumption of the existence in At\(^{216}\) of an alpha group with energy 7.57 MeV, they explain this discrepancy by the supposition that ThB transforms into Bi\(^{212}\) (ThC), which is in an excited state with energy 1.15 MeV, while the alpha decay of At\(^{216}\) proceeds directly to the ground level. This explanation seems to us untenable for a number of reasons. If ThC represented a postulated excited state of Bi\(^{212}\), then the alpha energy of the excited state would be 1.15 MeV lower than the measured value (6.1 MeV), i.e. would be approximately equal to 5.0 MeV.
From Fig. 1 it is seen that the value 6.1 MeV fits well on the energy curve between Bi\(^{211}\) and Bi\(^{213}\), whereas the value 5.0 MeV does not fit at all. Moreover, this explanation contradicts the known properties of the parallel decay series[^3], beginning with Pa\(^{228}\) with a half-life of 22 hours, since in this series At\(^{216}\), arising in the alpha decay of Er\(^{220}\), is transformed into Bi\(^{212}\), which has properties identical with ThC; consequently, an energy of 6.1 MeV appears, which would be impossible if At\(^{216}\), on decaying, passed to the ground level of the isotope for which ThC is the excited state. The supposition that the whole Pa\(^{228}\) series has been incorrectly described is extremely unlikely, since the formation of RdTh (Th\(^{228}\)) on the \(K\)-capture branch of Pa\(^{228}\), the formation of ThX (Ra\(^{224}\)) in the \(K\)-capture of Ac\(^{224}\), and ThC′ (Po\(^{212}\)) in the \(\beta^-\)-decay of ThC (Bi\(^{212}\)) have been well established. In general it is very unlikely that ThA (Po\(^{216}\)) is \(\beta^-\)-unstable and that therefore the alpha group with energy 7.57 MeV from Tn must be produced by some mechanism not connected with At\(^{216}\). At\(^{216}\) cannot originate from Fr\(^{220}\), formed in the \(\beta^-\)-branching of Em\(^{220}\), since Em\(^{220}\) is certainly \(\beta^-\)-stable. It is possible that the correct explanation is one analogous to that given by Feather[^35] for the observations of Karlik and Bernert.
The examples given above of the use of alpha-decay data serve to illustrate some methods which have found practical application.
Beta stability in isotopes of heavy elements
Discussion of the question whether At\(^{216}\) can be formed in the radioactive thorium series shows the full importance of the possibility of predicting the beta stability of certain isotopes. Many of the short-lived alpha emitters are beta-unstable, but this instability remains unnoticed because of the predominance of alpha decay. Nevertheless, the degree of beta instability can often be calculated with the aid of closed decay cycles, and, conversely, beta energies can serve as valuable links in calculating alpha energies or in predicting branched decay. In the present article we shall not deal with the calculation of beta energies; the data of Table I merely indicate the existence of beta stability or the presumed stability of the given isotope. All predicted statements are enclosed in parentheses. A recently published table by Biswas and Mukherjee[^36], in which the types of instability of various nuclei are given, differs in certain points from Table I and does not include predictions concerning unobserved types of instability or unknown isotopes.
The greatest uncertainty in the prediction of beta stability lies in the choice of those isotopes of astatine and francium which-
Table I
Beta-stability of heavy elements
| Element | Beta-stable | Unstable with respect to electron capture | β-unstable | β-unstable and unstable with respect to electron capture |
|---|---|---|---|---|
| Bismuth | $\mathrm{Bi}^{209}$ | $\mathrm{Bi}^{197}—\mathrm{Bi}^{206}$, $(\mathrm{Bi}^{207})$ | $\mathrm{Bi}^{210}—\mathrm{Bi}^{214}$ | $(\mathrm{Bi}^{208})$ |
| Polonium | $\mathrm{Po}^{208}$, $\mathrm{Po}^{210}$, $\mathrm{Po}^{211}$, $(\mathrm{Po}^{212})$, $(\mathrm{Po}^{213}?)$, $(\mathrm{Po}^{214})$, $(\mathrm{Po}^{216})$ | $\mathrm{Po}^{202}$, $(\mathrm{Po}^{203})$, $\mathrm{Po}^{204}—\mathrm{Po}^{207}$, $(\mathrm{Po}^{209})$ | $\mathrm{Po}^{215}$, $(\mathrm{Po}^{217})$, $\mathrm{Po}^{218}$ | |
| Astatine / Emanation | $(\mathrm{Em}^{212}?)$, $(\mathrm{Em}^{214})$, $(\mathrm{Em}^{215}?)$, $(\mathrm{Em}^{216}—\mathrm{Em}^{218})$, $\mathrm{Em}^{220}$, $\mathrm{Em}^{222}$ | $\mathrm{At}^{204}—\mathrm{At}^{211}$, $(\mathrm{At}^{212}?)$, $\mathrm{Em}^{213}$ | $(\mathrm{At}^{215}?)$, $(\mathrm{At}^{217},\ \mathrm{At}^{218})$, $(\mathrm{Em}^{219}?)$, $(\mathrm{Em}^{221})$ | $(\mathrm{At}^{212})$, $(\mathrm{At}^{214})$, $(\mathrm{At}^{216})$ |
| Francium / Radium | $(\mathrm{Fr}^{219}?)$; $(\mathrm{Ra}^{218},\ \mathrm{Ra}^{220},\ \mathrm{Ra}^{221})$, $\mathrm{Ra}^{222}—\mathrm{Ra}^{224}$, $\mathrm{Ra}^{226}$ | $(\mathrm{Fr}^{218})$; $(\mathrm{Ra}^{219}?)$ | $(\mathrm{Fr}^{221})$, $\mathrm{Fr}^{223}$; $\mathrm{Ra}^{225}$, $\mathrm{Ra}^{227}$, $\mathrm{Ra}^{228}$ | $(\mathrm{Fr}^{220},\ \mathrm{Fr}^{222})$ |
| Actinium / Thorium | $\mathrm{Ac}^{225}$; $(\mathrm{Th}^{234},\ \mathrm{Th}^{236})$, $\mathrm{Th}^{237}—\mathrm{Th}^{230}$, $\mathrm{Th}^{232}$ | $(\mathrm{Ac}^{222})$, $\mathrm{Ac}^{223}$; $(\mathrm{Th}^{323})$, $\mathrm{Th}^{325}$ | $\mathrm{Ac}^{226}$, $\mathrm{Ac}^{227}$, $\mathrm{Ac}^{228}$; $\mathrm{Th}^{231}$, $\mathrm{Th}^{233}$, $\mathrm{Th}^{234}$ | $(\mathrm{Ac}^{224},\ \mathrm{Ac}^{226})$ |
| Protactinium / Uranium | $\mathrm{Pa}^{231}$; $\mathrm{U}^{230}$, $\mathrm{U}^{233}—\mathrm{U}^{235}$, $(\mathrm{U}^{236})$, $\mathrm{U}^{238}$ | $(\mathrm{Pa}^{236})$, $\mathrm{Pa}^{227}—\mathrm{Pa}^{229}$; $(\mathrm{U}^{237})$, $\mathrm{U}^{228}$, $\mathrm{U}^{229}$, $\mathrm{U}^{231}$ | $\mathrm{Pa}^{233}$, $\mathrm{Pa}^{233}$, $\mathrm{Pa}^{234}$; $\mathrm{U}^{237}$, $\mathrm{U}^{239}$ | $\mathrm{Pa}^{230}$, $(\mathrm{Pa}^{232})$ |
| Neptunium / Plutonium | $\mathrm{Np}^{237}$; $\mathrm{Pu}^{236}$, $\mathrm{Pu}^{238}—\mathrm{Pu}^{240}$, $(\mathrm{Pu}^{242},\ \mathrm{Pu}^{244})$ | $\mathrm{Np}^{231}$, $(\mathrm{Np}^{232})$, $\mathrm{Np}^{233}—\mathrm{Np}^{235}$; $(\mathrm{Pu}^{232},\ \mathrm{Pu}^{233})$, $\mathrm{Pu}^{234}$, $(\mathrm{Pu}^{235})$, $\mathrm{Pu}^{237}$ | $\mathrm{Np}^{238}$, $\mathrm{Np}^{239}$; $\mathrm{Pu}^{241}$, $(\mathrm{Pu}^{243})$ | $(\mathrm{Np}^{236},\ \mathrm{Np}^{238})$ |
| Americium / Curium | $\mathrm{Am}^{241}$, $(\mathrm{Am}^{243}?)$; $\mathrm{Cm}^{242}$, $(\mathrm{Cm}^{244}—\mathrm{Cm}^{246},\ \mathrm{Cm}^{248})$ | $\mathrm{Am}^{238}—\mathrm{Am}^{240}$; $\mathrm{Cm}^{238}$, $(\mathrm{Cm}^{239})$, $(\mathrm{Cm}^{240}?)$, $\mathrm{Cm}^{241}$, $(\mathrm{Cm}^{243}?)$ | $\mathrm{Am}^{242}$, $(\mathrm{Am}^{244})$; $(\mathrm{Cm}^{247},\ \mathrm{Cm}^{249})$ | $(\mathrm{Am}^{242})$ |
| Berkelium | $(\mathrm{Bk}^{247})$ |
...which are beta-stable, if such isotopes exist at all. Measurements of the alpha energy of \( \mathrm{At}^{216} \), carried out in our laboratory, gave the value \(7.79\ \mathrm{Mev}\); together with the alpha energy of \( \mathrm{Po}^{216}\) (ThA) and the decay energy of \( \mathrm{Pb}^{212}\) (ThB), this value makes it possible to calculate that \( \mathrm{At}^{216}\) is unstable (by \(0.4\ \mathrm{Mev}\)) with respect to \(K\)-capture with transformation into \( \mathrm{Po}^{216}\). In an analogous way, using the recently measured alpha energy of \( \mathrm{At}^{214}\), one can show that \( \mathrm{Po}^{214}\) (RaC′) is beta-stable. Under such circumstances, when both \( \mathrm{Po}^{216}\) and \( \mathrm{Po}^{214}\) are beta-stable, it is natural to expect that \( \mathrm{Po}^{213}\) will be beta-stable, although a number of cases are known in which there are two beta-unstable odd-odd isotopes of lower mass number than the heaviest beta-stable even-even isotope. Carrying out a closed decay cycle for \( \mathrm{Po}^{213}\), \( \mathrm{At}^{213}\), \( \mathrm{Pb}^{209}\), and \( \mathrm{Bi}^{209}\), one can show that, in order for \( \mathrm{At}^{213}\) to be heavier than \( \mathrm{Po}^{213}\), the alpha-decay energy of \( \mathrm{At}^{213}\) must be greater than \(9.20\ \mathrm{Mev}\). The only thing that can be said on the basis of the extrapolation in Fig. 1 is that \( \mathrm{At}^{213}\) may indeed have so large an alpha-decay energy. As a result, at present the question of the beta stability of \( \mathrm{At}^{213}\) cannot be resolved.
The most probable beta-stable isotope of astatine is \( \mathrm{At}^{215}\). It can be shown here that \( \mathrm{Po}^{215}\) is approximately \(0.8\ \mathrm{Mev}\) heavier than \( \mathrm{At}^{215}\), but it is entirely unclear whether \( \mathrm{At}^{215}\) is stable with respect to \( \mathrm{Em}^{215}\).
As regards the question of the beta stability of \( \mathrm{At}^{215}\) with respect to \( \mathrm{Em}^{215}\), it can be shown that this case is a limiting one with respect to the applicability of the estimates, quite analogous to the case \( \mathrm{At}^{213} — \mathrm{Po}^{213}\). One can construct the following decay cycle with the known decay energies indicated in the scheme.
