Nuclear Isomerism

N. Dmitriev, Leningrad

Isomers are nuclei that have the same atomic weight and the same charge, but different physical properties. According to modern views, atomic nuclei consist of neutrons and protons. Therefore isomers may be defined as nuclei consisting of the same number of neutrons and protons, but differing from one another in the different distribution of bonds between these neutrons and protons.

The concept of isomerism, as is well known, arose in chemistry. In chemistry, chiefly organic chemistry, we often encounter isomers, but there is molecular isomerism, as distinct from nuclear isomerism. Isomeric molecules in chemistry are those that consist of the same atoms but differ from one another in the different distribution of bonds between the atoms; this latter difference leads to differences in the physical and chemical properties of the molecules. At present physicists possess an experimental method that makes it possible to distinguish isomers of one and the same isotope from one another only in the case when the isomers are radioactive nuclei. This, however, does not prove that isomers do not exist among stable nuclei. As we shall see below, the modern theory of the nucleus allows for the possibility of the existence of isomers among such nuclei. The fact that they have not yet been observed experimentally apparently indicates that some new experimental method is needed for their detection. It is possible that in this respect we are in approximately the same position in which physicists found themselves 25–30 years ago with regard to isotopes, when nothing was known about them until Aston’s creation of the mass spectrograph made it possible to detect isotopes experimentally.

As for the isomers of radioactive elements, they can now be readily detected owing to the fact that they have different half-lives. In some cases the type of particles emitted in the decay of isomers of one and the same isotope may also be different. Thus, for example, it was found that in silver one radioactive isomer emits electrons, while another emits positrons. Radioactive isomers in most—

most cases manifest themselves in phenomena of artificial radioactivity as a result of the bombardment of elements by some nuclear particles: neutrons, protons, deuterons, etc. However, one example of nuclear isomerism is also known from the field of natural radioactivity (\(UX_2\) and \(UZ\)—see below).

The phenomenon of isomerism in the field of artificial radioactivity was first discovered thanks to work on the artificial radioactivity of bromine, carried out at the Radium Institute of the Academy of Sciences of the USSR \(^{1}\). Before this work, Amaldi and others \(^{2}\) had found in bromine, after irradiating it with neutrons, two radioactive periods: 18 min and 4.2 hours. Both of these periods were accompanied by the emission of electrons. It was established chemically that the active atoms are bromine atoms. Since bromine has two stable isotopes: \(\mathrm{Br}^{79}_{35}\) and \(\mathrm{Br}^{81}_{35}\), the two observed periods in bromine were ascribed to the radioactive isotopes \(\mathrm{Br}^{80}_{35}\) and \(\mathrm{Br}^{82}_{35}\). These radioactive isotopes are formed as a result of the simple capture reaction

\[ \left. \begin{aligned} \mathrm{Br}^{79}_{35} + n^{1}_{0} &\longrightarrow \mathrm{Br}^{80}_{35},\\ \mathrm{Br}^{81}_{35} + n^{1}_{0} &\longrightarrow \mathrm{Br}^{82}_{35}. \end{aligned} \right\} \tag{1} \]

As a result of the electron decay of \(\mathrm{Br}^{80}\) and \(\mathrm{Br}^{82}\), stable krypton isotopes are formed

\[ \left. \begin{aligned} \mathrm{Br}^{80}_{35} &\longrightarrow \beta^{-} + \mathrm{Kr}^{80}_{36},\\ \mathrm{Br}^{82}_{35} &\longrightarrow \beta^{-} + \mathrm{Kr}^{82}_{36}. \end{aligned} \right\} \tag{2} \]

Thus the number of radioactive periods of bromine was equal to the number of stable isotopes, and it would seem that there was no reason to expect the presence of any further periods in radiobromine, because in such heavy elements as bromine the usual reaction was only a capture reaction.

Therefore, in the work carried out at the Radium Institute of the Academy of Sciences of the USSR by B. V. Kurchatov, I. V. Kurchatov, L. V. Mysovskii, and L. I. Rusinov, on the basis of the considerations given above, the task of searching for new periods in bromine was not at all posed. Quite unexpectedly, in this work a third period was discovered in radiobromine. It was discovered accidentally during the study of the \(\gamma\)-rays accompanying the two known periods of bromine. While observing at the Radium Institute the intensity of these \(\gamma\)-rays by means of Compton electrons in a Wilson chamber, one of the participants in this work, L. V. Mysovskii, noticed that an old preparation, more than a day having passed since it had been obtained, gave \(\gamma\)-rays of very great intensity. When a new radiobromine preparation was obtained, the intensity of the \(\gamma\)-rays from the new preparation was measured by the same method. On comparison it turned out that the old preparation gave rays of almost the same intensity as the new one. This could be explained only by the fact that a large

part of the γ-radiation owed its appearance not to the already known periods of 18 min. and 4.2 hours, but to a new, longer period. In order to verify this assumption it was decided to study the old preparation with a Geiger–Müller counter: ordinarily such old preparations were discarded on the assumption that they were unsuitable. Testing with the counter and comparing the activity of the old preparation with that of the new one showed that bromine does indeed have a long period, equal to 36 hours. Subsequently this period was observed by a whole series of investigators: A. I. Alikhanov and his co-workers, S. Z. Roginskii, Johnson and Hemelin, Fleischmann, Snell, and others. The discovery of a third period in bromine aroused extremely great interest among physicists working in the field of the atomic nucleus. This fact was so unexpected that some investigators at first did not even believe in the existence of the 36-hour period, until they themselves obtained this period experimentally. Thus, at the present time the existence of a 36-hour period in bromine is beyond any doubt.

