THE 96-PROTON SUBSHELL IN HEAVY NUCLEI

In the nuclear shell model, in addition to the principal shells corresponding to the so-called “magic numbers” of protons or neutrons, more sharply expressed “subshells,” consisting of a “semimagic” number of nucleons, have recently also been observed. Papers \(^{1,2,3}\) indicate the existence of subshells of 34 and 70 neutrons and 38 and 58 protons. For heavy nuclei, a double shell of 82 protons and 126 neutrons is generally known. In addition, in paper \(^{4}\), from an analysis of alpha-decay energies, indications were obtained for the existence of subshells of 88 and 92 protons. In the paper reviewed \(^{5}\), the existence of a “subshell” of 96 protons is revealed. From the systematics of alpha radioactivity \(^{6}\) it follows that the effective nuclear radii, calculated from the theory of alpha decay, take the smallest values for nuclei with a filled shell. The author of paper \(^{5}\) calculated, from the most recent measurements of alpha-particle energies, the effective radii \(r\) of even-even nuclei with atomic numbers \(Z\) from 84 to 98. From the formula

\[ r = r_0 A^{1/3}, \]

where \(A\) is the mass number, the constant \(r_0\), which depends little on \(Z\) in the region of heavy nuclei, was calculated. The results of the calculation are presented in a figure, from which it is seen that at \(Z = 96\) there is a minimum, indicating the existence of a shell of 96 protons. The figure shows no indications of the existence of subshells of 88 or 92 protons, which are discussed in \(^{4}\).

The shell of 82 protons is caused by the filling of the \(h^{11/2}\) level. It may be assumed that a new shell begins to be formed with \(\mathrm{Bi}^{209}\) through the filling of the \(h^{9/2}\) level, since the spin of \(\mathrm{Bi}^{209}\) is \(9/2\). However, as the number of protons increases, the \(h^{9/2}\) level rises upward and in its place the \(f^{7/2}\) or \(f^{5/2}\) level will be filled. In connection with this, one may expect the filling of a subshell at 90 and at 96 protons, but the plateau at \(Z = 90\) is barely noticeable in the figure. Additional evidence for the filling of the subshell of 96 protons may also be the increase in the half-lives of alpha decay for the isotopes of berkelium \((Z = 97)\); an analogous slowing of alpha decay is also observed for the isotopes of Bi \((Z = 83)\) as a consequence of the filling of the shell of 82 protons.

The presence of spins \(5/2\) in the nuclei \(\mathrm{Np}^{237}\) and \(\mathrm{Am}^{241}\) confirms the existence of the \(f^{5/2}\) level, although the spin \(3/2\) found in the nuclei \(\mathrm{Ac}^{227}\) and \(\mathrm{Pa}^{231}\) contradicts such a level scheme.

The paper also gives particular reports of new, more precise spectrometric measurements of alpha-particle energies: \(\mathrm{Ra}^{222}\)—6.565 MeV, \(\mathrm{Th}^{226}\)—6.342 MeV, \(\mathrm{Th}^{232}\)—3.998 MeV, \(\mathrm{U}^{230}\)—5.886 MeV, \(\mathrm{U}^{232}\)—5.318 MeV, and \(\mathrm{U}^{238}\)—4.187 MeV. These experimental data were used to calculate the values of \(r_0\) presented in the figure.

V. K.

CITED LITERATURE

1. H. Duckworth and R. Preston, Phys. Rev. 82, 468 (1951).
2. G. Dube and S. Iha, Phys. Rev. 85, 1042 (1952).
3. V. A. Kravtsov, Izvestiya AN SSSR, ser. fiz. 18, 5 (1954).
4. S. Sengupta, Phys. Rev. 87, 1136 (1952).
5. G. Seaborg, Phys. Rev. 92, 1074 (1953).
6. I. Perlman, A. Ghiorso, and G. Seaborg, UFN 47, 220 (1950).