Metastable Excited States of Stable Nuclei

A. P. Grinberg, Leningrad

The existence of the phenomenon of nuclear isomerism was first established beyond doubt at the beginning of 1937 for the case of radiobromine1. Studies in the field of artificial radioactivity in the following years provided many further examples of this interesting phenomenon, and by the present time several dozen known isomeric pairs can be counted. In all these cases isomerism was observed in unstable isotopes of various elements, and therefore experimentally it manifested itself above all in the fact that a given isotope was found to have two periods of β-decay. One of them is associated with decay from the ground state of the unstable isotope; the other arises from the discharge of excitation of a metastable state of the same isotope, and theory predicts two possible modes, two schemes, of this discharge: it may occur either by a delayed γ-transition of the excited state to the ground state, or by emission of a β-particle by the excited nucleus1.

Already at the very beginning of the investigations concerning nuclear isomerism, Bethe, as well as Pontecorvo, pointed out the circumstance that metastable states can evidently occur not only in β-active nuclei, but also in stable nuclei. In the latter case the existence of a metastable level is more difficult to detect experimentally, since its discharge, probably in the majority of cases, should be accompanied only by soft γ-radiation and soft electron radiation of conversion origin (and also, correspondingly, by the characteristic X-radiation accompanying conversion). On the other hand, the absence of β-rays and hard γ-rays would be a very favorable circumstance for the experimenter, making it possible to study the metastable state under clean conditions.

It is not difficult to foresee the possible ways in which excited nuclear states of the type under consideration may be formed. It may be asserted that such states must be formed as a result of the same processes as excited states of the ordinary type (in which

the discharge of the excitation by means of $\gamma$ emission occurs in a time of the order of $10^{-13}$ sec.). This assertion follows already from the fact that, before obtaining a metastable excited state, it is first necessary to create an ordinary excited state of the nucleus. Indeed, since the transition from the metastable level to the ground level is, by definition, strongly forbidden, transitions of the nucleus from the ground state directly into the metastable state are therefore very improbable; thus, the nucleus must be excited to some higher “activation” level, the discharge of which may partially lead to the formation of a metastable state.

The methods for obtaining excited states of the nucleus are well known. Excitation energy may be imparted to the nucleus by: $\gamma$ quanta, protons, deuterons, neutrons, $\alpha$ particles, and, finally, electrons; in addition, an excited state of the nucleus may be formed after the $\beta$ decay of a neighboring nucleus. Looking somewhat ahead, one may note that all these methods have indeed proved suitable also for producing isomeric states of stable nuclei.

In all, up to the present time the existence of a metastable state has been discovered in the following nine stable nuclei:

\[ \mathrm{Kr}^{83},\ \mathrm{Sr}^{87},\ \mathrm{Ma},\ \mathrm{Ag},\ \mathrm{Cd},\ \mathrm{In}^{113},\ \mathrm{In}^{115},\ \mathrm{Gd}\ \text{and}\ \mathrm{Pb}. \]

The first attempt to prove the existence of an isomeric state of a stable nucleus was made by Bothe and Maier-Leibnitz$^{2}$, who assumed the presence of a metastable level of the $\mathrm{C}^{13}$ nucleus in order to explain the energy features of the reaction $\mathrm{B}^{10}(\alpha,p)\mathrm{C}^{13}$; their experiments did not, however, give decisive confirmation of this point of view.

For the first time, the presence of such a state was established in $\mathrm{In}^{115}$ as a result of investigations carried out by Goldhaber, Hill, and Szilard$^{3}$. It turned out that the activity of indium with a period of about four hours, previously attributed to the isotopes $\mathrm{In}^{112}$ and $\mathrm{In}^{114}$1), must be attributed to $\mathrm{In}^{115*}$—the metastable state of the stable isotope $\mathrm{In}^{115}$.