The energy of the γ-rays of the 36-hour period was measured from their absorption in lead and iron, and also from the energies of Compton electrons (in a Wilson chamber with a magnetic field). The γ-rays proved to be rather soft; their energy is equal to 0.65 MeV.^1 In the work of L. V. Mysovskii, I. V. Kurchatov, R. A. Eikhelberger, and G. D. Latyshev^3 the β-spectrum of the 36-hour period of radiobromine was studied in detail. The measurement was carried out from the deflection of electrons in a Wilson chamber with a magnetic field. On the basis of the data of this work, the upper limit of the β-spectrum of the 36-hour period proved to be 820–890 kV, which is in good agreement with the value obtained by Alikhanov, Alikhanyan, and Dzhelepov using counters.

To explain the existence of a third period in bromine, three different hypotheses were possible:

1. There exists a third, hitherto unknown, stable isotope of bromine. From this isotope, by the ordinary reaction of simple capture, a new radioactive isotope of bromine with a period of 36 hours is formed.

2. The new radioactive isotope with a period of 36 hours was formed from one of the two already known stable isotopes of bromine, but not by the capture reaction, rather by a reaction of some other type.

Finally, the third and last hypothesis consists in the fact that the new 36-hour period belongs to one of the already known radioactive isotopes of bromine, i.e., Br^80 or Br^82. In other words, according to this hypothesis it followed that one of these radioactive isotopes possesses two different half-life periods, i.e., that it exists in two isomeric forms. Until that time nuclear isomers were not known in phenomena of artificial radioactivity.

In view of the fact that there were likewise no data on the existence of a third stable isotope of bromine, the second hypothesis was initially accepted. It was assumed that, when a neutron strikes a bromine nucleus, the neutron knocks another neutron out of the nucleus and itself does not remain in the nucleus. Of the two known stable isotopes of bromine, only \(\mathrm{Br}^{79}\) could give this reaction, since from \(\mathrm{Br}^{81}\) such a reaction would yield the known radioactive isotope \(\mathrm{Br}^{81}\). The reaction may be written as follows:

\[ \begin{aligned} {}^{79}_{35}\mathrm{Br} + {}^{1}_{0}n &\longrightarrow {}^{78}_{35}\mathrm{Br} + {}^{1}_{0}n + {}^{1}_{0}n,\\ {}^{78}_{35}\mathrm{Br} &\longrightarrow e + h\nu + {}^{78}_{36}\mathrm{Kr}. \end{aligned} \tag{3} \]

If one calculates the energy balance of this reaction, it turns out that it can be caused only by fast neutrons whose energy is greater than 6.5 MeV.

However, it was subsequently established by various experimenters that the activity of all three radioactive periods of bromine (18 min., 4.2 hours, and 36 hours) increases if the neutrons are slowed down. The only reaction known at present whose yield increases upon slowing down neutrons is the reaction of simple capture of a neutron by a nucleus. Therefore, on the basis of the experimental data on the enrichment of the reaction by slow neutrons, the conclusion was drawn that all three radioactive periods of bromine are formed as a result of the reaction of simple capture. Thus the second of the above hypotheses could not be accepted.

TABLE 1

In order to choose between the first and third hypotheses, Blewett\(^4\) carried out a careful mass-spectrographic study of the isotopic composition of bromine. As a result of his work it turned out that there is no third stable isotope of bromine in an appreciable amount, and that the already known isotopes \(\mathrm{Br}^{79}\) and \(\mathrm{Br}^{81}\) are present in equal amounts. Table 1 gives the results of Blewett’s work.

The existence in bromine of isotopes with masses 77 and 83 would have been the most probable to expect. However, as is evident from Table 1, if these isotopes do exist, it is in amounts smaller than \(1/3000\). In order to explain the magnitude of the observed activity by the formation from these isotopes of a new radioactive isotope of bromine,

it would be necessary to assume incredibly large effective cross sections of the reaction, so large that they are completely unacceptable. Thus, on the basis of the results of Blewett’s work, we must reject the first hypothesis concerning the origin of the 36-hour period.

Consequently, there remains only one possibility for explaining the existence of the 36-hour period. It is set forth in the third hypothesis and consists in the fact that one of the two radioactive isotopes of bromine—$\mathrm{Br}^{80}$ or $\mathrm{Br}^{82}$—can decay with two different periods, i.e., this isotope exists in the form of two isomers. Thus the experimentally firmly established fact of the existence of the 36-hour period in bromine has led us to the necessity of assuming the existence of isomers.

If we compare the results of the experiments of Bothe and Gentner$^{5}$ on the photoelectric disintegration of bromine by $\gamma$-rays with the results obtained under the action of slow neutrons on bromine, then it can be established quite precisely which of the two isotopes of radiobromine—$\mathrm{Br}^{80}$ or $\mathrm{Br}^{82}$—possesses isomers.

When lithium is bombarded with protons, $\gamma$-rays of very high energy (about 17 MeV) arise. Under the action of these rays on bromine, photoelectric disintegration of bromine nuclei occurs, accompanied by the emission of a neutron from the nucleus and the formation of radioactive bromine nuclei

\[ \begin{aligned} {}^{79}_{35}\mathrm{Br} + h\nu &\longrightarrow {}^{1}_{0}n + {}^{78}_{35}\mathrm{Br},\\ {}^{81}_{35}\mathrm{Br} + h\nu &\longrightarrow {}^{1}_{0}n + {}^{80}_{35}\mathrm{Br}. \end{aligned} \tag{4} \]

Bothe and Gentner discovered, after irradiating bromine with $\gamma$-rays ($h\nu \sim 17$ MeV), three radioactive electron periods: 5 min., 16 min., and 4.5 hours. Within the limits of experimental error, the period of 16 min. coincides with the period of 18 min. observed under the action of slow neutrons, just as the period of 4.5 hours can be identified with the period of 4.2 hours observed under the action of slow neutrons. Thus two periods—18 min. and 4.2 hours—arise both under the action of $\gamma$-rays and under the action of slow neutrons. If we compare reaction (1) with (4), we shall see that only one radioactive isotope arises in both cases—this is $\mathrm{Br}^{80}$. Consequently, the periods 18 min. and 4.2 hours belong to the isotope $\mathrm{Br}^{80}$. In other words, $\mathrm{Br}^{80}$ exists in the form of two isomers. Now it is easy to assign the remaining bromine periods to definite isotopes. As is seen from (4), the 5 min. period, observed only under the action of $\gamma$-rays, belongs to $\mathrm{Br}^{78}$. On the other hand, from (1) it is seen that the 36-hour period, formed only under the action of slow neutrons, belongs to the isotope $\mathrm{Br}^{82}$.

