Nuclear Isomerism

N. N. Dmitriev, Leningrad

In a previously published article¹ experimental data were presented on the nuclear isomers Br, Sr, Ag, In, Gd, Yb, Pt, Au, Ir, U. There, too, the general theory of isomerism was set forth and the experimental data were interpreted from the point of view of this theory. Within a short interval of time new data have appeared, which we present in this article.

Of particular interest is the isomerism of uranium Z and uranium X₂, because its study has made it possible to introduce certain corrections into the decay scheme of the uranium series.

Until now it had been known that uranium Z and uranium X₂ have one and the same atomic number \((z = 91)\) and one and the same atomic weight \((A = 234)\), and that both decay with emission of electrons, transforming into uranium II. In addition, it was known that their half-life periods are different: for uranium Z the period is 6.7 hours, while for uranium X₂ the period has the value 1.14 min. It was also known that the upper limits of the electron spectra of these two elements are different. On the basis of the data cited above it was concluded that uranium Z and uranium X₂ are isomers. However, no more or less satisfactory theoretical explanation of the isomerism of uranium Z and uranium X₂ had so far been given.

In a comparatively recently published work, Feather and Bretscher², on the basis of their own experimental data and the data of other authors, considered the question of the isomerism of uranium Z and uranium X₂ from the point of view of the theory of isomerism most acceptable at the present time, which was proposed by Weizsäcker with Bohr’s participation. As is known¹, according to this theory one of the isomers (uranium Z or uranium X₂) must be a metastable state, and the other the ground state of one and the same isotope. In this case the metastable level must lie close to the ground level and differ from the ground level by a large value of the nuclear spin. Therefore, in order to decide whether the isomerism of uranium Z and uranium X₂ can be explained from the point of view of Weizsäcker’s theory, it is necessary to decide whether a nucleus with atomic number 91 and atomic weight 234 can have a metastable level. A necessary condition for the existence of the latter is that the excitation energy of the first excited state \((E_1)\) must

be small. Uranium Z and uranium X₂ belong to the type of nuclei having an odd atomic number and an even atomic weight. For all other radioactive elements of this type (except MsTh₂) the excitation energy of the first excited state \(E_1\) has been determined experimentally from the study of \(\gamma\)-rays and of the fine structure of \(\alpha\)-particles accompanying the decay of these elements. The values of \(E_1\) are given in Table 1, cited by Fezer and Bretscher\(^2\).

TABLE 1

From Table 1 it is seen that in all the investigated elements the excitation energy \(E_1\) is indeed very small. On this basis one may suppose, as Fezer and Bretscher do, that for the element UZ—UX₂ as well \(E_1\) will be small, i.e. the first excited level lies close to the ground level, and therefore this level may be metastable. Thus it becomes possible to treat the isomerism of uranium Z and uranium X₂ from the point of view of Weizsäcker’s theory.

According to this theory, the principal question is which of the two isomers, in the present case uranium Z or uranium X₂, is the metastable state and which is the ground state.

Of the various possibilities Fezer and Bretscher choose the one which corresponds to the smallest lifetime of the metastable state with respect to the emission of \(\gamma\)-rays. In connection with this, generally speaking, three different cases are possible, namely:

\[ \text{a)}\quad UX_1 \begin{array}{c} \overset{\beta_1}{\nearrow} UX_2\\ \underset{\beta_2}{\searrow} UZ^{*} \end{array} \]

\[ \text{b)}\quad UX_1 \begin{array}{c} \overset{\beta_1}{\nearrow} UX_2^{*}\\ \underset{\beta_2}{\searrow} UZ \end{array} \]

\[ \text{c)}\quad UX_1 \xrightarrow{\beta} UX_2^{*} \xrightarrow{\beta} \qquad \begin{array}{c} \\[-1.2em] \underset{\gamma}{\searrow} UZ \end{array} \]