The alpha-decay energy of \( \mathrm{Em}^{215}\) can be estimated from Fig. 1 and then
close the cycle in order to determine which is heavier, \(Em^{215}\) or \(At^{215}\); on the other hand, these isobars may be regarded as equal and the alpha energy which \(Em^{215}\) would have to possess in order to satisfy this condition can be determined. It turns out that if the alpha energy of \(Em^{215}\) is less than 8.79 Mev, then \(Em^{215}\) is beta-stable and \(At^{215}\) beta-unstable. From Fig. 1 it is seen that this requirement falls within the limits of the estimate (8.7—8.9), and it may be asserted that the difference between \(Em^{215}\) and \(At^{215}\) probably does not exceed 100 kev. It should be noted that the most probable change which may have to be introduced into the experimental value of the decay series given above is a certain increase in the mass of \(At^{215}\). The possible beta-stable isotopes of astatine considered above are \(At^{213}\) and \(At^{215}\). The higher isotopes of astatine are, evidently, beta-unstable.
Since astatine has no isotope which could be experimentally regarded as beta-stable, the question arises of the existence of such an isotope of astatine in general and, in particular, of whether this element is similar to the other two elements absent in nature—technetium \((Z=43)\) and promethium \((Z=61)\),—which, to all appearances, do not possess beta-stable isotopes. In considering this question, certain strikingly similar features are found in all three elements, which shed light on the reason for their lack of beta-stable isotopes. The point is the position of these elements relative to the positions of the stable configurations, or “closed shells,” of the nucleus *).
In the case of technetium it is necessary to consider the influence of the equality of the number of neutrons in the nucleus to 50, apparently imparting additional stability to nuclei in which it is fulfilled. It should be kept in mind that, in general, only one isotope of an odd element can be stable with respect to its isobar of the even element. It may be assumed that for technetium this isotope is \(Tc^{97}\), since it lies in the middle between \({}_{39}Y^{93}\) and \({}_{45}Rh^{101}\). However, \(Tc^{97}\) has two extra pairs of neutrons in comparison with the stable configuration of 50 neutrons, and since one may regard the binding energy of these neutrons as anomalously small, this may be just sufficient for this nucleus to be heavier than one of its isobars, especially if one additionally assumes that for odd elements the influence of the “closed shell of neutrons” on the binding energy of the extra neutrons will be still smaller. The only thing that can be concluded from these considerations is that an odd ele-
) Proofreading note. After the completion of this article we became acquainted with a paper by A. Bronevsky (Comptes Rendus 223*, 916 (1949)), from which it appears that this author had already earlier noted that the positions of the missing elements 43 and 61 are close to the positions of closed neutron shells.
ment situated near the upper boundary of the elements having a stable isotope with a neutron number corresponding to anomalous stability should be subject to the action of this factor, but at present too little is known about the details of nuclear binding to be able to predict whether this element is niobium (41) or technetium (43).
Promethium (element 61) is in an analogous position with respect to the neutron number 82. Here we have a whole series of stable isotopes, namely: \({}_{54}\mathrm{Xe}^{136}\), \({}_{56}\mathrm{Ba}^{138}\), \({}_{57}\mathrm{La}^{139}\), \({}_{58}\mathrm{Ce}^{140}\), \({}_{59}\mathrm{Pr}^{141}\), \({}_{60}\mathrm{Nd}^{142}\), \({}_{62}\mathrm{Sm}^{144}\). The remarkable stability of 82 neutrons leads to the fact that, although \(\mathrm{La}^{139}\) and \(\mathrm{Pr}^{141}\) differ by exactly two protons, they are nevertheless both beta-stable; this same property of special stability apparently is also the reason for the absence of a stable element in the next odd element—promethium—on grounds analogous to those set forth for technetium.
The next neutron number which is apparently stabilizing lies in the region of lead and is, presumably, 126. In the heavy elements the complication of nuclei usually proceeds by adding two neutrons for each proton, and therefore one should expect that the number of elements having isotopes with the same number of neutrons will be smaller than the corresponding number for the light elements. For the neutron number 126 there are beta-stable nuclei \({}_{82}\mathrm{Pb}^{208}\), \({}_{83}\mathrm{Bi}^{209}\), and \({}_{84}\mathrm{Po}^{210}\). We have already considered above the interesting possibility of the existence of beta-stable \({}_{86}\mathrm{Em}^{212}\). As in the case of neutron numbers 50 and 82, one may expect that the odd element in this region will not have a beta-stable isotope, and here we postulate that this element is astatine (85).
The only possible beta-stable isotopes of francium are \(\mathrm{Fr}^{219}\) and \(\mathrm{Fr}^{221}\), since it is known that \(\mathrm{Fr}^{223}\) transforms into \(\mathrm{Ra}^{223}\) (\(\mathrm{AcX}\)). It is impossible to assert with complete certainty that \(\mathrm{Fr}^{219}\) is stable, but we shall accept this assumption for the time being. The question that must be resolved consists in determining which of the isobars \(\mathrm{Fr}^{219}\) and \(\mathrm{Em}^{219}\) is the heavier, since \(\mathrm{Ra}^{219}\) is almost certainly unstable with respect to \(K\)-capture.
Using the values of the alpha energies shown in Fig. 1 (see Table III), and the value 1.40 for the decay energy of \(\mathrm{AcB}^{211}\), one can construct a cycle containing these isobars and also including \(\mathrm{At}^{215}\), \(\mathrm{AcA}^{215}\), \(\mathrm{AcB}^{211}\), and \(\mathrm{AcC}^{211}\). The corresponding calculation shows that \(\mathrm{Fr}^{219}\) is beta-stable with respect to \(\mathrm{Em}^{219}\) (\(\mathrm{An}\)) by approximately 300 keV. In view of the arguments given concerning the beta-instability of \(\mathrm{Em}^{219}\), it can be said with confidence that \(\mathrm{Em}^{221}\) is a \(\beta^{-}\)-emitter, and therefore the question of the beta-stability of \(\mathrm{Fr}^{221}\) reduces to the question of the stabi-
...activity of Ra\(^{221}\) with respect to \(K\)-capture. Closing the cycle, including Ra\(^{221}\), Fr\(^{221}\), Em\(^{217}\), Po\(^{213}\), At\(^{217}\), and Bi\(^{213}\), we find that Fr\(^{221}\) is heavier than Ra\(^{221}\) by 100 kev; in view of the uncertainty of some of the data, this small difference does not permit a definite conclusion to be drawn. We shall provisionally assume that the only beta-stable isotope of francium is Fr\(^{219}\).
Transuranium Elements
For beta-stable nuclei and nuclei with an excess of neutrons, the alpha-decay energy of comparable nuclei increases progressively in going to atomic numbers greater than that of uranium. This effect was already pointed out in the discussion of Fig. 4. This means that comparable nuclei (in the sense of their position relative to the center of beta stability of each element) must possess ever greater alpha energies and shorter half-periods in passing beyond uranium. If it is assumed that alpha decay is the only way in which very heavy nuclei spontaneously transform into lighter nuclei, then this effect could be derived independently of the measured values of the alpha energy, solely on the basis of the fact that over the geological period no transuranium elements have remained on the earth.
To illustrate this regularity, Table II gives the alpha energies of analogous nuclei of even elements in this region. Nuclei in the same horizontal row are regarded as analogous. Several values obtained as a result of interpolation and extrapolation are also given and are enclosed in parentheses.
Table II
Regularities of the alpha energies of comparable nuclei
| U\(^{232}\) — 5.40 | Pu\(^{238}\) — 5.60 | Cm\(^{244}\) — 5.88 |
| U\(^{233}\) — 4.89 | Pu\(^{239}\) — 5.24 | Cm\(^{245}\) — (5.7) |
| U\(^{234}\) — 4.84 | Pu\(^{240}\) — 5.2 | Cm\(^{246}\) — (5.6) |
| U\(^{235}\) — 4.63 | Pu\(^{239}\) — 5.24 | |
| U\(^{236}\) — (4.6) | or | |
| Pu\(^{241}\) — 5.1 | ||
| Pu\(^{243}\) — (4.9) |
The prediction of the properties of the nuclei of isotopes lying beyond curium is one of the applications of these regularities. The lightest beta-stable isotope of element 98 is 98\(^{246}\), or possibly 98\(^{248}\). With the aid of the regularities noted above it can be predicted that the alpha energies of 98\(^{246}\) and 98\(^{248}\) should be, respectively, 6.8 and 6.6 Mev. The regularities for the half-periods of doubly even isotopes, presented in Fig. 6, make it possible to extrapolate to element 98 and to predict that the alpha half-periods of the isotopes 98\(^{246}\) and 98\(^{248}\) should have values approximately equal to several days and to one month, respectively.
Fig. 6. Relations between half-life and energy for doubly even nuclei. Roman numerals indicate short-range fine-structure groups; the symbol “O” denotes a transition to the ground level. (An obvious error was made in the original: instead of \(Ra^{222}\), \(Ra^{220}\) was printed. Translator’s note.)
Alpha Radioactivity in the Region of the Rare-Earth Elements
It will perhaps not be erroneous to assert that an alpha-active isotope can be obtained from almost any element in the upper half of the periodic table, if a sufficient number of neutrons is removed. The possible behavior of such alpha emitters was considered by Coman[^19]. For the elements immediately following lead, the deviations from the region of beta stability within which alpha decay becomes appreciable are not yet so large that this alpha activity can be observed against the background of \(K\)-capture. To this category of alpha emitters should belong gold and mercury, which are analogous to the alpha emitters of bismuth having mass numbers of the order of 200. In the lower regions of the periodic system, where the general slope of the packing curve is less favorable to alpha emission, appreciable alpha decay, one must suppose, will occur only at a sufficient degree of instability with respect to \(K\)-capture or positron decay, i.e., when the lifetime will be very short and the detection of alpha decay will prove difficult. If, however, it were to turn out that in some portion of the packing curve the slope is especially large, then even a moderate deficiency of neutrons could increase the effect so much that observation of alpha emitters would become possible. It is possible that just such a region has recently been discovered in our laboratory.
Thomson et al.[^3] prepared a series of alpha-active elements of the rare earths, having half-lives lying within the limits from several minutes to several days, the energy of the alpha particles lying between 4.2 and 3.1 Mev. Although these activities have not yet been identified with certainty, it is very probable that they belong not to samarium or to the lighter rare earths, but to the neutron-deficient isotopes of gadolinium, terbium, dysprosium, and holmium. The most attractive hypothesis is that the high ability of these nuclei to emit alpha particles is due to their special position with respect to the stable configuration of 82 neutrons, just as the most energetic alpha particles from the heavy elements are emitted by nuclei with a number of neutrons of the order of 126. For the rare earths the difference will consist in the fact that, with a deficiency of neutrons, these nuclei in almost all cases will lie outside the limits of beta stability, and, because of the smaller slope of the packing curve, the energies of alpha emitters with 84 neutrons will be relatively smaller than those of emitters with 128 neutrons. On the basis of these considerations, one may think that the recently discovered group of alpha emitters consists of such isotopes as \( \mathrm{Gd}^{148} \), \( \mathrm{Tb}^{149} \), \( \mathrm{Dy}^{150} \), \( \mathrm{Ho}^{151} \), or of isotopes close to them. It will probably not be possible to detect alpha emission in isotopes heavier than \( \mathrm{Gd}^{149} \)
by two mass units or heavier than Ho \(^{151}\) by four units. Confirmation of the picture set forth can be found in a number of experimental data obtained earlier. Thus, for example, it was long ago noticed that Sm \(^{146}\), which is obviously beta-stable, is absent from natural samarium and apparently should be regarded as an alpha emitter. This indicates that, in the region under consideration, samarium is the only element having an isotope that lies within the limits of beta stability and possesses a large alpha energy. On the basis of the picture being developed, there may be a temptation to identify the long-lived alpha emitter of natural samarium with Sm \(^{147}\) or Sm \(^{148}\), but the available, more reliable and direct data point to Sm \(^{152}\) \(^{37}\).