The magnitude of the upper limit of the $\beta$-spectrum for the isomeric periods of bromine (18 min. and 4.2 hours) was determined by A. I. Alikhanov and collaborators$^{6}$, and also more recently by Snell$^{7}$. According to the data

According to A. I. Alikhanov and co-workers, the upper limit of the β-spectrum for the period of 18 min is \(2.00 \pm 0.10\) MeV, and for the period of 4.2 hours it is \(2.05 \pm 0.10\) MeV. As is evident from these data, the upper limits of the β-spectrum for both measured periods are very close to one another. However, whether they coincide exactly cannot be stated on the basis of these data, because the experimental error is twice as large as the observed difference in the values. According to Snell’s data, the upper limit of the β-spectrum for the period of 18 min is 2.2 MeV, and for the period of 4.2 hours it is 2.0 MeV. However, Snell does not give the experimental error, and therefore no judgments about the equality or inequality of the limits of the β-spectrum can be made on the basis of his data. Thus the question of whether the limits of the β-spectrum in the bromine isomers coincide exactly or are different remains open.

The γ-rays from the isomeric periods of bromine have as yet been studied insufficiently well. According to the data of the same Snell, the 18-minute period is accompanied by soft γ-rays, whose energy is apparently less than 0.5 MeV, while the period of 4.2 hours is not accompanied by γ-rays.

As regards the relative activities of the two isomeric periods, their activities, according to measurements by many authors, are practically identical.

After the discovery of isomerism in bromine, isomers emitting light particles (electrons and positrons) in their decay were found in a whole series of “semihigh” (atomic weight about 100) and heavy (atomic weight about 200) elements. Among the semihigh elements, isomerism was discovered in strontium \((Z = 38)\), silver \((Z = 47)\), and indium \((Z = 48)\). Moreover, in indium and silver as many as two pairs of isomers were found. Among the heavy elements, isomers were discovered in the noble metals: gold, platinum, and iridium, and also in the heaviest element itself—uranium. Many of these isomers were discovered as a result of bombarding elements with very fast neutrons (with energies up to 20 MeV). Such fast neutrons were obtained by bombarding lithium with deuterons accelerated in a cyclotron to an energy of 6.3 MeV.

Let us now consider briefly how the isomers were discovered in each of the elements listed above (apart from the case of bromine, which was discussed in detail earlier).

When strontium \(Sr_{38}\) was bombarded with deuterons, Stewart, Lawson, and Cork\(^8\) discovered in this element two periods: \(3.0 \pm 0.1\) hours and \(55 \pm 5\) days. It turned out that both periods are accompanied by the emission of electrons. Chemical separation of the active element showed that the active element is strontium. Since strontium has 4 stable isotopes with masses: 84 (0.5%), 86 (9.6%), 87 (7.5%), and 88 (82.4%), it was difficult to determine the active nuclei. However, it turned out that if the element following strontium in the Mendeleev table, yttrium \(Y_{39}\), is subjected to ...

under bombardment by very fast neutrons (with an energy of about 20 MeV), then in it one can detect the same 2 periods as in strontium as a result of bombardment of the latter by deuterons. Since yttrium has only one stable isotope, \(Y_{39}^{89}\), the only reaction among the reactions of known types that can lead to the formation of radiostrontium is the following:

\[ Y_{39}^{89}+n_{0}^{1}\longrightarrow Sr_{38}^{89}+H_{1}^{1}. \]

Thus the radioactive isotope of strontium is \(Sr_{38}^{89}\), subsequently decaying with the two periods indicated above according to the reaction

\[ Sr_{38}^{89}\longrightarrow \beta + Y_{39}^{89}. \]

Consequently, \(Sr_{38}^{89}\) exists in the form of two isomeric forms, one of which decays with a period of 3 hours, and the other—with a period of 55 days.

The reaction of formation of radiostrontium upon irradiation of stable strontium by deuterons can now be written in the form

\[ Sr_{38}^{88}+H_{1}^{2}\longrightarrow Sr_{38}^{89}+H_{1}^{1}. \]

The decay of the isomer with a period of 3 hours is accompanied by \(\gamma\)-rays, the energy of which has not yet been measured. The decay of the isomer with a period of 55 days is not accompanied by \(\gamma\)-rays. As for the maximum energy of the electrons, for the 3-hour period it is equal to 0.61 MeV, and for the 55-day one it is equal to 1.9 MeV.