In case a), UZ is the metastable state, and UX₂ is the ground state (the excited state is denoted by an asterisk). In case b), on the contrary, UX₂ is the metastable state, and UZ is the ground state; moreover, both UX₂ and UZ are formed in this case from UX₁ as a result of the β-decay of the latter. Finally, in case c), just as in case b), UX₂ is the metastable state and UZ is the ground state. But in this case, unlike case b), UZ is formed from UX₂ as a result of the latter emitting γ-rays. With the aid of the experimental data they obtained on the β-decay of UZ, Fezer and Bretscher found that the shortest lifetime of the metastable state with respect to the emission of γ-rays would occur in case c), and, consequently, in their opinion this case is the most probable. Thus, according to the data of these authors, it turns out that uranium X₂ is the metastable state, and uranium Z is the ground state of one and the same radioactive isotope. In this case uranium Z is formed from uranium X₂ as a result of the latter emitting soft γ-rays, and not in the β-decay of UX₁, as had been assumed until now.

Fig. 1. Sargent curves for natural radioelements. Point 1 corresponds to the soft component of β-radiation (0.56 MeV), point 2 corresponds to the hard component (1.55 MeV). The closed lines drawn around the points give the possible error in determining the positions of the points.

Fezer and Bretscher investigated the γ- and β-rays of uranium Z. The maximum energy of the electrons, determined from the absorption of electrons in aluminum, proved to be equal to 1.16 MeV. If this value is taken as the upper limit of the β-spectrum, then the point corresponding to UZ \((\lambda = 2.9 \cdot 10^{-5}\ \mathrm{sec.}^{-1})\) lies exactly midway between the Sargent curve corresponding to a change of nuclear spin by 0 or 1, and the Sargent curve corresponding to a change of spin by 2 units.

limits. These curves are shown in Fig. 1. On the basis of these curves, and also by comparing the course of the electron-absorption curve from uranium Z with the course of the electron-absorption curve from UX₂ and RaE, the authors came to the conclusion that the β-radiation of uranium Z consists of at least two components with upper limits that differ greatly from one another. They found that the absorption curve obtained by them can be resolved into two curves corresponding to two components of the β-rays, of which the soft component has an upper limit of 0.56 MeV and a relative intensity of 0.944, while the hard component has an upper limit equal to 1.55 MeV and a relative intensity of 0.056.

The effective energy of γ-quanta from uranium Z, determined from absorption in lead and other materials, proved to be equal to 0.7 MeV; moreover, per one β-decay of uranium Z there is, on the average, \(1.50 \pm 0.25\) quantum.

The relative activities of both isomers were also determined. It turned out that the ratio of the activity of uranium X₂ to the activity of uranium Z is equal to \((665 \pm 65):1\).

On the basis of the data given above on the γ- and β-radiations of uranium Z, and also on the basis of data on the γ- and β-radiations of uranium X₁ and uranium X₂, Feather and Bretscher constructed the decay scheme of UX₂ and UZ, shown in Fig. 2. In this scheme the numbers to the right of the level lines give the energy of the corresponding level in MeV relative to the ground level of uranium II, conventionally taken as zero. The symbols β and γ denote the kind of radiation (electrons and γ-rays, respectively). The numbers below the symbols β and γ give the energy of the given radiation, and the numbers above give its relative intensity. The scale upward and downward from the line \(AA'\) is different. The numbers to the left of the level lines give the corresponding values of the nuclear spin. From this scheme it follows that UZ must emit two groups of γ-rays. The subsequent study by Feather and Bretscher of the γ-rays by means of the coincidence method showed that, indeed, the γ-rays consist of two groups. This fact is a direct experimental confirmation of the correctness of this part of the scheme.

Fig. 2. Scheme of the levels and decay of the nuclei UZ and UX₂ (for an explanation of the notation see the text)

From the point of view of the theory of metastable levels, the greatest interest in this scheme is the energy difference \(\varepsilon\) between the ground level (the \(UZ\) level) and the metastable one (the ground level \(UX_2\)), and the difference of the spin values between these levels. As for the energy \(\varepsilon\), Fezer and Bretscher were unable to determine it (therefore in their scheme it is denoted simply by \(\varepsilon\)). In order likewise to assign spin values to the levels, the authors had to make use of Sargent’s curve. Moreover, as the authors themselves point out, in some respects there were several different possibilities in constructing this scheme. Hence, naturally, there follows a certain uncertainty in the results arising from this scheme.