RATE OF ALPHA DECAY
According to a simplified treatment of the alpha-decay process, the alpha particle exists in the nucleus as a certain whole, and the probability of its emission is governed by the potential field of this nucleus. Consequently, the factors determining the decay constant are the atomic number, the alpha energy or the velocity of the \(\alpha\)-particle, and the nuclear radius. For a given decay energy, an increase in atomic number decreases the decay constant, and a decrease in nuclear radius decreases the decay constant as a result of the increase of the potential barrier. The quantum-mechanical interpretation of the decay process is embodied in the well-known formula \(^{2}\), which has several variants; this formula has been able, with exceptional success, to explain the great sensitivity of the decay constant to changes in the decay energy. According to the theory, the influence of the atomic number should be considerably less abrupt, which is in fact confirmed by experiment. It is not possible, by an independent calculation, to determine the nuclear radius with the required accuracy, and therefore the formula is used to calculate an “effective radius,” which can thus serve as a quantitative test of any theory. It turns out that this “effective radius” undergoes rather significant changes, deviating in some cases from the \(A^{1/3}\) law by as much as 25%. One of the factors that lengthen the half-life and enter into the expression for the effective radius is the change of spin that occurs in the decay. However, we shall see below that many new experimental data indicate a whole series of regularities, including a broad class of nuclei with anomalously long lifetimes, which cannot be explained by changes of spin. It must be concluded that the simplified one-body model is inadequate in these cases and that, in certain kinds of nuclei, the process of formation of alpha particles is slower. Such nuclei include those that contain an odd number of neutrons or pro-
tons, or both simultaneously; in this sense alpha radiation is forbidden in nuclei with nonzero spin, irrespective of any effect that may be caused by a change of spin in the decay process.
References to most of the data used in establishing these regularities may be found in the work cited above³. The alpha energies and half-periods of alpha decay for all the alpha groups used are given in Table III. Those groups that were not covered by the named work³, or for which additional data have appeared, are discussed in the Appendix. In Figs. 6–9 the data of Table III are represented graphically; the curves shown give the dependence of energy on half-period for non-forbidden alpha-decay processes. These curves, as will be explained, are determined by even-even nuclei. Alpha decay of other types is, as a rule, relatively forbidden, and the last column of Table III gives the divergence factor between the observed half-period and the theoretical value for the case in which the decay process is not forbidden.
Even-odd nuclei
Figure 6 presents the dependence of half-period on energy for even-even nuclei, the lines being drawn through points of identical \(Z\). With the exception of certain insignificant deviations, all the points lie on a series of parallel straight lines. The uncertainty of some individual points responsible for deviations from the straight line—for example \( \mathrm{Pu}^{240} \), \( \mathrm{U}^{238} \)—is so great that it is quite possible that further measurements will apparently lead to some refinement of the form of the curves.
Of the known even-even nuclei, only \( \mathrm{Po}^{210} \), \( \mathrm{Po}^{208} \), \( \mathrm{Po}^{206} \), and \( \mathrm{Po}^{204} \) fall sharply away from the general straight line, and for reasons to be discussed below these nuclei are presented on another graph (Fig. 9). It is possible that these nuclei, or their decay products, possess anomalously small radii in comparison with the heaviest isotopes of polonium and/or with most isotopes of higher elements. These are those isotopes of polonium which in Fig. 1 lie in the region adjacent to the break in the curve of energy as a function of mass number; naturally, on the half-period–energy curve these isotopes also exhibit a break. However, even allowing for the smaller decay energy, the half-periods of these isotopes are anomalously large, which once again reflects the contraction of the nuclear radius in this region. Further discussion of these isotopes is given below; there, other isotopes with anomalously large half-periods are also considered.
Throughout the remainder of this article these curves for even-even nuclei will serve as the basis for comparison with the curves
Table III
Alpha energies and half-lives
| Nucleus | Alpha energy | Intensity of alpha groups | Measured half-life | Alpha-branching ratio | Alpha half-life | Hindrance factor |
|---|---|---|---|---|---|---|
| Doubly even nuclei | ||||||
| $\mathrm{Cm}^{242}$ | 6.18 | 150 days | 150 days | |||
| $\mathrm{Cm}^{240}$ | 6.37 | 26.8 days | $>0.8$ | $\sim 30$ days | ||
| $\mathrm{Pu}^{240}$ | 5.2 | $\sim 6000$ years | $\sim 6000$ years | |||
| $\mathrm{Pu}^{238}$ | 5.60 | 92 years | 92 years | |||
| $\mathrm{Pu}^{236}$ | 5.85 | 2.7 years | 2.7 years | |||
| $\mathrm{Pu}^{234}$ | 6.26 | 8.5 h | $\sim 0.03$ | $\sim 10$ days | ||
| $\mathrm{U}^{238}$ | 4.25 | $4.51 \times 10^9$ years | $4.51 \times 10^9$ years | |||
| $\mathrm{U}^{234}$ | 4.84 | $2.35 \times 10^5$ years | $2.35 \times 10^5$ years | |||
| $\mathrm{U}^{232}$ | 5.40 | 70 years | 70 years | |||
| $\mathrm{U}^{230}$ | 5.96 | 20.8 days | 20.8 days | |||
| $\mathrm{U}^{238}$ | 6.83 | 9.3 min | 12 min | |||
| $\mathrm{Th}^{232}$ | 4.05 | $1.39 \times 10^{10}$ years | $1.39 \times 10^{10}$ years | |||
| $\mathrm{Th}^{230}$ | 0 4.76 | 0.80 | $8.0 \times 10^4$ years | $1.0 \times 10^5$ years | ||
| $\mathrm{Th}^{230}$ | 1 4.69 | 0.20 | $4.0 \times 10^5$ years | |||
| $\mathrm{Th}^{228}$ | 0 5.52 | 0.70 | 1.90 years | 2.64 years | ||
| $\mathrm{Th}^{228}$ | 1 5.43 | 0.28 | 6.79 years |
Continuation
| Nucleus | Alpha energy | Intensity of alpha groups | Measured half-life | Alpha-branching ratio | Alpha half-life | Deviation factor |
|---|---|---|---|---|---|---|
| Th²²⁶ | 6.41 | 30.9 min. | 30.9 min. | |||
| Ra²²⁶ | 0 4.88 | 0.91 | 1622 years | 1780 years | ||
| Ra²²⁶ | I 4.68 | 0.09 | 1.8×10⁴ years | |||
| Ra²²⁴ | 5.78 | 3.64 days | 3.64 days | |||
| Ra²²³ | 6.62 | 38 sec. | 38 sec. | |||
| Em²²² | 5.59 | 3.83 days | 3.83 days | |||
| Em²²⁰ | 6.39 | 54.5 sec. | 54.5 sec. | |||
| Em²¹⁸ | 7.25 | 0.019 sec. | 0.019 sec. | |||
| Po²¹⁸ | 6.12 | 3.05 min. | ∼ 1 | 3.05 min. | ||
| Po²¹⁶ | 6.89 | 0.158 sec. | 0.158 sec. | |||
| Po²¹⁴ | 7.83 | 1.5×10⁻⁴ sec. | 1.5×10⁻⁴ sec. | |||
| Po²¹² | 8.95 | 3.0×10⁻⁷ sec. | 3.0×10⁻⁷ sec. | |||
| Even-odd nuclei | ||||||
| Pu²⁴¹ | 5.1 (calc.) | ∼ 10 years | 2×10⁻⁵ | 5×10⁵ years | 9 | |
| Pu²³⁹ | 4.24 | 2.4×10⁴ years | 4 | |||
| U²³⁵ | 0 5.64 | 0.10 | 7.07×10⁸ years | 7.1×10⁹ years | 1000 | |
| U²³⁵ | I 4.48 | 0.90 | 7.7×10⁸ years | 13 |
Continuation
| Nucleus | Alpha energy | Intensity of alpha groups | Measured half-life | Alpha-branching ratio | Alpha half-life | Deviation factor |
|---|---|---|---|---|---|---|
| \(U^{233}\) | 4.90 | \(1.6\times10^5\) years | \(1.6\times10^7\) years | 2 | ||
| \(U^{231}\) | 5.6 (est.) | 4.2 days | \(6\times10^{-5}\) | 200 years | 40 | |
| \(U^{229}\) | 6.53 | 58 min. | 0.2 | 5 hours | 9 | |
| \(Th^{229}\) | 0 5.14 | 0.1 | 7000 years | \(7\times10^4\) years | 350 | |
| \(Th^{229}\) | I 5.04 | 0.2 | 7000 years | \(3.5\times10^4\) years | 45 | |
| \(Th^{229}\) | II 4.94 | 0.7 | 7000 years | \(10^4\) years | 3 | |
| \(Th^{227}\) | 0 6.16 | 0.20 | 18.6 days | 93 days | 300 | |
| \(Th^{227}\) | I 6.13 | 0.038 | 18.6 days | |||
| \(Th^{227}\) | II 6.10 | 0.25 | 18.6 days | 74.5 days | 100 | |
| \(Th^{227}\) | III 6.08 | 0.038 | 18.6 days | |||
| \(Th^{227}\) | IV 6.03 | 0.013 | 18.6 days | |||
| \(Th^{227}\) | V 5.97 | 0.025 | 18.6 days | |||
| \(Th^{227}\) | VI 5.92 | 0.013 | 18.6 days | |||
| \(Th^{227}\) | VII 5.87 | 0.20 | 18.6 days | 93 days | 10 | |
| \(Th^{227}\) | VIII 5.84 | 0.038 | 18.6 days | |||
| \(Th^{227}\) | IX 5.82 | 0.15 | 18.6 days | 124 days | 8 | |
| \(Th^{227}\) | X 5.77 | 0.025 | 18.6 days | 745 days | 25 |
Continuation
| Nucleus | Alpha energy | Intensity of alpha groups | Measured half-life | Alpha-branching ratio | Alpha half-life | Deviation factor |
|---|---|---|---|---|---|---|
| Th²²⁵ | 6.68 | 7.8 min. | 0.9 | 8.7 min. | 5 | |
| Ra²²³ | 0 5.82 | 0.55 | 11.2 d. | 20.2 d. | 10 | |
| Ra²²³ | I 5.71 | 0.36 | 31 d. | 4 | ||
| Ra²²³ | II 5.63 | 0.90 | 124 d. | 5 | ||
| Ra²²¹ | 6.83 | 0.83 | 31 sec. | 31 sec. | 7 | |
| Em²¹⁹ | 0 6.94 | 0.085 | 3.92 sec. | 4.7 sec. | 14 | |
| Em²¹⁹ | I 6.68 | 0.085 | 46 sec. | 10 | ||
| Em²¹⁹ | II 6.56 | 46 sec. | 3 | |||
| Em²¹⁷ | 7.88 | 10⁻³ sec. | 10⁻³ sec. | 4 (?) | ||
| Po²¹⁵ | 7.50 | 1.83×10⁻³ sec. | ∼1? | 1.8×10⁻³ sec. | 1 | |
| Po²¹³ | 8.49 | 4·10⁻⁶ sec. | 4×10⁻⁶ sec. | 1 | ||
| Odd-even nuclei | ||||||
| Am²⁴¹ | I 5.58 | 490 yr | 490 yr | 2 | ||
| Am²³⁹ | 5.87 | 12 hr. | 10⁻⁴ | 13.7 yr | 3 (?) | |