Let us consider isomerism in indium. Indium has two stable isotopes: \(In_{49}^{113}\) (4.5%) and \(In_{49}^{115}\) (95.5%). Already Amaldi et al.\(^{2}\), when irradiating indium with slow neutrons, observed three radioactive periods: 13 sec., 54 min., and several hours. These 3 periods were obtained as a result of the simple capture of slow neutrons and belong, therefore, to two radioactive isotopes of indium: \(In^{114}\) and \(In^{116}\). The very fact that three periods exist indicated that one of these radioactive isotopes exists in two isomeric forms. Recently Lawson and Cork\(^{9}\) used for irradiation of indium both slow and very fast neutrons with an energy of about 20 MeV. In bombarding indium with slow neutrons they likewise found three periods: 13 sec., 54 min., and 4.1 hours. In bombarding indium with very fast neutrons, two additional new periods were obtained: 72 sec. and 45 days. All these 5 periods of indium are accompanied by the emission of electrons. It turned out that the period of 4.1 hours has a large activity with fast neutrons and a very small one under the action of slow neutrons. As was said above, under the action of very fast neutrons reactions with the emission of two neutrons have a high probability. Therefore the period of 4.1 hours may be ascribed to the radioactive isotope \(In^{112}\) or \(In^{114}\), formed from \(In^{113}\) or \(In^{115}\) as a result of a reaction with the emission of two

neutrons. From comparing the ratio of activities under fast and under slow neutrons with the ratio of the numbers of stable isotopes, the authors conclude that the period of 4.1 hours must belong to the isotope \(In^{114}\), and not to \(In^{112}\). The period of 72 sec. appears only with fast neutrons, and therefore the authors ascribe it to the isotope \(In^{112}\) (a reaction with the emission of two neutrons).

Determination of the intensity of the different periods showed that the intensities of the periods of 13 sec. and 54 min., obtained as a result of the action of both fast and slow neutrons, stand in one and the same ratio to one another. On this basis Lawson and Cork concluded that both these periods belong to one and the same isomeric isotope. This isotope must have mass 114 or 116. Since these periods are activated better by slow neutrons than by fast ones, the authors consider that both these periods belong to the isotope \(In^{116}\). In other words, this isotope exists in the form of two isomers. The period of 45 days was observed only as a result of the action of fast neutrons, and therefore it may belong to the isotope \(In^{112}\) or \(In^{114}\) (a reaction with the emission of two neutrons). The authors tentatively ascribe it to \(In^{114}\). Consequently, according to these investigators, the five periods observed by them are distributed as follows among the radioactive isotopes of indium:

Thus indium has two pairs of radioactive isomers: \(In^{114}_{48}\) and \(In^{116}_{48}\). The maximum energy of the electrons of the periods 13 sec. and 54 min. was determined by Mitchell and Langer\(^{10}\) and is equal, respectively, to 3.1 and 1.4 MeV. The maximum energy of the electrons of the other indium periods has not yet been measured experimentally.

As was said above, electron-decaying isomers have also been found among the heaviest elements (\(A \sim 200\)). Among the heavy elements, isomers were found in the noble metals: gold, platinum, and iridium. All these isomers were found by MacMillan, Kamen, and Ruben\(^{11}\).

Let us dwell first on the isomers of gold. As is known, gold has only one stable isotope, \(Au^{197}_{79}\). In addition to the period of 2.7 days found after neutron bombardment in gold by Fermi and his co-workers, MacMillan and others found, on irradiating gold with very fast neutrons (with an energy of about 20 MeV), two more periods: 13 hours and 4–5 days. Both these periods are accompanied by electron decay. Chemical separation showed that both radioactive elements are isotopes of gold. Since, on irradiation with such fast neutrons, reactions with the emission of two neutrons are possible, the authors consider,

that both new periods in gold were created precisely as a result of such a reaction:

\[ \mathrm{Au}_{79}^{197} + n_{0}^{1} \longrightarrow \mathrm{Au}_{79}^{196} + 2n_{0}^{1} \]

\[ \mathrm{Au}_{79}^{196} \longrightarrow \beta + \mathrm{Hg}_{80}^{196}\ \text{(stable).} \]

Thus radiogold exists in the form of two isomeric forms of the nucleus \(\mathrm{Au}_{79}^{196}\).

In platinum, MacMillan and his co-workers likewise discovered the existence of electron-decaying isomers. Platinum has 5 stable isotopes:

After irradiation of platinum with slow neutrons, the authors observed three periods: 31 min., 18 hr., and 3.3 days. These three periods may belong to the isotopes \(\mathrm{Pt}^{193}\), \(\mathrm{Pt}^{197}\), and \(\mathrm{Pt}^{199}\). But \(\mathrm{Pt}^{193}\) and \(\mathrm{Pt}^{199}\), upon \(\beta\)-decay, should give unstable gold isotopes

\[ \mathrm{Pt}_{78}^{193} \longrightarrow \beta + \mathrm{Au}_{79}^{193}\ \text{(unstable),} \]

\[ \mathrm{Pt}_{78}^{199} \longrightarrow \beta + \mathrm{Au}_{79}^{199}\ \text{(unstable),} \]

and only \(\mathrm{Pt}^{197}\) gives a stable gold isotope

\[ \mathrm{Pt}_{78}^{197} \longrightarrow \beta + \mathrm{Au}_{79}^{197}. \]

Consequently, chemical separation of gold from the irradiated platinum should have yielded two periods. In fact, the separation yielded only one period—31 min. From this the authors conclude that the periods of 18 hr. and 3.3 days belong to two isomers of the nucleus \(\mathrm{Pt}_{78}^{197}\).

The same authors observed isomerism in iridium. Iridium has two stable isotopes: \(\mathrm{Ir}_{77}^{191}\) (38.5%) and \(\mathrm{Ir}_{77}^{193}\) (61.5%). After irradiation with slow neutrons, iridium gave 3 periods: 19 hr., 2 months, and 1.5 min., with saturation intensities respectively: 120, 280, and 28 counts per 1 sec. The third period, previously unknown, was observed in three different iridium samples, one of which was of very high purity, so that the authors believe that it could not have been caused by impurities. By analogy with other elements, in this case, upon irradiation with slow neutrons, the isotopes \(\mathrm{Ir}^{192}\) and \(\mathrm{Ir}^{194}\) should have been formed. Thus one of these isotopes should possess two electron-

periods, i.e. it must have two isomeric forms. When fast neutrons with energies up to 20 MeV acted on iridium, the same periods were obtained as under the action of slow neutrons, but the ratio of the saturation intensities was different. In this case the intensity of the periods 1.5 min. and 19 h., relative to the intensity of the 2-month period, was much smaller than in the case of slow neutrons. From this the authors conclude that, apparently, the 2-month period belongs to \(Ir^{192}\), while the periods 1.5 min. and 19 h. belong to the isotope \(Ir^{194}_{77}\), which thus exists in the form of two isomers.