The difference of spin values \(l\) between the uranium level \(Z\) and the ground uranium level \(X_2\), as well as the energy difference between these two levels, were quite unambiguously determined by N. Dmitriev\(^3\). It proved possible to find \(\varepsilon\) and \(l\) by using Bethe’s formula for the lifetime of a metastable state, and with the aid of the experimental data of Fezer and Bretscher. We give here briefly the course of the reasoning and the results.

As is known\(^1\), the lifetime of a metastable state with respect to the emission of \(\gamma\)-rays \(\tau_\gamma\), the energy difference \(\varepsilon\), and the difference \(l\) of the spin values are connected by the following relation:

\[ \tau_\gamma = 5 \cdot 10^{-21} l!^2 \left(\frac{20}{\varepsilon}\right)^{2l+1} \text{ sec.}, \tag{1} \]

where \(\varepsilon\) is expressed in MeV. The quantity \(\tau_\gamma\) was determined experimentally by Fezer and Bretscher and was found to be \(\tau_\gamma = 17.4\) hours \(= 6.2 \cdot 10^4\) sec. Substituting this value of \(\tau_\gamma\) into formula (1), we obtain one equation with two unknowns (\(\varepsilon\) and \(l\)). With regard to the quantity \(\varepsilon\), on the basis of the data of Table 1 a definite assumption can be made. Namely, from Table 1 it is seen that, for elements of the same type as the element \(UZ—UX_2\), \(\varepsilon = E_1\) varies within very narrow limits, deviating only slightly from the mean value \(\varepsilon = 50\) keV (with the exception of ThC). Therefore it was natural to assume that, for the element \(UZ \to UX_2\), \(\varepsilon\) would have a value lying within the limits of its variation for other elements of this type, i.e. within \(40—60\) keV. Taking at first the mean value \(\varepsilon = 50\) keV, N. Dmitriev, with the aid of formula (1), found that to this value of \(\varepsilon\) there corresponds the value \(l = 4\). The author also showed that this value \(l\) uniquely satisfies not only the mean value, but also any value of \(\varepsilon\) in the interval \(40—60\) keV. Thus it was found in a quite unambiguous manner that the difference of the spin values must be equal to 4 units. In this case we did not have to resort to the aid of Sargent’s curves, as Fezer and Bretscher had to do. The value \(l = 4\) found by N. Dmitriev agrees with the value of this quantity obtained in another way by Fezer and Bretscher (from the scheme of Fig. 2). This speaks in favor of the correctness of this value of \(l\).

Continuing in this way, the author also succeeded in finding the value of the energy difference between the ground level of the nucleus \(\varepsilon\) and the metastable one, which Fezer and Bretscher could not find with the aid of their scheme. To find \(\varepsilon\), the author again proceeded from formula (1), taking in it this time as known \(l\) (\(l=4\)) and \((\tau_\gamma = 6.2 \cdot 10^4\) sec.), and regarding \(\varepsilon\) as the unknown quantity. Solving equation (1) with respect to \(\varepsilon\), N. Dmitriev obtained for \(\varepsilon\) the value \(\varepsilon = 51.2 \text{ keV}\). As we see, the value of \(\varepsilon\) obtained in this way lies very close to the mean value \(\varepsilon = 50 \text{ keV}\) found for nuclei of the same type as the nucleus \(UZ—UX_2\). Thus the author showed that the metastable level lies 51.2 keV above the ground one and that its spin differs from the spin of the latter by 4 units.