| Np²³⁷ | 4.85 | 2.2×10⁶ yr | 2.2×10⁶ yr | 4 | ||
| Np²³⁵ | 5.15 | 435 d. | 5×10⁻⁵ | 2.5×10⁴ yr | 4 (?) |
Continuation
| Nucleus | Alpha energy | Intensity of alpha groups | Measured half-period | Alpha-branching ratio | Alpha half-period | Hindrance factor |
|---|---|---|---|---|---|---|
| $\mathrm{Np}^{233}$ | 5.65 | 35 min | $10^{-5}$ | 10 years | 1 (?) | |
| $\mathrm{Pa}^{231}$ | 0 5.10 | 0.87 | $3.43 \times 10^4$ years | $3.95 \times 10^4$ years | 40 | |
| $\mathrm{Pa}^{231}$ | I 4.82 | 0.13 | $3.43 \times 10^4$ years | $2.64 \times 10^5$ years | 5 | |
| $\mathrm{Pa}^{229}$ | 5.79 | 1.5 days | 0.01 | 150 days | 3 (?) | |
| $\mathrm{Pa}^{227}$ | 6.57 | 38 min | 0.8 | 50 min | 6 | |
| $\mathrm{Ac}^{227}$ | 5.04 | 21.7 years | 0.012 | 1810 years | 7 | |
| $\mathrm{Ac}^{225}$ | 5.90 | 10.0 days | 5 | |||
| $\mathrm{Ac}^{223}$ | 6.76 | 2.2 min | $\sim 1$ (?) | 2.2 min | 7 | |
| $\mathrm{Fr}^{221}$ | 6.45 | 4.8 min | $\sim 1$ (?) | 4.8 min | 5 | |
| $\mathrm{Fr}^{219}$ | 7.44 | 0.02 sec | 0.02 sec | 3 (?) | ||
| $\mathrm{At}^{217}$ | 7.15 | 0.021 sec | $\sim 1$ (?) | 0.021 sec | 1 | |
| $\mathrm{At}^{215}$ | 8.15 | $10^{-4}$ sec | $\sim 1$ (?) | 10 sec | 4 (?) | |
| Doubly odd nuclei | Doubly odd nuclei | Doubly odd nuclei | Doubly odd nuclei | Doubly odd nuclei | Doubly odd nuclei | Doubly odd nuclei |
| $\mathrm{Am}^{242}$ | 5.4 (calc.) | $\sim 2 \times 10^5$ years | 20 (?) | |||
| $\mathrm{Pa}^{230}$ | 5.5 (est.) | 17.7 days | $3.5 \times 10^{-5}$ | 1400 years | 250 (?) | |
| $\mathrm{Pa}^{228}$ | 6.20 | 22 hours | $\sim 0.02$ | $\sim 50$ days | 150 (?) |
Continuation
| Nucleus | Alpha energy | Intensity of alpha groups | Measured half-life | Alpha-branching ratio | Alpha half-life | Deviation factor |
|---|---|---|---|---|---|---|
| Pa$^{226}$ | 6.93 | 1.7 min. | $\sim 1$ (?) | 1.7 min. | 6 | |
| Ac$^{224}$ | 6.28 | 2.9 h | 10. | 29 h | 40 | |
| Fr$^{220}$ | 6.81 | 27.5 sec. | $\sim 1$ (?) | 27.5 sec. | 13 | |
| At$^{216}$ | 7.94 | $10^{-3}$ sec. | $\sim 1$ (?) | $10^{-3}$ sec. | 10 | |
| Particularly forbidden nuclei | Particularly forbidden nuclei | Particularly forbidden nuclei | Particularly forbidden nuclei | Particularly forbidden nuclei | Particularly forbidden nuclei | Particularly forbidden nuclei |
| Isotopes of bismuth and others with 126 or fewer neutrons | Isotopes of bismuth and others with 126 or fewer neutrons | Isotopes of bismuth and others with 126 or fewer neutrons | Isotopes of bismuth and others with 126 or fewer neutrons | Isotopes of bismuth and others with 126 or fewer neutrons | Isotopes of bismuth and others with 126 or fewer neutrons | Isotopes of bismuth and others with 126 or fewer neutrons |
| Bi$^{214}$ | 0 5.61 | 0.45 | 19.7 min. | $4 \times 10^{-4}$ | 76 d | 400 |
| Bi$^{214}$ | I 5.55 | 0.55 | 19.7 min. | $4 \times 10^{-4}$ | 63 d | 150 |
| Bi$^{213}$ | 5.97 | 47 min. | 0.02 | 39 h | 350 | |
| Bi$^{212}$ | 0 6.20 | 0.27 | 60.5 min. | 0.337 | 11 h | 1000 |
| Bi$^{212}$ | I 6.16 | 0.70 | 60.5 min. | 0.337 | 4.3 h | 600 |
| Bi$^{212}$ | IV 5.70 | 0.011 | 60.5 min. | 0.337 | 272 h. (11.3 d) | 150 |
Continuation
| Nucleus | Alpha energy | Intensity of alpha groups | Measured half-period | Alpha-branching ratio | Alpha half-period | Deviation factor |
|---|---|---|---|---|---|---|
| \(\mathrm{Bi}^{211}\) | 0 6.74 | 0.84 | 2.16 min | 0.997 | 2.6 min | 700 |
| \(\mathrm{Bi}^{211}\) | I 6.38 | 0.16 | 13.5 min | 150 | ||
| \(\mathrm{Bi}^{210}\) | 4.86 | 5.0 days | \(\sim 3\times 10\) | \(5\times 10^{4}\) years | \(10^{4}\) (?) | |
| \(\mathrm{Bi}^{199}\) | 5.58 | 25 min | \(\sim 2\times 10\) | 2 years | 3000 (?) | |
| \(\mathrm{Bi}^{197}\) | 6.3 | 2 min | ? | \(>2\) min | \(>10\) (?) | |
| \(\mathrm{Em}^{212}\) | 6.30 | 23 min | ? | 23 min | 10 | |
| \(\mathrm{Fr}^{212}\) | 6.37 | 19 min | 0.5 | 38 min | 16 (?) | |
| \(\mathrm{At}^{211}\) | 6.00 | 7.5 hr | 0.40 | 19 hr | 50 | |
| \(\mathrm{Po}^{210}\) | 5.40 | 138 days | 138 days | 30 | ||
| \(\mathrm{Po}^{209}\) | 5.02 | 200 years | \(>0.9\) | 200 years | 150 | |
| \(\mathrm{Po}^{208}\) | 5.24 | 3 years | 3 years | 30 | ||
| \(\mathrm{Po}^{207}\) | 5.2 | 5.7 hr | \(\sim 10^{-4}\) | 7 years | 50 (?) | |
| \(\mathrm{Po}^{206}\) | 5.3 | 9 days | 0.1 | 90 days | 6 (?) | |
| \(\mathrm{Po}^{204}\) | 5.45 | 4 hr | \(\sim 10^{-4}\) | 5 years | 1000 | |
| \(\mathrm{Au}^{<190}\) | 5.3 | 4.3 min | \(10^{-4}\) | 1 month | 400 (?) |
half-life–energy curves for nuclei of other types. In its form, this family of curves does not fit into the quantitative interpretation of the alpha-decay process in which the parameter \(Z\) is regarded as constant for each individual curve and the nuclear radius is regarded as a monotonic function of the mass number, this being true independently of the type of nucleus. This method of treating alpha-decay data has already been used by Bertelot\({}^{38}\) and Biswas\({}^{39}\), who attempted to correlate all the various types of nuclei with the corresponding curves. We shall see later that rather good agreement between the data for doubly even nuclei and theory can be obtained if certain reasonable assumptions are made concerning the nuclear radius. In the following paragraphs it will be seen that nuclear types which are not doubly even do not fall into this family of curves.
Attention should be paid to the position of the polonium isotope curve in Fig. 6, since calculations indicate that \(\mathrm{Po}^{213}\) and, possibly, \(\mathrm{Po}^{214}\) exhibit here the effect of a decrease in the nuclear radius, an effect especially noticeable for \(\mathrm{Po}^{210}\) and the lighter polonium isotopes and leading to a lengthening of the half-life. In this sense it is incorrect to draw the principal polonium curve through these points (\(\mathrm{Po}^{213}\) and \(\mathrm{Po}^{214}\)).
In the subsequent discussion, devoted to nuclei with an odd number of nucleons, an important place is occupied by the question of the role of fine structure in the degree of forbiddenness of alpha decay. On this point there is a sharp difference between doubly even nuclei and all the others. Among even-even nuclei, three cases of fine structure stand out clearly, and within the accuracy of the experimental data all the groups fall on the curves of Fig. 6. In other words, the partial alpha half-lives for both groups of each of the nuclei \(\mathrm{Ra}^{226}\), \(\mathrm{Th}^{230}\) (Io), and \(\mathrm{Th}^{228}\) (RdTh) agree with the values that would be expected from the corresponding group energies.
It may be noted that for nuclei with an odd number of nucleons the mechanism of alpha-decay forbiddenness is such that the transition to the ground state is the most forbidden.
Even–odd nuclei
If, on the graph of the dependence of half-life on energy, one plots the points corresponding to nuclei with even \(Z\) and an odd number of neutrons, it may be observed that almost all these points lie appreciably above the curves for the corresponding elements with an even number of neutrons. This is illustrated by Fig. 7, in which the even–odd nuclei are marked by their symbols, while the principal curves coincide with the curves for doubly even nuclei shown in Fig. 6.
Fig. 7. Dependence of the half-life period on the energy for odd–even nuclei.
Vertical axis: decimal logarithm of the alpha half-life period.
Horizontal axis: alpha-decay energy (MeV).
Of special interest are those cases in which odd-even nuclei emit two or more groups of alpha particles. The partial alpha half-lives for alpha decay of these groups were calculated (Table III) and, together with the corresponding energy values, plotted on the graph. It may be noted that, on the basis of the adopted criterion, the short-range groups are less forbidden than the alpha group corresponding to the transition to the ground state. This effect can be clearly illustrated by the example of \( \mathrm{Th}^{229} \), which has three alpha groups; comparing them with the curve for doubly even thorium isotopes (Fig. 6), we see that the group with energy \(5.14\ \mathrm{Mev}\) (transition to the ground level) is forbidden by a factor of 350, whereas the groups at \(5.04\ \mathrm{Mev}\) and \(4.84\ \mathrm{Mev}\) are forbidden, respectively, by factors of 45 and 3. All other cases of fine structure are qualitatively similar to \( \mathrm{Th}^{229} \) in the sense that the transition to the ground level is the most forbidden, while groups of low energy may be relatively unforbidden.
It is significant that all odd-even nuclei (in any case, those which have been obtained with a degree of purity sufficient for the work) may have transitions to levels other than the ground level; this is confirmed by direct observations of alpha groups and by the presence of gamma radiation of high intensity. The case of \( \mathrm{Th}^{229} \), from the \((4n+1)\) family, has already been mentioned; three alpha groups have been measured for it. Also belonging to this category of sharply expressed complex fine structure are \( \mathrm{Th}^{227}(\mathrm{RdAc}) \), \( \mathrm{Ra}^{223}(\mathrm{AcX}) \), and \( \mathrm{Em}^{219}(\mathrm{An}) \) from the actinium-uranium family.