Up to now we have been speaking of the existence of two such isomeric radioactive forms of one and the same isotope, each of which emits electrons. However, there are experimental data indicating that one isomeric form can, upon decay, emit electrons, and the other—positrons, i.e. also light particles, but with the opposite sign of charge. This type of isomerism was first observed in silver by Pool, Cork, and Thornton \(^{12}\), and later studied in more detail by Pool \(^{13}\), Pool and Kempel \(^{14}\). Silver has two stable isotopes: \(\mathrm{Ag}^{107}_{47}\) (52%) and \(\mathrm{Ag}^{107}_{47}\) (48%). After irradiation with slow neutrons, silver gives two well-known periods: 20 sec. and 2 min. After irradiation of silver with neutrons of very high energy (up to 20 MeV), the above-mentioned authors observed two more new periods: 24.5 min. and 8.2 days. These periods were also obtained by the authors as a result of bombarding rhodium with \(\alpha\)-particles of energy 11 MeV, palladium with deuterons of energy 6.3 MeV, and cadmium with fast neutrons of energy up to 20 MeV and, finally, by the action on silver of \(\gamma\)-rays of energy 17 MeV. \(\gamma\)-rays of such high energy were obtained by the investigators as a result of bombarding lithium with protons of energy 3.2 MeV. The \(\alpha\)-particles, protons, and deuterons were accelerated with the aid of a cyclotron. If we compare the atomic weights of the stable isotopes of all the listed elements with the fact that in all the indicated cases radiogold is obtained, then we inevitably come to the conclusion that both new periods in silver belong to the radioactive isotope \(\mathrm{Ag}^{106}\). In other words, \(\mathrm{Ag}^{106}\) exists in the form of two isomeric forms.

It was found, moreover, that the 24.5-min. period is accompanied by the emission of positrons, while the 8.2-day period is accompanied by the emission of electrons, \(\gamma\)-rays, and a small number of positrons. The nuclear reactions leading to the formation of \(\mathrm{Ag}^{106}\) are given here:

\[ \text{Period } 24.5\ \text{min. (positrons)} \]

\[ \mathrm{Rh}^{103}_{45} + \mathrm{He}^{4}_{2} \to \mathrm{Ag}^{106}_{47} + n^{1}_{0} \]

\[ \mathrm{Pd}^{105}_{46} + \mathrm{H}^{2}_{1} \to \mathrm{Ag}^{106}_{47} + n^{1}_{0} \]

\[ \mathrm{Ag}^{107}_{47} + n^{1}_{0} \to \mathrm{Ag}^{106}_{47} + n^{1}_{0} + n^{1}_{0} \]

\[ \mathrm{Ag}^{107}_{47} + \gamma^{0}_{0} \to \mathrm{Ag}^{106}_{47} + n^{1}_{0} \]

\[ \mathrm{Cd}^{106}_{48} + n^{1}_{0} \to \mathrm{Ag}^{106}_{47} + \mathrm{H}^{1}_{1} \]

Period 8.2 days (electrons, $\gamma$-rays, positrons)

\[ \mathrm{Pd}_{46}^{105}+\mathrm{H}_{1}^{2}\to \mathrm{Ag}_{47}^{106}+n_{0}^{1} \]

\[ \mathrm{Ag}_{47}^{107}+n_{0}^{1}\to \mathrm{Ag}_{47}^{106}+n_{0}^{1}+n_{0}^{1} \]

\[ \mathrm{Cd}_{48}^{106}+n_{0}^{1}\to \mathrm{Ag}_{47}^{106}+\mathrm{H}_{1}^{1} \]

Both periods are obtained best of all by bombarding $\mathrm{Ag}^{107}$ with fast neutrons.

For one $\beta$-particle of the 8.2-day period there are 35 $\gamma$-quanta. Usually the $\gamma$-rays accompanying decay arise in the following way. After emission of the $\beta$-particle the nucleus remains in an excited state. Returning from this excited level to the ground state, the nucleus emits a $\gamma$-quantum. If, between this excited level and the ground state, there are intermediate levels, then several $\gamma$-quanta may be emitted. However, the occurrence of such a large number of $\gamma$-quanta per one $\beta$-particle in the 8.2-day period cannot be explained in this way, because experimentally only three groups of $\gamma$-rays have been found. To explain the origin of these $\gamma$-rays one may make use of the fact that, according to Fermi’s theory of $\beta$-decay, instead of emitting a $\beta$-particle the nucleus may capture an electron from the $K$ shell of the atom, and this process is accompanied by the emission of $\gamma$-rays. In this case the probability of this process for heavy elements may be much greater than the probability of emission of a $\beta$-particle. Capture of $K$-electrons by the nucleus was observed experimentally by Alvarez in the nucleus $\mathrm{V}^{48}$. Pool and Campbell suppose that part of the $\gamma$-quanta accompanying the 8.2-day period in $\mathrm{Ag}^{106}$ arises precisely as a result of capture of $K$-electrons by the nucleus $\mathrm{Ag}^{106}$.