The authors obtained $\mathrm{In}$ activity (4.1 hours) by irradiating indium with fast neutrons from an $\mathrm{Rn}$-$\alpha$ + Be source, and also from an $\mathrm{Rn}$-$\alpha$ + B source, the spectrum of which does not contain neutrons as hard as the spectrum of the first. The same $\mathrm{In}$ activity (4.1 hours) was obtained by them upon irradiating indium with neutrons from a $d+d$ source, whose energy does not exceed $\sim 2.5$ MeV.

It was further shown that bombardment of indium with photoneutrons from a very strong Ra-$\gamma$ + Be source, possessing energies of several hundred KeV, does not lead to the formation of the four-hour period of indium, although the intensity of other periods, for example $\mathrm{In}$ (54 min.), is obtained as considerable. Thus, the reaction for the formation of $\mathrm{In}$ activity (4.1 hours) has an energy threshold below which it does not proceed, and this threshold lies between 200—

1) Its assignment to an isotope of indium was established by a chemical method.

300 KeV and 2.5 MeV. This shows that the activity In (4.1 hours) is not formed from stable indium isotopes (In\(^{113}\) and In\(^{115}\)) by the reaction \((n, 2n)\), since such a reaction can be produced only by neutrons with an energy of about 8 MeV; consequently, this activity is not associated with the isotope In\(^{112}\) or In\(^{114}\). The carrier of this activity likewise cannot be the isotope In\(^{116}\), since the supposition that the latter is formed from In\(^{115}\), as a result of the capture of a fast neutron, is not consistent with the fact that photoneutrons do not excite this activity. For the same reason, the supposition is also excluded that this activity belongs to the isotope In\(^{114}\), formed from the rare In\(^{113}\) by the reaction \((n, \gamma)\); moreover, in this case one would have to ascribe to the isotope In\(^{113}\) an abnormally large capture cross section for fast neutrons in comparison with neighboring elements.

To explain all the results obtained, Goldhaber proposed that the activity In (4.1 hours) is formed as a result of the reaction In\(^{115}\) \((n, n)\) In\(^{115*}\), i.e., that it belongs to an isomer of the stable nucleus In\(^{115}\). According to Goldhaber, not every collision of a neutron with an indium nucleus leads to the formation of an unstable isotope of this element; some of the neutrons undergo inelastic collisions with indium nuclei, as a result of which an excited state of the stable nucleus is formed, and some of such nuclei, losing a certain fraction of the excitation energy, enter a metastable state.

The existence proposed by Goldhaber of the isomer In\(^{115*}\) with half-life \(T = 4.1\) hours is fully confirmed by subsequent experimental data. From the point of view of his hypothesis, one can, as already indicated, expect to obtain the activity In (4.1 hours) by means of other possible methods of exciting the nucleus. Indeed, it was found\(^{3}\) that this activity of indium is also formed as a result of the β-decay of radioactive Cd\(^{115}\), obtained by the reactions Cd\(^{116}\) \((n, 2n)\) and Cd\(^{114}\) \((n, \gamma)\). This cadmium isotope, decaying with period \(T = 2.5\) days and emitting β-particles, is transformed into a new radioactive nucleus with period \(T = 4.1\) hours, evidently into In\(^{115*}\) and, perhaps, partly also into stable In\(^{115}\). It was shown by the chemical method that the carrier of the latter activity in this chain decay is the isotope of indium.

The isomer In\(^{115*}\) was then obtained by bombarding indium with protons of energy 6.7 MeV\(^{4}\). In this case also, the belonging of the activity obtained, with period \(T = 4.1\) hours, to the isotope of indium was confirmed by the chemical method. Thus, here too a reaction of a new type is established: In\(^{115}\) \((p, p)\) In\(^{115*}\), as a result of which a radioactive isotope of the irradiated element is formed—something that could not occur in the previously known reactions with protons. The authors set up an ingenious control experiment in order to make sure that the activity In (4.1 hours) arises under the action of protons and not of scattered neutrons, a strong source of which is the cyclotron chamber when fast protons are created in it. For this purpose, two sheets of indium foil, separated by a sheet of lead, were exposed in the vacuum receiver of the cyclotron

foil. Protons and scattered neutrons fell on the front sheet of indium foil facing the beam; neutrons fell on the second sheet in the same number, but protons did not. The activity of In (4.1 hours) was detected after irradiation only in the front sheet of indium foil.