The anomalously large partial alpha half-lives of the above-mentioned odd-even nuclei for transitions to the ground level make it reasonable to assume the existence of other cases in which transitions to the ground level have not been observed. There was every reason to believe that \( \mathrm{U}^{235} \) is an example of such behavior, since gamma radiation of high intensity, with energy \(160\ \mathrm{kev}\), had been found in it, apparently occurring in cascade with the only observed alpha group (for references and details see the Appendix). We have now discovered a group with relative intensity \(10 \pm 1\%\), corresponding to a transition to the ground level; in unresolved or partly resolved \( \mathrm{U}^{235} \), this group is masked by alpha particles of \( \mathrm{U}^{234} \) (see the Appendix). A consequence of these observations is that, while the transition at \(4.48\ \mathrm{Mev}\) is forbidden by somewhat more than a factor of 10, the transition to the ground state (\(4.64\ \mathrm{Mev}\)) is forbidden by a factor of 1000. In view of these new facts, a new determination of the specific activity and half-life of \( \mathrm{U}^{235} \) is an urgent task, especially since the half-life value of this isotope figures in calculations of the age of the Earth.
Taking into account the behavior of \(U^{235}\), it would be interesting to investigate the connection between the gamma radiation and the alpha radiation of some other even-odd nuclei of the type \(Pu^{239}\) and \(U^{233}\). It is quite possible that in these cases as well the observed alpha particles do not correspond to transitions to the ground state and that these transitions are strongly forbidden. Gamma radiation of medium intensity is observed both in \(U^{233}\) and in \(Pu^{239}\), but it has not yet been clarified whether these transitions are connected in cascade with the observed alpha particles. Indirect indications, also supporting the assumption that the observed alpha particles do not correspond to transitions to the ground level, may be obtained from Figs. 1 and 7. From Fig. 1 it is seen that the alpha-decay energies of \(Pu^{239}\), \(U^{233}\), and \(Ra^{223}\) are anomalously small; in other words, the decay energies of these isotopes are only slightly greater than the energies of the corresponding higher isotopes \(Pu^{240}\), \(U^{234}\), and \(Ra^{224}\). From this one could conclude that the energies of gamma rays should be added to these energies, as was done with \(U^{235}\) and \(Am^{241}\). From Fig. 7 it can be seen that, with respect to the half-life—energy relationship, the observed alpha particles of \(Pu^{239}\) are comparable with the short-range (main) group of \(U^{235}\), while \(U^{233}\) is very similar to the most short-range group of \(Th^{229}\), and the known alpha groups of \(Ra^{223}\) to the short-range groups of \(Th^{227}\). From the relationships in Fig. 7 it may be concluded that the transitions to the ground level in \(Pu^{239}\) and \(U^{233}\) are even more forbidden, as are also the corresponding groups of their decay products. The significance of the half-life—energy relationship in the case of fine structure of alpha decay will be discussed below.
In Fig. 7 one may note that \(Po^{213}\) and \(Po^{215}\) fall on the main curve for polonium and therefore apparently represent cases of non-forbidden alpha decay. Before accepting that these nuclei are exceptions, it is necessary to draw attention to the circumstance that the main curve in this region of polonium isotopes is determined by \(Po^{213}\) and \(Po^{214}\), and that, owing to the decrease in the nuclear radius, these nuclei themselves are forbidden (see the section on the quantitative treatment of alpha decay). There is also the possibility that the observed alpha particles of \(Po^{213}\) and \(Po^{215}\) do not correspond to transitions to the ground state.
Odd-even and odd-odd nuclei
The half-lives of nuclei of these types are presented in Fig. 8; the same reference lines for even-even nuclei that are given in Figs. 6 and 7 are also shown in Fig. 8. Between these curves, dashed curves have been drawn by interpolation, representing the positions that isotopes with odd \(Z\) would have if their alpha-decay constants (as in even-even nuclei)
Figure text
Vertical axis: Decimal logarithm of the alpha-radioactivity half-life period (in years)
Horizontal axis: Energy of alpha decay (MeV)
Legend:
- odd-even
- doubly odd
Element labels visible in the plot: Americium, Neptunium, Protactinium, Actinium, Francium, Astatine.
Fig. 8. Dependence of the half-life period on the energy for odd-even and doubly odd nuclei.
not forbidden. It may be noted that they are almost always forbidden and that doubly odd nuclei deviate more from their curves than is the case even for odd-even nuclei. The quantitative data underlying these generalizations may be found in Table III.
With regard to odd-even nuclei one may doubt whether the deviations from the counting curves shown in Fig. 8 and in Table III convey the true picture of the forbidden character of transitions to the ground level, since, as was the case for even-odd nuclei, it is not at all clear whether the observed alpha particles correspond to these transitions. Thus, for example, the observed alpha particle of \( \mathrm{Am}^{241} \) with energy \(5.48\) MeV almost certainly does not correspond to the full decay energy, since gamma rays of high intensity with an energy of \(62\) keV are observed simultaneously. If there exists an unobserved alpha group with energy \(5.54\) MeV, which is very probable, then its partial half-life must be very long and the emission of these particles strongly forbidden. How many other nuclei behave analogously to \( \mathrm{Am}^{241} \) is unknown.
At present two cases of fine structure of alpha decay among odd-even nuclei are known, namely \( \mathrm{Pa}^{231} \) and \( \mathrm{Fr}^{221} \). In both cases the group with the smaller energy is less forbidden, and the \(6.5\) MeV group in \( \mathrm{Fr}^{221} \) even seems not to be forbidden at all.
Considering the data for odd-even nuclei in Table III, one may note that a significant fraction of the partial alpha half-lives are calculated on the basis of very rare alpha branches associated with a process in which electron capture predominates. There is considerable uncertainty in estimating the number of cases of \(K\)-capture, and the experience of our laboratory suggests that this number is more likely underestimated. This means that the true partial alpha half-lives are probably larger than has conventionally been assumed up to now.
The only example of an odd-even nucleus for which both the energy and the alpha half-life are known with sufficient reliability and for which there is no prohibition is \( \mathrm{At}^{217} \). There is no simple explanation for this exception to the general rule, unless one assumes that \( \mathrm{At}^{217} \) represents yet another case in which the transition to the ground state is not measured.
Several examples of doubly odd nuclei show that for this type of nucleus alpha radiation is forbidden. In view of the limitations imposed by the uncertainties of the data, one may nevertheless consider that alpha decay of doubly odd nuclei is still more forbidden than is the case even for even-odd and odd-even nuclei.
Particularly forbidden nuclei
The special significance of this group, represented in Fig. 9, will be discussed below. It includes all the known alpha emitters of bismuth and the isotopes of francium, emanation, astatine, and polonium with 126 or fewer neutrons. In the case of polonium this group includes several isotopes of the doubly even type, and, as was stated above, it would apparently be necessary to include in it \( \mathrm{Po}^{213} \) and \( \mathrm{Po}^{214} \).
Discussion of forbidden alpha decay
From the data of Figs. 6, 7, and 8 it follows, apparently, that the general regularity in the phenomenon of alpha radioactivity is that nuclei with an odd number of neutrons, of protons, or of both undergo forbidden decay in comparison with doubly even nuclei. This applies especially to transitions to the ground level in those cases where more than one alpha group is measured. When it is possible to measure several alpha groups, the most forbidden proves to be the transition to the ground state; the short-range groups, on the other hand, prove to be considerably less forbidden. Conversely, the few known cases of fine structure in doubly even nuclei give no indication of any prohibition for any of the groups, and the partial alpha half-periods are in agreement with their corresponding alpha energies.
According to theory, one of the factors in the forbiddance of alpha decay is the change of spin accompanying the transition; furthermore, any anomalously small nuclear radius will also manifest itself in the forbiddance of alpha decay. There are grounds for thinking that such an effect of a reduced nuclear radius is observed in \( \mathrm{Em}^{212} \), \( \mathrm{Fr}^{212} \), \( \mathrm{At}^{211} \), in the isotopes of polonium with mass 214 or less, and, probably, in all the isotopes of bismuth. It would be unreasonable, however, to regard this effect as the principal one in heavy nuclei with an odd number of protons or neutrons, since, if their radii differ at all from the radii of neighboring even nuclei, they do so only in the direction of some increase. Nor is it possible to explain the anomalous half-periods of these nuclei by changes of spin.
According to theory, the dependence on spin is such that, in order to explain an alpha decay with a duration 10 times greater than normal, one would have to assume a change of spin by 5 units. Although such large changes of spin have been observed for beta transitions corresponding to the decay of a doubly odd nucleus with its transformation into a doubly even one, it is nevertheless unreasonable to suppose that such large changes will occur (at any rate as a general rule) for alpha decay, in which the initial and daughter nuclei belong to one and the same
Fig. 9. Dependence of the alpha half-life period on energy for especially forbidden nuclei.
Vertical axis: decimal logarithm of the alpha half-life period, in years.
Horizontal axis: alpha-decay energy, MeV.
Visible curve labels include: platinum, iridium, mercury, uranium, thorium, radium, polonium, bismuth, actinium.
of the same type. Moreover, for radioactive series of the type \((4n+1)\) or \((4n+3)\), in which practically all members have anomalous decay constants, one would have to postulate an alternation, among successive members of the series, of large and small spin quantum numbers differing from one another by several units. For one case of alpha decay, namely for \(\mathrm{U}^{235}\), the spin quantum numbers of the ground state were measured. For \(\mathrm{U}^{235}\) a value \(5/2\) (or \(7/2\))\({}^{40}\) was obtained, and for \(\mathrm{Pa}^{231}\) a value \(3/2\)\({}^{41}\); the change of spin in the transition thus proves to be equal to 1 or 2. To explain the prohibition of the transition to the ground level of \(\mathrm{U}^{235}\) exclusively by a change of spin, a change of spin by approximately 10 units would be required.
Since the modern theory of alpha decay in its explicit form cannot explain the forbidden transitions of all observed categories, a qualitative modification of the theory is proposed below, agreeing in its main features with the Condon–Gurney theory. Consideration of the formula for the alpha-decay constant shows that it consists of two parts: an exponential term, characterizing the penetrability of the barrier, and a coefficient before the exponential term, which is a slowly varying function and is taken to be constant. This may be written in the form
\[ \lambda = C e^{-f(v,Z,r)} . \]
Here \(\lambda\) is the decay constant, \(C\) is the coefficient mentioned above, and \(v\), \(Z\), and \(r\) are, respectively, the velocity of the alpha particle, the atomic number, and the effective radius of the nucleus. It may be assumed that \(C\) is connected with the frequency of collisions of the alpha particle in the initial nucleus with the potential barrier and is numerically approximately equal to the reciprocal of the time for the alpha particle to traverse the nucleus. In such a model it is tacitly assumed that the emitted alpha particle is formed in the nucleus itself and that the probability of such formation is the same for all nuclei. We put forward the supposition that the influence of an odd nucleon consists precisely in retarding the formation of the alpha particle. The odd nucleon, presumably a nucleon in a higher quantum state, must be one of the constituents of the emitted alpha particle if the latter leaves the nucleus with its full kinetic energy; it therefore couples with a nucleon at a lower level having antiparallel spin. In addition, one or more nucleons may change their quantum states. If we assume that these processes require a considerable time, then this gives rise to the possibility of explaining forbidden decay in nuclei with an odd number of nucleons. For the same reason, two odd nucleons must lead to a still greater hindrance of alpha decay than single odd nucleons, as is confirmed by comparing doubly odd nuclei with odd-even or even-
odd types (see Table III, Figs. 7 and 8). According to this view one may also expect that, in all cases where the emission of low-energy alpha particles is forbidden, it may partly or even completely replace the transition to the ground state, since for the lower-lying nucleons the probability of their pairing is greater and, in any case, the formation of alpha particles from them must be forbidden to a lesser degree.