Three groups of $\gamma$-rays were found for the 8.2-day period, namely: 0.3, 0.7, and 1.0 MeV. For the 24.5-min period, no $\gamma$-rays were found, except those which could have been caused by annihilation of the positrons accompanying this period. The intensity of the activity of the 8.2-day period proved to be 20 times greater than the intensity of the activity of the 24.5-min period. The upper limit of the $\beta$-spectrum has the following value: for electrons of the 8.2-day period it is equal to 1.3 MeV; for positrons of this same period it has the value 0.41 MeV; and for positrons of the 24.5-min period the upper limit has the value 1.9 MeV. On the basis of the experimental data given above, for the 8.2-day period the ratio

probability of capture of a $K$-electron : probability of emission of an electron : probability of emission of a positron

is equal to $640:40:1$. Uhlenbeck and Kuiper calculated curves for the dependence of the ratio of the probability of capture of a $K$-electron to the probability of emission of a positron on the energy $W_0$ necessary for the transition, and on the atomic number. Taking this ratio to be $640:1$, one can find from these curves the corresponding $W_0$. The quantity $W_0$ proved to be equal to $2.2\,mc^2$, which gives for the upper limit of the positron spectrum the value 0.6 MeV.

Pool and Campbell believe that the latter value is the more correct one, and not the one which they obtained experimentally, equal to \(0.41\ \mathrm{MeV}\). The value \(0.41\ \mathrm{MeV}\) was obtained by them as a result of measuring the deflection of positron tracks in a Wilson chamber with a magnetic field. However, only 15 positron tracks were measured; the authors believe that, owing to so small a number of measured tracks, they were unable to measure the fastest positrons with an energy of \(0.6\ \mathrm{MeV}\).

On the basis of the experimental data given above and their interpretation, one can construct a scheme of the energy levels of the isomeric nucleus \({}^{106}_{47}\mathrm{Ag}\). As a result of the emission by the \({}^{106}\mathrm{Ag}\) nucleus of a positron, or capture of a \(K\)-electron of the shell, the stable nucleus \({}^{106}_{46}\mathrm{Pd}\) is formed by the reaction

\[ {}^{106}_{47}\mathrm{Ag}\longrightarrow \beta^{+}+{}^{106}_{46}\mathrm{Pd}. \]

As a result of electron emission, the stable nucleus \({}^{106}_{48}\mathrm{Cd}\) is formed,

\[ {}^{106}_{47}\mathrm{Ag}\longrightarrow \beta^{-}+{}^{106}_{48}\mathrm{Cd}. \]

For constructing the scheme of levels of the \({}^{106}_{47}\mathrm{Ag}\) nucleus we shall conventionally take the energy of the stable nucleus \({}^{106}_{46}\mathrm{Pd}\) as zero and count from it all energies (Fig. 1). Let us find the position of the level of the \({}^{106}_{47}\mathrm{Ag}\) nucleus corresponding to the period \(24.5\) min. In positron emission the mass of the atom decreases by twice the electron mass

Fig. 1.

(~1 MeV), since one electron leaves the shell. Thus, in the decay of \( \mathrm{Ag}^{106} \) with a period of 24.5 min., there is lost, first, 1 MeV (2 electron masses) and, second, an energy equal to the upper limit of the positron spectrum, i.e. 1.9 MeV (there are no \(\gamma\)-rays). Therefore, setting off from the zero level the quantity 1.9 MeV and then 1 MeV, we obtain the position of the \( \mathrm{Ag}^{106} \) level (period 24.5 min.) with respect to the level of stable \( \mathrm{Pd}^{106}_{46} \). The position of the \( \mathrm{Ag}^{106} \) level for the period 8.2 days can be determined in the following way: from the zero level let us set off the levels 0.3, 0.7, and 1 MeV, corresponding to the observed \(\gamma\)-ray lines. Adding, further, to 1 MeV the magnitude of the upper limit of the positron spectrum of the period 8.2 days, equal to 0.6 MeV, and the energy of 1 MeV corresponding to twice the electron mass, we obtain the position of the \( \mathrm{Ag}^{106} \) level for the period 8.2 days. As is seen from the scheme, the level of the period 24.5 min. has turned out to lie above the level of the period 8.2 days by 0.3 MeV. Now one can represent on the scheme the transitions corresponding to capture of a \(K\)-electron and to emission of an electron. After emission of an electron by the nucleus, the mass of the atom will not change, since a new electron is captured by the atomic shell (there occurs a rearrangement of the shell in accordance with the structure of the atom of the new element formed after the emission of the electron). In the capture of a \(K\)-electron, naturally, the mass of the atom likewise does not change.

Therefore, setting downward from the \( \mathrm{Ag}^{106} \) level (with period 8.2 days) an energy of 1.3 MeV, equal to the upper limit of the electron spectrum, we obtain the position of the stable level \( \mathrm{Cd}^{106}_{48} \) (on the assumption of the absence of \(\gamma\)-rays). Finally, in order to explain the transition to stable \( \mathrm{Pd}^{106} \) after capture of a \(K\)-electron, Pool and Campbell had, as is seen from the scheme, to assume that after this capture the nucleus emits a neutrino, which carries away with it 1.6 MeV. In view of the inaccuracy of the experimental data, in particular in view of the absence of any data on the presence of this neutrino, the scheme given is perhaps not yet final and indisputable. Further study of the radio-silver isomers will make it possible to verify and refine this scheme, and thus a completely accurate picture of the levels of the nucleus of the \( \mathrm{Ag}^{106} \) isomer will be constructed.

In conclusion of the question of isomerism in silver, let us note that recently, both in the USSR and abroad, data have appeared indicating that still other isomers exist in silver. Thus, as a result of prolonged (several months) irradiation of silver with slow neutrons, a new, very long period of about 2 years has been found in silver. The period is accompanied by the emission of electrons. In view of the fact that this long period is formed as a result of the action of slow neutrons, the most probable reaction leading to its formation is the reaction of simple neutron capture. However, it is well known that

as a result of the reaction of simple capture, from the stable isotope $\mathrm{Ag}^{107}$ there is formed radioactive $\mathrm{Ag}^{108}$ with a period of 2.3 min., and from stable $\mathrm{Ag}^{106}$ there is formed $\mathrm{Ag}^{110}$ with a period of 22 sec. Since silver has only two stable isotopes, it follows that the newly discovered period of 2 years belongs to an isomer of the nucleus $\mathrm{Ag}^{108}$ or $\mathrm{Ag}^{110}$.