The magnitude of the cross section for the reaction of excitation of the isotope In\(^{115}\) by protons, which leads to the formation of In\(^{115*}\), is estimated as \(\sigma \simeq 10^{-29}\ \text{cm}^2\) for protons with an energy of 5.8 MeV. This cross section is considerably smaller than the cross sections of \((p,n)\) processes in this region of the periodic system. For example, for the reactions Cd\((p,n)\)In and Sn\((p,n)\)Sb the cross section is \(\sigma \simeq 10^{-26}\ \text{cm}^2\).

Next one should note the interesting experiments of Pontecorvo and Lazard\(^{5}\), who obtained excitation of indium nuclei by means of hard X rays with a continuous spectrum. These rays were excited by electrons accelerated in a pulsed generator with a peak voltage of 1.85 MV. The irradiated indium gave an activity with a period of \(3.9 \pm 0.5\) hours, i.e., here In\(^{115*}\) is formed.

Similar results were obtained by other investigators, who used for electron acceleration an electrostatic generator with a constant voltage of 1.73 MV\(^{6}\). They also determined the threshold of the reaction In\(^{115}(\gamma,\gamma)\); it corresponds to a voltage on the tube of \(1.35 \pm 0.1\) MV. From the remarks made above it is clear that this quantity characterizes the energy of the activation level of the In\(^{115}\) nucleus, but not the energy of its metastable level.

Having measured the activity of In (4.1 hours) as a function of the energy of the electrons exciting the X rays used to obtain this activity, Waldman and Dr.\(^{7}\) conclude that in In\(^{115}\) there exist two activation levels, with energies \(1.2 \pm 0.1\) MeV and \(1.55 \pm 0.1\) MeV. The magnitude of the cross section for the process In\(^{115}(\gamma,\gamma)\) cannot be specified exactly until there are definite data on which particular X-ray quanta are effective in this process. In any case it must be emphasized that this effect is very delicate and difficult to observe. It is enough to indicate that after irradiation of indium for 30 min at an electron energy of 1.73 MeV and a current of 10 \(\mu\)A, an initial intensity on a Geiger–Müller counter of 45 pulses per 1 min was obtained. On the other hand, however, the use of X rays for creating isomeric states of stable nuclei is the most favorable method from the point of view of the purity of the conditions for observing such an isomer, since the energy of X-ray quanta capable of exciting the nucleus is still insufficient for its disintegration, so that no phenomena of artificial radioactivity complicate the investigation.

The isomer In\(^{115*}\) was also obtained when indium was bombarded with \(\alpha\)-particles of energy 16 MeV\(^{8}\). It should be noted that an attempt to obtain this activity by means of \(\alpha\)-particles of energy 8.5 MeV gave a negative result\(^{4}\).

Recently it was shown that the threshold of the reaction In\(^{115}(\alpha,\alpha)\)In\(^{115*}\) lies near 11 MeV\(^{8b}\). The cross section of this reaction at \(E_\alpha = 16\) MeV is of the order \(3 \cdot 10^{-28}\ \text{cm}^2\).

Finally, bombardment of indium with electrons of energy 1.3 MeV also leads to the formation of In\(^{115*}\) \({}^{9}\). A number of control experiments showed that in this case only part of the activity produced is due to the action of X-rays (arising in the target itself when fast electrons are braked in it), whereas the greater part of the In\(^{115*}\) nuclei is formed as a result of excitation of indium nuclei by electrons. The cross section of this process is estimated by the figures \(\sigma \simeq 10^{-32}—10^{-33}\ \text{cm}^2\).