In agreement with experiment, the degree of hindrance of these groups, with allowance for their energies, should be less than for the transition to the ground level.
The anomaly in the dependence of the half-life on energy for \(\mathrm{Po}^{210}\) and for all natural isotopes of bismuth, as compared with that for other alpha emitters, has been noted many times, and this effect has been attributed to a sudden decrease in the radii of these nuclei. It is not superfluous to try to connect these anomalies in the sizes of nuclei, which follow from the properties of alpha decay, with modern views on the existence of stable configurations in the nucleus. An unambiguous solution of this question for nuclei with a rapidly changing radius, which are connected with one another by the phenomenon of alpha decay, requires a decision as to whether the increase of the barrier due to the decrease in nuclear size should be ascribed to the parent or to the daughter nucleus. In the one-body model it is assumed that the alpha particle moves in the nucleus of the decay product and that the barrier for it is the barrier of the decay product. This would mean, for example, that alpha decay of bismuth isotopes is forbidden because of the anomalously small radius of the thallium nucleus—the decay product. This model is probably inadequate, and the nucleus determining the potential barrier is a hybrid of the parent and daughter nuclei.
As already mentioned, alpha decay of all natural isotopes of bismuth exhibits a very high degree of hindrance, exceeding the values of the normal curve by hundreds to several thousand times. Part of this phenomenon may be ascribed to the odd nucleons of the bismuth isotopes, but the degree of hindrance is so great that part of it apparently should be attributed to the effect of a change in nuclear size. If it is assumed that the mean deviation from the normal curve is of the order of 500, and if it is taken that a factor of 10 or 20 can be explained by the presence of odd nucleons, then a factor of the order of 50 or 25 remains for the effect of nuclear contraction. From the formula for the decay constant it follows that a decrease of the nucleus by 10% leads to an increase of the half-life by a factor of 50. In the next section the quantitative side of the theory of alpha decay will be considered more fully, and we shall see that, with the exception of the light doubly even polonium isotopes (\(\mathrm{Po}^{212}\), \(\mathrm{Po}^{210}\), and \(\mathrm{Po}^{208}\)), the theory is well justified for doubly even nuclei. In the exceptions noted above we ascribe the entire effect of hindrance of alpha emission to the influence of nuclear contraction, since
for all other even-even isotopes not lying close to the region of nuclei with 82 protons and 126 neutrons, the agreement is fairly good. The degree of hindrance of \(Po^{210}\) and \(Po^{208}\) is such that, to explain it, one has to assume a nuclear contraction of the order of 10%. Since, without effects due to odd nucleons, the hindrance for the bismuth isotopes proves to be of the same order, one must also postulate for them a contraction of the nucleus by approximately the same amount, i.e. approximately 10% or less.
As for the new neutron-deficient alpha emitters of bismuth, it is impossible to say whether or not their properties differ from the regularities that were noted for the heavy alpha emitters of bismuth, since the ratio of the probabilities of alpha decay and \(K\)-capture for them is not known exactly, and therefore the calculated alpha half-periods given in Table III must be regarded only as a rough approximation. The two-minute period ascribed to \(Bi^{197}\) is only tenfold hindered if this isotope decays chiefly as a result of alpha emission, but there are no data on this question. On the other hand, a better determination of the alpha branch of 25-minute \(Bi^{199}\) shows that the alpha decay of this isotope is strongly hindered. If one attempts to explain these bismuth effects by the presence of closed shells in the nucleus, then at best at present one can only assert that the binding energy of one or more protons, when their total number is less than the number of protons in the closed shell (82), is anomalously large, just as the binding energy of some of the neutrons is also very large when their number is appreciably less than 126.
In view of the obvious predominance of alpha decay in the bismuth isotopes, one might have expected this regularity to appear still more sharply in the lead isotopes \((Z=82)\). In fact, however, alpha activity was not observed even in the extremely neutron-deficient lead nuclei corresponding to those light bismuth isotopes for which alpha activity again begins to appear. This fact can be satisfactorily explained by assuming that the decay energy of the lead isotopes is extremely low, but it is also possible that the half-periods at these decay energies are extremely large. The special character of lead’s position apparently consists in the fact that after passing through this region, i.e. for the nuclei of gold \((Z=79)\) and mercury \((Z=80)\), which have a deficiency of neutrons, alpha activity, according to the observations of Thompson et al. \(^{23}\), again begins to appear.
In addition to the bismuth isotopes there is another group which, apparently, is hindered with respect to alpha decay because of an anomaly in the nuclear radius. This concerns \(At^{211}\), \(Em^{212}\), and the polonium isotopes of mass 210 and less. The main factor here is
SYSTEMATICS OF ALPHA-RADIOACTIVE ISOTOPES
the presence in these isotopes of 126 or fewer neutrons. It may be noted that these nuclei are precisely those for which a sharp deviation is found from the regularities in the dependence of mass number on energy observed in heavy isotopes. In this region, apparently, even for doubly even nuclei alpha decay is forbidden.
In Fig. 3 an attempt is made to identify regions of anomalous nuclear stability. For this purpose two facts were used, namely: in all bismuth isotopes a high degree of hindrance of alpha decay is observed, and all nuclei having 126 or fewer neutrons also exhibit this property. The anomalously large half-lives apparently mean that in both cases there is a sharp change in the value of the nuclear radius. It is now quite clear that in nuclei with 126 or fewer neutrons there is a region below 126 neutrons in which the binding of the nucleus changes only weakly; when this number of neutrons is exceeded, however, a sharp decrease in the binding energy occurs. This effect appears as a maximum of the alpha energy for a nucleus with 128 neutrons, which then decays into a nucleus with 126 neutrons; examples of such a case are \(Bi^{211}\), \(Po^{212}\), and, possibly, \(At^{213}\) and higher nuclei of this type. In a similar way, nuclei with 126 or fewer neutrons possess low alpha energies and, no less importantly, half-lives anomalously large for the corresponding energies. If the several neutrons that are added to the other 126 neutrons are relatively weakly bound, then the alpha-decay energies of nuclei with 127 neutrons should lie between the energies of nuclei with 126 and 128 neutrons, since the alpha particle carries away one weakly and one strongly bound neutron. This would explain the observed alpha energy of \(Po^{211}\) \((AcC')\) and makes it possible to predict this energy for \(At^{213}\), as shown in Fig. 1. One may expect still another effect for these isotopes, namely the manifestation of a high degree of hindrance of alpha decay, so noticeable for nuclei with 126 or fewer neutrons. For \(Po^{211}\) this leads to a half-life value of not less than 50 milliseconds, which is 10 times greater than the value obtained on the basis of the Geiger—Nuttall relations \(^{42}\).
The influence under discussion of 126 neutrons on the energy surface is probably equally applicable to the proton number 82, but in the latter case the almost complete absence of a measurable alpha-decay potential immediately below bismuth reduces to nothing the value of any speculation on this question. However, the influence of a nucleon in excess of a closed shell on alpha decay can be illustrated by a considerably larger number of examples, with the proton number equal to 83, than is allowed by the scanty experimental material for the neutron number equal to 127. All alpha energies of the bismuth isotopes are much smaller,
than in the polonium isotopes (in comparison with the displacement of the following elements), and the lifetimes possess a degree of hindrance exceeding that which would be expected for isotopes with an odd number of nucleons.
Quantitative treatment of alpha decay
From what has been set out above it should be clear that, if quantitative agreement between the experimental data and the existing theory can be expected at all, it is only for doubly even nuclei. Preliminary calculations for these latter show that, in fact, agreement over a wide range of mass numbers and atomic numbers is rather good. Thus, the shape and position of the curves in Fig. 6 are well reproduced by the one-body theory for alpha radiation; this circumstance had already been pointed out earlier by Biswas \(^{39}\) and others, who in addition tried to place all the remaining types of nuclei on these curves.
Since the only unknown parameter in the formula is the nuclear radius, one may try, by superposing the curves for doubly even nuclei, to determine a function that would describe the behavior of the nuclear radius in the region of the heavy elements. Although exhaustive calculations have not yet been carried out, preliminary estimates indicate that better agreement with experiment is given rather by the simple function
\(r = 1.48 A^{1/3}\cdot 10^{-13}\ \text{cm}\), than by a similar function to which a term is added that takes account of the radius of the alpha particle or of the range of its forces, as some authors \(^{43,44}\) propose. Conversely, one may calculate the value which must be assigned to the radius of a doubly even nucleus in order to obtain the observed value of the decay constant, and then determine how much each such value differs from the rule \(r = 1.48 A^{1/3}\cdot 10^{-13}\ \text{cm}\). A dozen such computations for elements lying between curium and emanation showed that the mean deviation is of the order of 1%; this must be regarded as good agreement, if one takes into account that uncertainties in the alpha energy often lead to still larger errors in nuclear radii. Refinement of the energy measurements and correlation of the additional material should show whether there in fact exist serious deviations from this simple formula for the nuclear radius.
Calculations of the radius were also performed for six of the doubly even polonium isotopes, for which reliable data on decay energies and half-periods are available. It has long been clear that in the decay of \(\mathrm{Po}^{210}\) and, possibly, of all bismuth isotopes, a certain role in lengthening the half-periods is played by a reduction of the nuclear radius. In the case of the bismuth isotopes, part of the hindrance must be attributed to the general effect of odd nucleons, and part—
effect of the nuclear radius and, in part, possibly to a change in spin. However, for the doubly even polonium isotopes any appreciable hindrance must be ascribed to anomalies in the nuclear radius. In the one-body theory of alpha decay it is assumed that the nuclear radius essentially coincides with the radius of the decay product. Therefore, in the case of the alpha emitters of polonium we would be “measuring” the nuclear radii of the corresponding lead isotopes. Regardless of whether or not it is meaningful to identify the distance parameter in alpha decay with the radius of the product nucleus, it may be said with confidence that the binding energy, and hence also the radius of the product nucleus, play an important role in determining the form of the relation between the energy and the half-period. The hindrance of alpha decay in the polonium isotopes may be ascribed to the reduction of the radii of the nuclei of the daughter lead isotopes, which possess the stable configuration of 82 protons. In \( \mathrm{Po}^{212} \) and the lighter isotopes the number of neutrons in the decay products is 126 or less, and this circumstance must lead to a further increase in the hindrance because of the further reduction of the effective nuclear radius. If, finally, we suppose that the radius of the parent nucleus is also a determining factor for the effective radius of alpha emission, then the hindrance of alpha decay in polonium isotopes with mass number 210 or less must be still stronger, since the parent nuclei also possess 126 neutrons or fewer. It is interesting to note that the discrepancy between the calculated radii of the doubly even polonium isotopes and the radii obtained from the simple formula \(A^{1/3}\) is just what one might have expected. Whereas the radius of the \(\mathrm{Po}^{218}\) nucleus is smaller by only 1.4%, for the isotopes \(\mathrm{Po}^{216}\), \(\mathrm{Po}^{214}\), \(\mathrm{Po}^{212}\), \(\mathrm{Po}^{210}\), and \(\mathrm{Po}^{208}\) the discrepancies are found to be respectively 2.1, 2.8, 5.5, 8.1, and 9.0 percent.