We see that this case is analogous to the case of bromine (2 stable isotopes and 3 periods for the capture reaction).

It is interesting to note that in silver the ratio of the periods of the two isomers is very large (2 years and 2 min., or even 2 years and 2 sec.), whereas for the isomers of other elements it is considerably smaller: for strontium—55 days and 3 hours, for iridium—19 hours and 1.5 min., etc.

Let us also dwell briefly on the isomerism of the heaviest element itself—uranium. In the works of O. Hahn and L. Meitner and of other investigators there are data indicating that, when uranium $\mathrm{U}^{238}_{92}$ is irradiated with slow neutrons, as a result of the reaction of simple capture two isomers of the nucleus $\mathrm{U}^{239}_{92}$ are formed: one isomer decays with a period of 10 sec., and the other—with a period of 40 sec. Both periods are accompanied by the emission of electrons1.

Besides the described kinds of isomerism, there apparently exists also isomerism connected with the emission of heavy particles. The question that, for example, a “compound” nucleus $\mathrm{Al}^{28}_{13}$ can be in a metastable state was raised in the work of N. N. Dmitriev[^15].

Finally, let us point to one long-known case of isomerism in the region of natural radioactivity.

The radioelements $\mathrm{UX}_2$ and $\mathrm{UZ}$, formed from $\mathrm{UI}$, decay by two different paths with the emission of electrons and form $\mathrm{UII}$. Thus $\mathrm{UX}_2$ and $\mathrm{UZ}$ are two isomers of the isotope of protactinium.

Weizsäcker[^16] gave a theoretical explanation of the phenomenon of isomerism in accordance with N. Bohr’s theory of the nucleus and with the participation of Bohr himself. A radioactive nucleus formed as a result of a nuclear reaction is usually at one of its excited levels. It then passes to its ground level, emitting $\gamma$-rays in the process. Since the probability of emission of $\gamma$-rays is usually many times greater than the probability of emission of corpuscles, before the nucleus emits a par-

it will emit a γ-quantum and in doing so will pass to its ground level. In other words, decay of the nucleus with emission of a particle is possible only from the ground level. Now let us suppose that among the excited levels of the nucleus there are such levels, the transition from which is so strongly forbidden that the probability of this transition from the level to lower levels is less than the probability of emission of a particle from this level. In this case the nucleus will emit a particle before it passes to the ground state. In other words, in this case decay is possible not only from the ground level. Levels with such a large forbiddenness of transition are called metastable. Thus, in the case where a metastable level exists in the nucleus, the decay of the nucleus is possible by two different paths (Fig. 2): 1) from the metastable level and 2) from the ground level. In this case, generally speaking, the half-lives from the two levels will be different. The type of particles emitted from these levels may also be different. We see that by assuming the existence of metastable levels one can explain both electronic isomerism and electron–positron isomerism (in Ag\(^{106}\)), as well as all other kinds of isomerism. The assumption of the existence of metastable levels in the nucleus does not necessarily require any particular model of the nucleus or any analogies—this assumption can be introduced simply from consideration of the nucleus as a certain complex radiating quantum-mechanical system.

Fig. 2.

The lifetime \(\tau\) of the excited state with respect to the emission of γ-rays is expressed by the following formula\(^{14}\):

\[ \tau = 5 \cdot 10^{-21}(\Delta l)!^{2}\left(\frac{20}{\Delta E}\right)^{2(\Delta l)+1}. \tag{5} \]

Here \(\Delta l\) is the change in the mechanical moment (spin) of the nucleus in the transition from the excited state to the ground state, and \(\Delta E\), expressed in this formula in MeV, is the energy difference between the ground state and the excited state. As is seen from this formula, the lifetime will be large for large \(\Delta l\) and for small \(\Delta E\). This means that the metastable level must lie close to the ground level (small \(\Delta E\)), and the difference between the mechanical moments of the metastable level and the ground level must be large.

In heavy nuclei the minimum value \(\Delta E\), representing the excitation energy of the first excited state, has a magnitude of about 200 kV; \(\Delta E=50\) often occurs, and sometimes even \(\Delta E=10\) kV. The mechanical moment of the nucleus is unlikely to change by more than 4–5 units. The values of \(\tau\) for these values of \(\Delta E\) and \(\Delta l\), calculated by formula (5), are given in Table 2.

TABLE 2

From Table 2 we see that metastable states of a nucleus can exist for many days and even years. In particular, if a metastable state exists for a very large number of years (for example, \(\sim 10^{10}\) years), then practically this state is stable. In other words, according to this theory, isomers can exist among stable nuclei. These isomers are also stable nuclei and differ from nuclei in the ground state only by a small amount of internal energy \(\Delta E\) and by a large amount of spin \(\Delta l\).

Let us apply the theory of isomerism set forth above to the level scheme of the isomeric nucleus \(\mathrm{Ag}^{106}\) (Fig. 1). From this scheme we see that the level of the nucleus \(\mathrm{Ag}^{106}\) corresponding to the period 24.5 min. lies above the level corresponding to the period 8.2 days by 0.3 MeV. One of these levels is, from Weizsäcker’s point of view, metastable, and the other is the ground state. Since the metastable level lies above the ground state, we must regard the level of the nucleus \(\mathrm{Ag}^{106}\) for the period 24.5 min. as metastable, and the level of period 8.2 days as the ground state. The energy difference between the ground and metastable levels in this case is 0.3 MeV. The mean lifetime \(\tau\) is equal to

\[ \tau=\frac{T}{0.693}, \]

where \(T\) is the half-life. In the present case, for the metastable state \(T=24.5\) min. Consequently, the mean lifetime of the metastable state \(\tau\) will be equal to

\[ \tau=\frac{24.5}{0.693}=35.4\ \text{min.} \]

Using this value of $\tau$ and taking $\Delta E = 0.3\ \mathrm{MeV}$, we can determine, by means of the formula given above for $\tau$ (formula 5), what the change in the mechanical angular momentum $\Delta l$ must be in the transition from the metastable state to the ground state.