Of great interest for understanding the nature of nuclear isomerism is the radiation emitted by In\(^{115*}\). Preliminary data on the composition of the radiation of this isotope\({}^{10a}\) indicate that In\(^{115*}\) emits \(\gamma\)-rays consisting of a hard component \(E_\gamma = 320 \pm 50\) KeV and a soft component (probably the \(K\)-radiation of indium), as well as electrons with \(E_m = 550 \pm 50\) KeV. The latter figure, obtained from the absorption curve of electrons in Al, is probably erroneous, since subsequent measurements with a magnetic spectrograph\({}^{10b}\) showed that the electron radiation of In\(^{115*}\) consists of two separate groups with energies \(\sim 308\) and \(332\) KeV, which corresponds to internal-conversion electrons from the \(K\)- and \(L\)-shells of the indium atom at \(E_\gamma = 336 \pm 1\) KeV. The intensity of the \(\gamma\)-rays is comparatively small, so that the internal-conversion coefficient here is apparently very high. It was also found that there is no indication of the presence of a continuous \(\beta\)-spectrum connected with the activity of In (4.1 hours). Thus the supposition that In\(^{115*}\) decays partly by \(\beta\)-emission, transforming into its stable isobar Sn\(^{115}\), is not confirmed.

The second of the two stable isotopes of indium—In\(^{113}\), as it turned out, can also be brought into an excited metastable state\({}^{11}\). When indium is irradiated with protons of energy 7.2 MeV, two activities are observed: one corresponds to In\(^{115*}\) (4.1 hours), the other to Sn\(^{113}\) (\(\sim 100\) days). The radioactive tin decays, emitting the \(K_\alpha\) X-rays of indium (identified by means of differential filters) and two weak groups of soft electrons corresponding to \(K\)- and \(L\)-conversion of \(\gamma\)-rays with energy 85 KeV. After the decay of this tin isotope, an active substance with period \(T = 105 \pm 10\) min. is again obtained, emitting \(\gamma\)-rays with energy 390 KeV and soft electrons in the form of two groups corresponding to \(K\)- and \(L\)-conversion of these \(\gamma\)-rays in the indium atom. This substance was also obtained both in a precipitate of indium separated chemically from an old activated tin sample and by bombardment of cadmium with protons.

The entire body of experimental data is interpreted in the following way. Sn\(^{113}\) captures a \(K\)-electron (with emission of the \(K_\alpha\)-rays of indium) and transforms into In\(^{113}\) in an excited state; the latter passes into the metastable state In\(^{113*}\) by emitting \(\gamma\)-rays with energy \(E_\gamma = 85\) KeV; this metastable state is discharged with period \(T = 105\) min., transforming into In\(^{113}\), while emitting \(\gamma\)-rays with energy \(E_\gamma = 390\) KeV and the corresponding groups of conversion electrons. The coefficient

internal conversion for these γ-rays is estimated by the value \(a = 70 \pm 10\%\). The cross section of the reaction \(\mathrm{In}^{113}(p,n)\mathrm{Sn}^{113} \to \mathrm{In}^{113*}\) is approximately \(2 \cdot 10^{-26}\ \mathrm{cm}^2\).

Below we give the proposed transformation scheme.

Isomerism of the type under consideration is also assumed in masurium\({}^{12}\). When molybdenum \((Z=42)\) is irradiated with deuterons or slow neutrons, a \(\beta\)-active isotope of molybdenum with a period of 67 hours is obtained, after the decay of which an active substance is again obtained—evidently an isotope of masurium \((Z=43)\) (this was also confirmed chemically). It turned out that this isotope of Ma, decaying with a period of 6.6 hours, emits comparatively slow electrons. The electron spectrum, taken with a magnetic spectrograph, proved to consist of two lines with energies of 116 and 133 KeV, which corresponds to the conversion of γ-rays with energy \(E_\gamma = 136\) KeV on the \(K\)- and \(L\)-shells of the Ma\(_{43}\) atom. In addition, with the same period of 6.6 hours γ-rays are emitted (the energy of which was measured approximately, and the result may be considered to coincide with the figure 136 KeV), as well as X-rays, the identification of which by the method of differential filters and with the aid of a bent-crystal spectrograph showed that these are \(K_{\alpha}\)-rays of masurium. All these facts are interpreted in the following way. The original active isotope of molybdenum, emitting \(\beta\)-particles, is transformed partly into stable nuclei of masurium and partly into nuclei of masurium in an excited metastable state, with an excess energy of 136 KeV. This energy is then emitted in the form of γ-radiation, which undergoes internal conversion to a considerable degree (an estimate of the internal conversion coefficient gave a figure of the order of 50%).