It should be mentioned that a further separation of the factors affecting the nuclear radius can be obtained on the basis of a study of such isotopes as \(\mathrm{Em}^{212}\). In this case both the parent and daughter nuclei have 126 or fewer neutrons, but in the daughter nuclei the number of protons is 84 instead of 82, as in the decay products of the polonium isotopes. It may be observed that the decay of \(\mathrm{Em}^{212}\) is less hindered than that of \(\mathrm{Po}^{210}\) or \(\mathrm{Po}^{208}\), which is possibly accidental.
APPENDIX
Remarks on the activity of individual isotopes
Most of the data used in the present article can be found in the compilation “Table of Isotopes”\(^3\). In this compilation, however, some new isotopes are not considered; moreover, for our purposes we considered it necessary to review or expand
to expand part of the material or supply it with additional remarks.
Cm\(^{238}\)
As indicated in Table 3, this isotope is an alpha emitter with an energy of 6.50 MeV and a half-period of 2.5 hours. It is undoubtedly unstable with respect to electron capture (see Table I), and although its branching was not determined, it is very probable that the measured half-period is essentially determined by the half-period of electron capture. For this reason this isotope is not presented in Fig. 6, which illustrates the regularities of doubly even nuclei.
Cm\(^{240}\)
According to the predictions, this isotope of curium is also unstable with respect to \(K\)-capture. However, it has been shown that the branching of this mode of decay is less than 20%, and therefore the error is small if the measured half-period is taken to be equal to the alpha-decay half-period.
Cm\(^{244}\)
This isotope, discovered by S. G. Thompson\(^{46}\) upon irradiation of Am\(^{241}\) with helium ions of energy 38 MeV, is a long-lived alpha emitter with an alpha energy of 5.78 MeV. According to Thompson, the mass number of this isotope may be either 243 or 244; on the basis of the detailed survey we have made of other curium isotopes\(^{45}\), we incline in favor of the number 244. On the basis of not entirely reliable yield data, Thompson estimates the half-period at 10 years. This point was not used in Fig. 6, although by chance it falls approximately at the expected place.
Am\(^{242}\)
There is great uncertainty in the half-period of the ground state of Am\(^{242}\) given in the text. The alpha-decay half-period indicated in Table III is based on the yield of Np\(^{238}\) in alpha decay, it being assumed that, as a result of neutron capture by the isotope Am\(^{241}\), the excited isomer \(\odot\)Am\(^{242}\), having a half-period of 16 hours, is formed in the same amounts simultaneously with Am\(^{242}\). It is necessary here to allow for the possibility of a considerable error of either sign. The alpha energy was determined by closing a cycle including the beta-decay energies of Am\(^{242}\) and Np\(^{238}\) and the alpha energy of Cm\(^{242}\). The beta-decay energy of Am\(^{242}\) used to close the cycle is then taken equal to the energy of the beta particle (0.6 MeV). If there are \(\gamma\)-rays in the cascade with the beta particle, then the decay energy and correspondingly the alpha energy of Am\(^{242}\) will be higher.
Am\(^{241}\)
The abundance of soft gamma rays and \(L\)-X-rays led to the conviction that the principal alpha group lies in a cascade with a gamma ray. Preliminary measurements\(^{47}\) of alpha and gamma rays apparently confirm this assumption. Therefore, in obtaining the decay-energy value shown in Fig. 1 (\(5.64\) MeV), the gamma energy was added to the energy of the alpha particle.
Am\(^{239}\)
The alpha-branching factor (\(\sim 0.1\%\)) given in the summary\(^{3}\) was redetermined, and the new value, equal to \(0.01\%\), was used by us in determining the alpha half-life.
Pu\(^{241}\)
The alpha half-life given in Table III is based on an estimate of the amount of U\(^{237}\) produced in alpha decay and on an estimate of the amount of Pu\(^{241}\), based on considerations of the yield of this isotope. The uncertainties are of such an order that the half-life calculated by this method is correct to within a factor of 2 or 3. The alpha energy is calculated by closing the decay cycle, which includes the beta-decay energies of Pu\(^{241}\) and U\(^{237}\) and the alpha-decay energy of Am\(^{241}\).
Pu\(^{239}\)
It was mentioned in the main text that some unidentified electromagnetic radiation is associated with Pu\(^{239}\), and that there is a possibility that the measured alpha-particle energy does not correspond to a transition to the ground level. This phenomenon, consequently, would be similar to the phenomenon observed in U\(^{235}\). If this is confirmed for Pu\(^{239}\), then the decay energy will be greater than that shown in Fig. 1.
Pu\(^{234}\)
The degree of alpha branching of this activity with a period of 8 hours is not precisely known, owing to the difficulty of separating this process from the electron-capture process. It is conventionally assumed that the branching ratio is 0.03. This leads to an alpha-half-life value of 10 days. The \(\alpha\)-decay energy has been slightly changed and is taken to be \(6.15\) MeV\(^{49}\).
Pu\(^{232}\)
According to estimates based on alpha and X-ray activity, the alpha branching of this isotope is \(20\%\) or less. The energy value given is also only approximate, since this alpha group falls in the same energy interval as the decay product U\(^{228}\), which itself is not precisely known.
Np \(^{235}\)
Instead of the value of alpha branching \(\sim 0.1\%\) given in the survey,\(^3\) we have adopted the value \(\sim 0.005\%\).\(^50\)
Np \(^{233}\)
This new isotope is produced by irradiating U \(^{235}\) and U \(^{238}\) with high-energy deuterons.\(^51\) The decay of this isotope proceeds predominantly by electron capture with a half-life of 35 min., but weak emission of alpha particles of energy 5.53 MeV is also observed. As is generally the case for all nuclei decaying by electron capture without the formation of daughter activities amenable to precise measurement, at present we can only approximately estimate the branching and the alpha half-life. The provisional value of the alpha branching is \(\sim 10^{-3}\%\).
U \(^{235}\)
The principal alpha group (4.396 MeV) is apparently not associated with a transition to the ground level, since gamma rays of high intensity\(^3\) are observed and therefore the decay energy shown in Fig. 1 includes the energy of this gamma radiation.
The intensity of the transition to the ground level was not known accurately, since this transition has been observed only very recently. On the basis of an apparent discrepancy of the order of 20% between the number of particles with energy 4.396 MeV relative to the \(\alpha\)-particles of U \(^{238}\)\(^52\) and the number of particles that ought to have been present, assuming that one particle is emitted in each decay according to mass-spectrographic analysis and the yields of the products of the actinium series, it was suggested,\(^52\) that 20% of the transitions terminate in an alpha group of higher energy, which is masked by the alpha particles of U \(^{234}\). Recently our laboratory obtained a preparation strongly enriched in U \(^{235}\), and we were able to resolve a long-range alpha group with relative intensity \(10 \pm 1\%\) and with energy 180 keV higher than the energy of the principal group. The experimental error of this determination is of the order of 20 keV. The possibility of isolating this alpha group permits the specific activity of U \(^{235}\) to be determined directly on a strongly enriched preparation, and it is not excluded that this will lead to the need to revise the accepted value of the half-life of U \(^{235}\). However, instead of attempting to correct the existing data, we shall retain the old value \((7.07 \cdot 10^{8}\) years), until the necessary precise measurements have been carried out.
U \(^{233}\)
As in Pu \(^{239}\), electromagnetic radiation of fairly considerable intensity is observed in this isotope, but was identifi-
SYSTEMATICS OF ALPHA-RADIOACTIVE ISOTOPES
only one alpha group has been recorded in all. It is possible, therefore, that the observed alpha group does not represent a transition to the ground level. Since the decay scheme has not been determined directly, Fig. 1 gives the measured alpha energy.
U \(^{231}\)
Up to now it has not been possible to measure the alpha energy of this isotope, which has an electron-capture half-period of 4.2 days, since it cannot be obtained free from U \(^{230}\) and U \(^{232}\), whose alpha activities are immeasurably higher. However, by isolating the decay products Th \(^{227}\) (RdAc) and Pa \(^{231}\), one can determine the degree of alpha branching. The corresponding calculation gave a value of 200 years for the half-period \(^{53}\). Starting from Fig. 1 and also closing the decay cycle (U \(^{231}\), Pa \(^{231}\), Ac \(^{227}\), Th \(^{227}\)), in which the decay energy in electron capture was estimated at 0.5 MeV, it was possible, on the basis of Thompson’s relation \(^{29}\), to determine the alpha energy. The corresponding value proved to be 0.5 MeV.
Pa \(^{231}\)
There are strong grounds for believing that both well-established groups of alpha particles used in the present article themselves possess fine structure. Thus, the more energetic group has a component of 5.04 MeV, which is 30 keV greater than the value adopted for the transition to the ground level. This circumstance changes little in the energy curve of Fig. 1, but it is significant in that it makes the transition to the ground level even more forbidden than is shown in Fig. 8. A less important consequence of this change is the need to revise the alpha energy of U \(^{231}\), since the estimate of this energy was based on a decay cycle including the alpha decay of Pa \(^{231}\). However, other errors in the calculation completely outweigh the small increase in alpha energy caused by the circumstance noted.
Pa \(^{230}\)
The degree of alpha branching of this seventeen-day activity was estimated from the ratio of the activities of U \(^{230}\) and Ac \(^{226}\), which are products of Pa \(^{230}\). In doing so it is assumed that the 17-day half-period is due chiefly to the process of electron capture, and not to \(\beta^-\)-radiation. The yields correspond to an alpha half-period of 1400 years. In Fig. 8 this value corresponds to an alpha energy of 5.5 MeV, obtained by interpolation from Fig. 1.
Th \(^{230}\) (Io)
Some features of the fine structure of the ion (Th \(^{230}\)) have been well studied and deserve to be taken into consideration.
...in establishing general regularities. A more careful investigation of the alpha-particle spectrum indicates that there apparently exist at least two groups, with energies 4.68 and 4.61 MeV\({}^{56}\), which is consistent with the existence of the well-known gamma radiation at 68 keV\({}^{57,58}\). According to Feather’s estimate\({}^{35}\), the ratio of the 4.68 MeV group to the 4.61 MeV group is \(\sim 4:1\). Rosenblum, Valadares, and Vial\({}^{56}\), in addition, obtained some data indicating a low-intensity group whose energy might correspond to a transition to a level lying 170 keV above the ground state. The corresponding gamma radiation apparently has already been observed experimentally\({}^{57,58}\). Because of the unreliability of the intensity data, this group is included neither in Fig. 6 nor in Table III.
Th \(^{228}\) (Rd Th)
There are later data for the intensities of two alpha groups, namely 0.72 and 0.28 for groups with energies, respectively, 5.423 and 5.339 MeV\({}^{59}\).
Th \(^{224}\)
The experimental value of the alpha energy (7.20 MeV) is consistent with the existence of a short half-life, but the latter has not yet been measured. The same is true for several other short-lived isotopes, such as Ac \(^{222}\), Ra \(^{220}\), Fr \(^{218}\), Em \(^{216}\), and Po \(^{211}\).
Ac \(^{228}\) (Ms Th\(_2\))
A measurement of the alpha-particle energy of a rare branch was reported\({}^{60}\), giving a value of 4.54 MeV, which agrees with the predictions based on Fig. 1. However, according to Fig. 8, at such an energy Ac \(^{228}\) should have an alpha half-life exceeding \(10^6\) years, which for alpha branching gives a ratio smaller than \(1:10^9\). It is extremely doubtful that such a low alpha branch could have been detected in this case.