Substituting in this formula $\tau = 35.4\ \mathrm{min.} = 2120\ \mathrm{sec.}$ and $\Delta E = 0.3\ \mathrm{MeV}$, we then obtain

\[ 2120 = 5 \cdot 10^{-21}(\Delta l)!^{2}\left(\frac{20}{0.3}\right)^{2(\Delta l)+1}. \]

Hence $\Delta l = 5$. Thus, in the transition from the $\mathrm{Ag}^{106}$ level with period 24.5 min. to the $\mathrm{Ag}^{106}$ level (period 8.2 days), the mechanical angular momentum of the nucleus $l$ changes by 5 units. Such a large change of angular momentum does not appear unacceptable if one recalls that some nuclei in the ground state have $l = \frac{9}{2}$.

Let us dwell further on possible schemes of isomer decay. Here two basic schemes are possible$^{17}$ (Fig. 2):

1. The transition from the metastable level to the ground level is accompanied by the emission of $\gamma$-rays, while decay from the ground level proceeds with the emission of particles. In this case, however, we shall have two different periods; the magnitude of the period corresponding to decay from the metastable level will be determined, as is easy to understand, by the probability of the forbidden transition. The upper limits of the spectrum for both periods in this case will be identical. With such a transition scheme, both periods can be observed experimentally only in the case when the longer period belongs to the metastable level.

2. The transition from the metastable level to the ground level is preceded by the emission of a particle. In this case the upper limits of the corpuscular spectrum will be different, and at least one of the periods will be accompanied by $\gamma$-rays. In this scheme the half-life of the metastable level may be both greater and smaller than the half-life of the ground level.

Fig. 3.

Let us also note that a case is possible in which the transition of one isomer into another is not accompanied by any corpuscular radiation, but only by the emission of very soft $\gamma$-rays; experimentally, such $\gamma$-rays are very difficult to detect.

In conclusion, let us touch upon the question of the origin of isomers. Since, from the point of view of the theory presented here, isomers are two different states of one and the same nucleus, the process of their formation must be one and the same. Fleischmann$^{18}$ experimentally studied the process of formation of bromine isomers. These isomers are formed as a result of the resonant capture of slow neutrons. If the process of formation of isomers is identical, then the reso

the resonance energy \(E_r\) for both periods (18 min. and 4.2 hours) would have to be the same. Measuring the resonance energy by absorption in boron, Fleischmann found: for the 18-min. period \(E_r = 52.2\ \mathrm{eV} \pm 5.7\%\), for the 4.2-hour period \(E_r = 53.2\ \mathrm{eV} \pm 4.6\%\). Consequently, within the limits of experimental error, the resonance energy for both isomeric periods of \(\mathrm{Br}^{80}\) proved to be the same. In addition, a comparison was made of the form of the resonance curve (Fig. 3) for both periods. It turned out that the form of this curve is the same for both periods, i.e. the curves, when superposed on one another, simply coincide. Thus it was shown that the process of formation of the bromine isomers is one and the same, which is in agreement with the theory set forth above.

LITERATURE

1. B. Kurtschatow, I. Kurtschatow, L. Myssowsky, L. Russinow, C. R., 200, 1201, 1935.
2. Amaldi et al., Proc. Roy. Soc., 149, 522, 1935.
3. L. V. Mysovskii, I. V. Kurchatov, R. A. Eikhelberger and G. D. Latyshev. Academy of Sciences of the USSR. Collection “To Academician V. I. Vernadsky,” 1936.
4. J. Blewett, Phys. Rev., 49, 900, 1936.
5. Bethe and Gentner, Naturwiss., 25, 90, 191, 1937.
6. A. Alichanian, A. Alichanow and B. Dzelepov, Phys. Z. Sowjetunion, 10, 78, 1936.
7. A. Snell, Phys. Rev., 52, 1007, 1937.
8. D. Stewart, J. Lawson and J. Cork, Phys. Rev., 52, 901, 1937.
9. J. Lawson and J. Cork, Phys. Rev., 52, 531, 1937.
10. A. Mitchell and L. Langer, Phys. Rev., 53, 505, 1938.
11. E. McMillan, M. Kamen, S. Ruben, Phys. Rev., 52, 375, 1937.
12. M. Pool, J. Cork and L. Thornton, Phys. Rev., 52, 239, 1937.
13. M. Pool, Phys. Rev., 53, 116, 1938.
14. M. Pool and E. Campbell, Phys. Rev., 53, 272, 1938.
15. N. N. Dmitriev, Reports of the All-Union Conference on the Atomic Nucleus, September 1937. Bulletin of the Division of Mathematical and Natural Sciences of the Academy of Sciences of the USSR, 1938.
16. C. Weizsäcker, Naturwiss., 24, 812, 1936.
17. H. Bethe, Rev. Mod. Phys. 9, 225, 1937.
18. K. Fleischmann, Z. Physik, 107, 205, 1937.
19. M. L. Pool and L. L. Quill, Phys. Rev., 53, 437, 1938.

1. In addition to the isomers described above, quite recently Pool and Quill[^19] discovered two more new isomers, both in rare-earth elements. One of these isomers was found in gadolinium,—this is $\mathrm{Gd}^{159}_{64}$, decaying with two periods: 3.5 min. and 17 hours. Both periods are accompanied by the emission of electrons. Another isomer was found in ytterbium,—this is $\mathrm{Yb}^{175}_{70}$, which decays with periods of 2.1 hours and 41 hours. Both these periods are likewise accompanied by the emission of electrons. ↩