In an earlier published article\(^{1}\) the isomerism of indium was described in detail. Recently, new experimental data have appeared on the isomers \(In^{116}\) with periods of 13 sec. and 54 min. Mitchell and Langer\(^{4}\) found that the upper limit of the electron spectrum of the 13-sec. period is 3.1 MeV, and that this period is not accompanied by \(\gamma\)-rays. The 54-min. period gives electrons with an upper limit of the spectrum equal to 1.4 MeV, and the decay of this period is accompanied by \(\gamma\)-rays with energy 1.4 MeV. The ratio of the activities of the two periods turned out to be approximately equal to unity. Let us recall that both of these indium isomers are formed as a result of resonance capture of slow neutrons by the nucleus of stable \(In^{115}\). Mitchell and Langer found that the resonance curves for the formation of the 13-sec. and 54-min. periods coincide with one another. If the resonance curves coincide, then the ratio of the activities of two isomers obtained with neutrons of different energies must be one and the same. It turned out that, within the limits of experimental error, the activity ratio of the isomers \(In^{116}\) remained the same when the slow neutrons were filtered by cadmium. From this the conclusion was drawn that the resonance curves coincide.

On the basis of the experimental data cited above, Mitchell and Langer constructed the level scheme of the isomers \(In^{116}\), shown in Fig. 3. In this scheme the energy in MeV is reckoned from the ground level of the stable nucleus \(Sn^{116}\), arbitrarily taken as the zero level. This nucleus is obtained as a result of the \(\beta\)-decay of both isomers of \(In^{116}\). As is seen from this scheme, the level corresponding to the longer period (54 min.) proves to be metastable. The energy difference between these levels is obtained as equal to 0.3 MeV. The position of the level of \(In^{116}\) corresponding to the capture of a slow neutron is determined on the basis of data on

Fig. 3. Scheme of levels and decay of the isomers of the nucleus \(In^{116}\). The numbers on the left give the spin values of the levels.

binding energy of the neutron: the distance between this level and the zero level is the binding energy of the neutron, which in this part of the periodic table is about \(8.5\) MeV. Thus, in the transition of \(\mathrm{In}^{116}\) to the ground state it must emit \(\gamma\)-rays with a total energy of about \(5.7\) MeV.

The difference in the spin values between the ground level and the metastable level was found on the basis of the following considerations.

The experimental fact that in decay from state \(a\) only electrons of the transition \(a \to d\) are observed, and not \(\gamma\)-rays of the transition \(a \to b\), shows that the probability of emission of \(\gamma\)-rays in the transition \(a \to b\) \((\lambda_\gamma)\) is much smaller than the probability of emission of electrons in the transition \(a \to d\) \((\lambda_\beta)\). From the value of the period (13 sec) one finds the decay constant \(\lambda\), which is the sum

\[ \lambda = \lambda_\beta + \lambda_\gamma = 5.32 \cdot 10^{-2}\ \mathrm{sec}^{-1}. \]

Thus the following relation must hold:

\[ \frac{\lambda_\gamma}{\lambda_\beta+\lambda_\gamma} = \frac{\lambda_\gamma}{5.32 \cdot 10^{-2}} \ll 1 . \tag{2} \]

Putting \(\varepsilon = 0.3\) MeV, one can, with the aid of formula (1), choose such an \(l\) that \(\tau_\gamma\) and, consequently, \(\lambda_\gamma\), satisfy condition (2). This turns out to be the value \(l=5\), which Mitchell and Langer also regard as real.

The assignment to each of the levels in the scheme of Fig. 3 of a definite value of the nuclear spin cannot yet be made in a fully reliable way. However, some considerations on this matter can be stated. First, the nucleus \(\mathrm{In}^{116}\), apparently, in the ground state \(d\) has spin equal to zero, because this nucleus belongs to the type of nuclei containing \(4n\) particles. Further, the points corresponding to both isomers of \(\mathrm{In}^{116}\) lie on the first Sargent curve, for which the change of spin \(l=0\). Hence it follows that the levels \(a\) and \(d\) have identical values, as do also the spins of the levels \(b\) and \(c\). From the equality of the spins of the levels \(a\) and \(d\) it follows that the spin for level \(a\) is equal to zero. Then level \(b\) must have spin equal to 5 units, since the difference is \(l=5\). But then level \(c\) must also have spin equal to 5 units. The resulting spin difference \(l=5\) between the levels \(c\) and \(d\) does not forbid the \(\gamma\)-transition \(c \to d\), owing to the presence of a large energy difference between these levels (1.4 MeV). Indeed, putting \(\varepsilon = 1.4\) MeV and \(l=5\), from formula (1) we obtain \(\tau_\gamma \sim 10\) sec, i.e. a short lifetime is obtained, and, consequently, the transition probability will still have a quite appreciable value. Let us note that, owing to the large difference of spins between the levels \(a\) and \(b\) (metastable and ground), the probabilities of transitions of \(\mathrm{In}^{116}\) from the level corresponding to capture of a slow neutron to the levels \(a\) and \(b\) should be very different. However, experiment shows that the relative activities of the two periods and, consequently, the probabilities of transitions to level \(a\) and to level \(b\) are practically the same. This indicates that, apparently, the transition from the level