Proposed scheme of the transformations of \(\mathrm{Sn}^{113}\) into \(\mathrm{In}^{113}\).

Possibly, however, the case of masurium is an example of isomerism of the usual type, since the possibility is not excluded that the nuclei of masurium in the ground state are unstable and decay with a very long period or with the emission of extremely soft electrons\({}^{12}\).

Next one may note the case of radiocadmium with a period of 50 min., obtained by irradiating cadmium with fast neutrons\({}^{13}\). It gives soft electron radiation. Chemically, it has been shown that this activity belongs to an isotope of cadmium, but it cannot be the result either of an \((n,\gamma)\) reaction—since there is no paraffin effect—or of an \((n,2n)\) reaction, since the activity is too great; moreover, its period does not coincide with the known periods of radiocadmium obtained by these reactions. Thus, one has to

to attribute the observed activity to conversion transitions of a metastable excited state of the cadmium nucleus to the ground state. The cross sections for reactions of nuclear excitation without capture of a fast neutron, i.e., reactions \((n,n)\), especially for heavy elements, have a rather large value \((\sigma \simeq 10^{-24}\ \mathrm{cm}^2)\); apparently, some of the cadmium nuclei excited in this way during the discharge enter the metastable state.

Soft electron radiation of cadmium was also observed by a number of other investigators\(^{14}\).

In addition to the above-mentioned activity with a period of 50 min., cadmium has also been found to have a similar activity with a longer period\(^{15}\). As a result of irradiating silver with protons, an active cadmium isotope is obtained with a period of 6.7 hours, whose radiation consists mainly of soft electrons with \(E \simeq 90\ \mathrm{KeV}\) and of X-rays.

Further study of this radiocadmium showed, however, that the soft electron radiation, and also a significant part of the X-radiation, belongs not to cadmium but to the product of its decay—the silver isotope, which is formed from Cd (6.7 hours) as a result of \(K\)-capture and then decays with a period of 40 sec.\(^{16}\). Thus, one of the two stable isotopes of silver—\(\mathrm{Ag}^{107}\) or \(\mathrm{Ag}^{109}\)—exists in an isomeric form.

Observations analogous to the case of Cd (50 min.) have been made for gadolinium, in which soft electron radiation was found when it was bombarded with slow neutrons\(^{17}\). It is assumed that the gadolinium isotope which strongly absorbs slow neutrons and does not thereby give artificial radioactivity possesses a metastable state which is discharged by internal conversion. It has been shown that the lifetime of this state is less than \(10^{-3}\) sec.\(^{18}\).

Comparatively recently data have been obtained indicating that there is an isomer \(\mathrm{Sr}^{87*}\)\(^{19}\).

When strontium is irradiated with deuterons or protons, an activity with a period \(T = 2.7 \pm 0.2\) hours is obtained, together with others; its carrier is a strontium isotope. In the indicated reactions \(\mathrm{Sr}+d\) and \(\mathrm{Sr}+p\), radioactive yttrium, \(\mathrm{Y}^{87}\) (85 hours), is obtained. As a result of \(K\)-capture it is transformed into \(\mathrm{Sr}^{87*}\), which then passes into \(\mathrm{Sr}^{87}\) with emission of \(\gamma\)-rays, with an energy of 370 KeV, and also of conversion \(K\)- and \(L\)-electrons of the corresponding energy. The coefficient of internal conversion of these \(\gamma\)-rays is approximately equal to 15%.

The isotope Sr (2.7 hours) also emits X-rays, apparently \(\mathrm{Sr}\ K_{\alpha}\); indications of this were obtained by the differential-filter method.

Other paths of excitation of the \(\mathrm{Sr}^{87}\) nucleus are also known. The same activity with a period of 2.7 hours is obtained in the reactions \(\mathrm{Rb}^{87}(p,n)\) \(^{1)}\) and \(\mathrm{Sr}^{87}(n,n)\).