Ac \(^{227}\)
The existence of two alpha groups, one of which is approximately 350 keV below the main group\({}^{61}\), has not been confirmed\({}^{62,63}\), and therefore we shall assume that Ac \(^{227}\) has a single alpha group with energy 4.95 MeV; it is not excluded, however, that more careful measurements will reveal a very fine structure of this group. At present the question has not been resolved as to whether the observed alpha particle corresponds to a transition to the ground state or not.
Ra \(^{226}\)
The existence in Ra \(^{226}\) of gamma radiation with an energy approximately equal to 0.19 MeV\({}^{64,65}\) is well established. Per 100 alpha-
...of decays. Stal’\(^{65}\) found more than 5 internal-conversion electrons, and he believes that the number of gamma rays not undergoing conversion also amounts to several percent. Rosenblum and Perren\(^{66}\) observed the corresponding short-range alpha group and note that the intensity was just of the magnitude that should have been expected on the basis of Stal’s measurements. Recently Rosenblum\(^{67}\) indicated that the intensity of the short-range group is about 9 percent, whereas Chang\(^{68}\) gives a value of 1.8%. In view of the agreement between the independent measurements of the gamma rays and of the alpha group made by Stal and Rosenblum, we use the larger value.
Fr \(^{212}\)
This extremely neutron-deficient isotope of francium (according to predictions the β-stable isotope of francium is Fr \(^{219}\)) was obtained by Hyde, Ghiorso, and Seaborg\(^{38}\) by bombarding thorium with high-energy protons. It was chemically separated, and it was shown that its mass number must be considerably below 218, since all heavier isotopes of francium for which the existence of the observed alpha energies and half-lives could be allowed would form known decay products of the natural radioactive series.
The identification of this isotope with Fr \(^{212}\) is based on the presence of a genetic relationship, due to alpha decay, with an isotope of astatine which is assumed to be identical with At \(^{208}\), and also on the presence of a relationship, due to \(K\)-capture, with a new isotope of emanation, to which, on the basis of its connection with Po \(^{208}\), the mass number 212 (Em \(^{212}\)) is assigned. The measured half-life of Fr \(^{212}\) is 19 min, and, judging from the rate of increase in the number of alpha particles of Em \(^{212}\), the alpha branch is approximately 50%. The energy of the alpha particles is 6.25 MeV.
Em \(^{218}\)
The values of the half-life of Em \(^{218}\) reported by different investigators differ greatly. For Em \(^{218}\), obtained as one of the products of the U \(^{230}\) series, Studer and Hyde\(^{7}\) obtained a half-life equal to 19 milliseconds. Wallen\(^{69}\), on the other hand, asserts that he has identified Em \(^{218}\) as an activity with a half-life of 1.3 seconds and arising as a rare β\(^{-}\)-branch of At \(^{218}\), which, in turn, arises in the rare β\(^{-}\)-branching of ThA \(^{218}\). There are several reasons why preference should be given to the value of Studer and Hyde; the chief of these is the considerably greater simplicity of the experimental method for obtaining Em \(^{218}\). Another reason consists in the good agreement of the values of Studer and Hyde for the energy and half-life with the law—
regularities shown in Fig. 6. As for Walen’s value for the half-period (1.3 seconds), it is too large for the energy given by Studer and Hyde and, conversely, if one does not accept this energy value, but estimates it on the basis of the half-period 1.3 sec., it turns out that the energy of Em \(^{218}\) is lower than that of At \(^{219}\), which clearly does not agree with the regularities of Fig. 1.
Em \(^{213}\)
As already mentioned, this new isotope of emanation is obtained from Fr \(^{221}\). The energy of the alpha particle is 6.18 MeV \(^{38}\). The measured half-period is 23 minutes \(^{37}\), and since we believe that Em \(^{213}\) is probably beta-stable, this period therefore corresponds to alpha decay.
At \(^{218}\)
In the review article \(^{3}\) it was erroneously reported that the energy of the alpha particles of At \(^{218}\), found by Karlik and Bernert \(^{34}\), is 6.72 MeV. The correct value is 6.63 MeV.
At \(^{213}\)
This isotope has never been observed, and the alpha energy was estimated by us (see Fig. 1) on the basis of the considerations that in this region a nucleus with 128 neutrons should have the maximum energy in comparison with other isotopes. This estimate was made in order to emphasize that precisely such a regularity should be expected, and that one should not hope to obtain the correct value of the alpha energy of At \(^{213}\) by interpolation between At \(^{212}\) and At \(^{214}\).
At \(^{212}\)
The half-period of this isotope, according to measurements \(^{70}\), is 0.25 sec., and from Fig. 8 one can estimate the alpha energy at 7.4 MeV, if one takes into account that the nucleus belongs to the doubly odd type and that the decay proceeds through a configuration with 126 neutrons. The error of this estimate probably exceeds 200 keV. It should be expected that the alpha energy will lie between the values for At \(^{211}\) and At \(^{213}\), and in this sense the values of the alpha energy assigned to At \(^{212}\) and At \(^{213}\) are consistent with one another.
At \(^{210}\) and the lighter isotopes of astatine
Kelly and Segrè \(^{71}\) give, for the alpha-branching ratio, the minimum value \(10^{-4}\), which leads to a value of 10 years for the alpha half-period. If one assumes that At \(^{210}\) is in the same relation to At \(^{211}\) as Po \(^{209}\) is to Po \(^{210}\), then from Fig. 1 one can estimate its alpha energy at 5.4 MeV. Plotting these values of energy and half-period in Fig. 8, one may note that alpha-
decay is forbidden by at least a factor of hundreds. This high degree of forbiddenness can be explained partly by the odd-odd character of this nucleus and partly by the presence of fewer than 126 neutrons. It is interesting to note that the inhibition of alpha decay is greater than in \( \mathrm{At}^{211} \) (provided that the adopted energy value is correct), and this fact can be explained by the general difference between odd-odd nuclei and odd-even ones.
In astatine at masses below 210, alpha radiation is again observed, but it has not yet been possible to identify the various activities reliably. The latter undoubtedly decay predominantly as a result of electron capture, but the branching ratio has not even been roughly estimated. Thus none of these nuclei can be used to clarify the regularities of the dependence of half-life on energy. Nevertheless, some measurements of alpha energy have been made, and the corresponding isotopes have been assigned the values indicated in Fig. 1. It must be emphasized that the half-lives quoted are experimentally measured periods, not the periods of alpha radiation.
Conventionally, \( \mathrm{At}^{209} \) is assigned a half-life of 5.5 hours and emission of alpha particles with an energy of \(5.65\) MeV. This estimate is based on the excitation function of bismuth obtained when the latter is irradiated with helium ions, and also on the probable existence of \( \mathrm{Po}^{209} \) among a complex set of activities\(^{72}\). Another alpha particle with an energy of \(5.65\) MeV and a half-life of 1.7 hours is assigned to \( \mathrm{At}^{208} \); this radiation was observed in the alpha decay of an activity attributed to \( \mathrm{Fr}^{212}\)\(^{28}\). The principal argument for regarding \( \mathrm{At}^{208} \) as the source of this alpha radiation was the formation of \( \mathrm{Po}^{208} \), with the rate of this formation corresponding to decay with a period of 1.8 hours. It should be noted that in fission reactions of bismuth another isotope of astatine is apparently formed, which is the precursor of \( \mathrm{Po}^{208} \), and its half-life is greater than 1.8 hours, while no noticeable alpha radiation is observed\(^{73}\). It is possible that here we are dealing with two isomers of \( \mathrm{At}^{208} \), whose relative amounts depend on the method of their formation.
On the basis of measurements of the excitation function, an alpha particle with an energy of \(5.76\) MeV and a half-life of 1.8 hours\(^{73}\) is assigned to \( \mathrm{At}^{207} \). Two other isotopes are identified somewhat arbitrarily with \( \mathrm{At}^{205} \) and \( \mathrm{At}^{204} \), although the interval of mass numbers is determined by excitation experiments. One of the activities has a half-life of 25 min and an alpha energy of \(5.9\) MeV, the other, respectively, 10 minutes and \(6.1\) MeV\(^{73}\).
\[ \mathrm{Po}^{209} \]
On the basis of yield data, it is believed that the half-life of alpha decay of this new isotope of polonium is 200 years\(^{71}\). After the introduction of a small correction, the alpha-particle energy proves to be
equal to 4.90 MeV \(^{23}\). The branching ratio of the electron-capture process is not known exactly, but from the intensity of the \(L\)-x rays it may be assumed that it does not exceed \(^{24}\) \(1:10\). Correspondingly, the electron-capture period would be more than 2000 years.
\(\mathrm{Po}^{205}\) and the lighter isotopes of polonium
As in the case of the light isotopes of astatine, very little is known about the alpha periods and mass numbers of these nuclei. However, the energies and mass numbers are known with an accuracy still sufficient for them to be plotted in Fig. 1 and for one to be convinced that the expected general trend is obtained. According to the presently accepted measurements, the half-life of \(\mathrm{Po}^{205}\) is 1.5 hours and the energy of the alpha particle is 5.2 MeV. An alpha particle with an energy of 5.35 MeV and a half-life of 4 hours is now assigned \(^{24}\) to \(\mathrm{Po}^{204}\), while \(\mathrm{Po}^{203}\) we still regard as an alpha emitter with an energy of 5.56 MeV and a half-life of 40 min. In both cases the alpha-branching ratio remains unknown.
\(\mathrm{Bi}^{208}\) (?)
In an earlier published communication \(^{10}\), an alpha particle of 5.0 MeV, found by Houlend and Perlman, was unjustifiably assigned to \(\mathrm{Bi}^{208}\). This alpha particle was observed as a very weak activity in the bismuth fraction obtained upon irradiation of bismuth with neutrons from a nuclear pile. It was considered that the reaction \((n, 2n)\) was taking place. This view was not attractive, since it was to be expected that the alpha energy of \(\mathrm{Bi}^{208}\) would in any case be no greater, and rather smaller, than that of \(\mathrm{Bi}^{209}\). At present an interesting possibility is being investigated, namely that the 5.0 MeV alpha group corresponds to a metastable state of \(\mathrm{Bi}^{210}\) (RaE), which is strongly forbidden with respect to the isomeric transition and beta decay. Partial, but not yet decisive, data on this question have already been obtained.
\(\mathrm{Bi}^{201}\)
A 60-minute activity with alpha particles of 5.15 MeV, which was formerly assigned to \(\mathrm{Bi}^{200}\) \(^{3}\), is now assigned to \(\mathrm{Bi}^{201}\), on the basis of its genetic connection with 8-hour Pb and 72-hour Tl, to which the mass number 201 is provisionally assigned \(^{21}\).
\(\mathrm{Bi}^{199}\)
This is the only one of the neutron-deficient alpha emitters of bismuth for which the alpha branching has been estimated. The determination of this isotope was based on observation of its appearance as a result of successive electron-capture processes in \(\mathrm{Pb}^{199}\) and in 7.5-hour \(\mathrm{Tl}^{199}\). The alpha branching was calculated
on the basis of the yield of Tl\(^{199}\), and the observed alpha radiation amounts to \(1.7 \cdot 10^{-3}\) percent, which gives an alpha half-period of 3 years.
Bi\(^{197}\)
The half-period of 2 minutes attributed to Bi\(^{197}\) is a minimum alpha-decay period, since in this case the assumption has been made that the measured half-period is determined by the alpha-decay process.
Au\(^{190}\)
Recent measurements show that this alpha emitter is an isotope of gold. By measuring another radiation with a half-life of 5 minutes, it was possible to estimate the alpha branching at \(10^{-2}\) percent\(^{23}\).
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