to \( \mathrm{In}^{116} \), corresponding to the capture of a slow neutron, to levels \(a\) and \(b\) occurs in cascade fashion (through a series of intermediate levels), accompanied by the emission of several groups of \(\gamma\)-rays, so that in the final result the probabilities of the nucleus reaching levels \(a\) and \(b\) prove to be identical. It would therefore be interesting to carry out an experimental study of the \(\gamma\)-rays arising upon the capture of slow neutrons by \( \mathrm{In}^{115} \) nuclei, with the aim of detecting these groups of \(\gamma\)-rays.

In the first article the question of the process of isomer formation was considered. Since, from the point of view of the modern theory, isomers are two different states of one and the same nucleus, the process of their formation must be one and the same. The identity of the formation process will be reflected in the fact that, for example, if both isomers are formed as a result of resonance capture of slow neutrons (as is the case for Br, In, etc.), then the resonance level at which the neutron is captured will be the same for both isomers. In this case the form of the resonance curves for both isomers must also be identical. The forms of the resonance curves can be compared experimentally in the following way. If the form of the resonance curves is identical, then the ratio of the activities of the isomers must remain unchanged under irradiation with neutrons of different energy. It was precisely in this way that it was found that the resonance curves of the bromine isomers \( \mathrm{Br}^{80} \) and the indium isomers \( \mathrm{In}^{116} \) (see the article above) have the same form and even simply coincide with one another.

Conversely, if we experimentally establish that the ratio of the activities of two radioactive periods of one and the same element, formed as a result of resonance capture of neutrons, remains unchanged under irradiation with neutrons of different energies, then on the basis of what has been said above we may suppose that these periods belong to two isomers of this radioelement. Thus, it turned out that the ratios of the activities of the two periods of radioactive rhodium (periods of 44 sec. and 4.2 min.), formed as a result of resonance capture of slow neutrons, do not change in the case when the slow neutrons are filtered by cadmium and rhodium\(^5\). Such filtering is equivalent to a change in the energy of the neutrons bombarding the rhodium. Therefore, on the basis of the considerations given above, it is supposed that the periods 44 sec. and 4.2 min. belong to two isomers of radioactive rhodium. Thus we see that comparison of the forms of resonance curves represents a new method for detecting isomers\(^1\).

At the present time one can speak of the existence of isomers in at least eleven elements of the periodic system, namely: \( \mathrm{Br}_{35} \), \( \mathrm{Sr}_{38} \), \( \mathrm{Ag}_{47} \), \( \mathrm{In}_{49} \), \( \mathrm{Gd}_{64} \), \( \mathrm{Ib}_{70} \), \( \mathrm{Ir}_{77} \), \( \mathrm{Pt}_{78} \), \( \mathrm{Au}_{79} \),

\(^1\) Quite recently, Soltan and Wertenstein\(^6\) found for \( \mathrm{Br}^{80} \), and Reddeman\(^7\) for rhodium, that the ratio of the activities of the isomers changes noticeably on passing to fast neutrons. This casts doubt on the question of the coincidence of the resonance curves for any energy. However, in order to draw a final conclusion, it is necessary to carry out a further series of experiments in this direction.

\((\mathrm{UZ} — \mathrm{UX}_2)_{91}, \mathrm{U}_{92}\). In this connection it must also be borne in mind that the phenomenon of isomerism has been observed in two isotopes of silver and in two isotopes of indium. As we see, isomers are encountered rather often among elements with atomic number greater than 35, right up to the end of the periodic system. At the same time the list of known isomers is being supplemented very rapidly.