\(^{1)}\) The authors note that in the decay of naturally radioactive \(\mathrm{Rb}^{87}\), metastable \(\mathrm{Sr}^{87*}\) apparently is not formed.

The assignment of the period of Sr (2.7 hours) to the isomer Sr$^{87*}$ has been definitively confirmed by irradiating the pure isotope Sr$^{87}$, obtained from Canadian solutions, with neutrons$^{19}$. At the same time it was shown that the measured strontium is also formed in the reaction Sr$^{86}$ $(n,\gamma)$ Sr$^{87*}$, and that the cross section for this reaction is no smaller than for the reaction Sr$^{87}$ $(n,n)$ Sr$^{87*}$. Finally, very recently the isomers Kr$^{83*}$ and Pb$^{*}$ have been found.

The metastable state of krypton is obtained as a result of the $\beta$-decay of radiobromine Br$^{83}$, which in turn is a product of the $\beta$-decay of selenium$^{20}$. Se$^{83}$ is formed by irradiating selenium with deuterons and slow neutrons. In addition, Br$^{83}$ and, consequently, Kr$^{83*}$ appear among the radioactive products of the fission of uranium and thorium when the latter are irradiated with neutrons. Probably in these cases as well the initial link in the chain of successive $\beta$-decays is Se$^{83}$, but this has not yet been established experimentally.

Kr$^{83*}$ decays with a period of 113 min, emitting very soft conversion electrons with an energy of $\sim 35$ KeV, corresponding to $E_\gamma = 49$ KeV; characteristic krypton X-rays emitted by this isomer have also been detected.

The metastable state of lead was obtained by exciting lead nuclei with hard X-rays, for which electrons with an energy of 1.5 MeV were used$^{21}$. The irradiated lead gives an activity with a period of $1.6 \pm 0.2$ min, its radiation apparently consisting mainly of internal-conversion electrons with an energy of $\sim 200$ KeV.

The minimum electron energy at which the resulting X-rays are still capable of exciting this activity is $0.65 \pm 0.02$ MeV; this, therefore, is the energy of the lowest activation level of the nucleus of this lead isotope.

All the experimental data indicated are collected below in the table (the half-life for In$_{49}^{115}$ is given as $T=4.1$ hours instead of the value in accordance with the latest data$^{23,24}$).

This summary of experimental data makes it possible to consider that the existence of metastable excited levels of stable nuclei has now been reliably established. There is no doubt that, as was the case in the study of isomerism of the ordinary type, this phenomenon will prove to be very widespread among the elements of the periodic system, and many new examples of it will be found.

For all cases of such isomerism known so far, the following general features are characteristic.

1. The metastable state can be obtained either 1) directly by exciting a stable nucleus to some activation level—by means of processes of inelastic scattering of the activating particles or through the action of their electric fields on nuclei [reactions of the type $(n,n)$, $(p,p)$, etc.], or 2) as a result of a nuclear reaction [examples: reactions Rb$^{87}$ $(p,n)$ Sr$^{87*}$, Cd$^{112}$ $(d,n)$ In$^{113*}$, Gd $(n,\gamma)$ Gd$^{*}$], or, finally, 3) as a result of radioactive decay of the parent substance.

A. P. Grinberg

1. The process of de-excitation of a metastable state is entirely analogous to cases of isomerism of the ordinary type: the excess energy is carried away by γ-rays and conversion electrons, and the internal-conversion coefficient reaches high values, in qualitative agreement with the conclusions of the theory of conversion of multipole radiation.

It must be emphasized that although β-emission, as a means of de-excitation of a metastable state, is theoretically just as probable as the emission of γ-rays, up to now not a single reliably established case can be indicated in which β-particles are emitted by an excited metastable nucleus.

REFERENCES

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1. For a review of work on nuclear isomerism, see N. Dmitriev, “Nuclear Isomerism,” Uspekhi Fizicheskikh Nauk, 19, 355, 1938; 21, 60, 1939. ↩↩