From Current Literature

Stability of Stable Isobars

Stable isobars usually differ in atomic number by two units (for example, $_{22}\mathrm{Ti}^{50}$—$_{24}\mathrm{Cr}^{50}$, $_{44}\mathrm{Ru}^{104}$—$_{46}\mathrm{Pd}^{104}$). There are known, however, three pairs of isobars which differ in nuclear charge by one unit: $_{48}\mathrm{Cd}^{113}$—$_{49}\mathrm{In}^{113}$, $_{49}\mathrm{In}^{115}$—$_{50}\mathrm{Sn}^{115}$, $_{51}\mathrm{Sb}^{123}$—$_{52}\mathrm{Te}^{123}$. Since these isobars occur in nature, their lifetime is at least of the order of the age of the Earth, i.e., $10^9$ years. This fact is remarkable, since on the basis of all data relating to $\beta$-active isotopes one should have expected that, if $\beta$ decay is energetically possible, the period would have to be relatively short—approximately of the order of $10^3$ years.

If in fact $\beta$ radioactivity with a relatively short period were present, then the isobar with the larger nuclear charge would have to transform by electron capture, which would lead to a noticeable decrease in the amount of this isobar and to a relative increase in the abundance of the isobar with the smaller atomic number. Since this is not observed for the indicated pairs of isobars, it remains to assume that in these cases $\beta$ decay is “strongly forbidden” by the selection rules. One may, in particular, suppose that the “forbiddenness” is due to a large difference in the spins of the nuclei of neighboring stable isobars.

To test this supposition in the case of the pair $\mathrm{In}^{115}$—$\mathrm{Sn}^{115}$, a spectroscopic determination of the spin of the $\mathrm{Sn}^{115}$ nucleus was carried out.^1 The spin of the $\mathrm{In}^{115}$ nucleus had been determined precisely earlier^2 and proved to be $9/2$. The author had at his disposal 39 mg of tin enriched in $\mathrm{Sn}^{115}$, which was subjected to investigation of the hyperfine structure of spectral lines. For this purpose a three-prism glass spectrograph with a focal length of 1 m, fastened to a Fabry–Perot etalon, was used. As the light source, a tube with a hollow cathode,^3 modified by the author, was used. The structure of three Sn II lines, $\lambda 5799.3$, $\lambda 6152.8$, $\lambda 6844.3$, and of one Sn I line, $\lambda 5631.9$, was studied. Analysis of the observed splittings in all cases confidently led to a value of the spin of $\mathrm{Sn}^{115}$ equal to $1/2$. Since the spin of the $\mathrm{In}^{115}$ nucleus, as indicated, is $4\,1/2$, the transformation $\mathrm{Sn}^{115}\to\mathrm{In}^{115}$ may be “forbidden” because it would be accompanied by a change of spin by 4. The author notes that in the case of another pair of neighboring stable isobars, $_{48}\mathrm{Cd}^{113}_{1/2}$—$_{49}\mathrm{In}^{113}_{9/2}$, the spin difference is also equal to 4. Finally, as regards the third pair, $\mathrm{Sb}^{123}$—$\mathrm{Te}^{123}$, only the spin of $\mathrm{Sb}^{123}$ is so far known (it is $7/2$).

To justify the hypothesis that the “forbiddenness” of transformations in the indicated pairs of stable isobars is connected with a large change in spin, the author refers to the example of two known pairs for which the difference in spins is large, but the radioactivity has been established. These are the pairs \({}_{19}\mathrm{K}^{40} \to {}_{20}\mathrm{Ca}^{40}\) and \({}_{37}\mathrm{Rb}^{87} \to {}_{38}\mathrm{Sr}^{87}\); in the first case the spin change is \(4 \to 0\), in the second \(3/2 \to 9/2\). However, the half-life periods in both these cases are very large: for \(\mathrm{K}^{40}\) the period is \(4.5 \cdot 10^8\) years, and for \(\mathrm{Rb}^{87}\)—\(6 \cdot 10^{10}\) years.

E. V. Shpolsky

References

1. M. Gurevitch, Phys. Rev. 75, 767 (1949).
2. S. Millman, I. Rabi, T. Zacharias, Phys. Rev. 53, 384 (1939).
3. See S. E. Frisch, Spectroscopic Determination of Nuclear Moments, State Publishing House of Technical-Theoretical Literature, 1948, p. 36 ff.