The ratio of the longer period to the shorter one in already known isomers varies within very wide limits, namely from 4 to 760. In six of the elements listed above—\(\mathrm{Sr}_{38}\), \(\mathrm{Ag}_{47}\), \(\mathrm{In}_{48}\), \(\mathrm{Gd}_{64}\), \(\mathrm{Ir}_{77}\), and \((\mathrm{UZ} — \mathrm{UX}_2)\)—this ratio is of the order of several hundreds (from 270 to 760); in three elements (\(\mathrm{Br}_{35}\), \(\mathrm{Yb}_{70}\), and \(\mathrm{Au}_{79}\)) this ratio lies between 10 and 20, and for two (\(\mathrm{Pt}_{78}\) and \(\mathrm{U}_{92}\)) it has a value from 4 to 7.

For all five elements for which there is information on the \(\gamma\)- and \(\beta\)-radiation accompanying the decay of the isomers (\(\mathrm{Br}_{35}\), \(\mathrm{Sr}_{38}\), \(\mathrm{Ag}_{47}\), \(\mathrm{In}_{48}\), and \(\mathrm{UZ} — \mathrm{UX}\)), one can note a common property. It consists in the fact that in all these elements one of the isomers decays without emission of \(\gamma\)-rays, while the other decays with their emission. In the lighter elements (\(\mathrm{Br}_{35}\) and \(\mathrm{Sr}_{38}\)) the \(\gamma\)-rays accompany the decay of the isomer with the short period, whereas in the heavier elements (\(\mathrm{Ag}_{47}\), \(\mathrm{In}_{48}\), and \(\mathrm{UZ} — \mathrm{UX}_2\)) the \(\gamma\)-radiation arises as a result of the decay of the isomer with the long period.

Corresponding to the emission of \(\gamma\)-rays, the upper limit of the \(\beta\)-spectrum for the latter three elements (\(\mathrm{Ag}_{47}\), \(\mathrm{In}^{116}_{48}\), and \(\mathrm{UZ} — \mathrm{UX}_2\)) lies higher for the isomer with the shorter period than for the isomer with the longer one. For \(\mathrm{Br}_{35}\), \(\mathrm{Sr}_{38}\) the opposite picture occurs.

The difference between the upper limits of the \(\beta\)-spectrum of the isomers lies in the range from 0 to 1.7 MeV, but for the majority of isomers studied in this respect it lies close to 1.5 MeV. Thus, for \(\mathrm{Br}^{80}_{35}\) it is close to zero; for \(\mathrm{Sr}^{83}_{38}\), 1.3 MeV; for \(\mathrm{In}^{116}_{48}\), 1.7 MeV; for \(\mathrm{Ag}^{106}_{47}\), 1.3 MeV (positrons) and 0.6 MeV (positrons and electrons).

One may note a certain common feature in all the level schemes given above (\(\mathrm{Ag}^{106}\), \(\mathrm{In}^{116}\), and \(\mathrm{UZ} — \mathrm{UX}_2\); see above). This common feature appears in the fact that the metastable state is the isomer with the shorter period, while the ground state is the isomer with the longer period. At the same time, decay from the metastable state is not accompanied by \(\gamma\)-rays, whereas decay from the ground state is accompanied by \(\gamma\)-rays. Further study of the \(\gamma\)- and \(\beta\)-rays accompanying the decay of isomers should answer the question of whether this holds for all elements possessing isomers.

References

1. N. Dmitriev, Usp. fizich. nauk, 19, 535, 1938.
2. N. Feather and Bretscher, Proc. Roy. Soc., 165, 530, 1938.
3. N. Dmitriev, Dokl. Akad. nauk SSSR, 20, No. 4, 1938.
4. A. Mitchell and M. Langer, Phys. Rev., 53, 505, 1938.
5. B. Pontecorvo, Nature, 141, 785, 1938.
6. A. Soltan and L. Wertenstein, Nature, 141, 76, 1938.
7. H. Reddemann, Naturwiss., 26, 125, 1938.