Elliott's generating procedure is used to derive wave functions for nuclei in which the level is filling with neutrons and protons. It is assumed that the low-lying states of these nuclei have well-defined isotopic spin and that the configuration is pure. This representation, which mixes states of different seniority, is used to calculate beta-decay transition probabilities, and magnetic-dipole and electric-quadrupole properties of nuclei. The results are in much better agreement with experiment than are those obtained by use of a seniority classification for the nuclear states. In particular, there is a selection rule which explains the anomalously long half-life for the → and → beta decays. The theoretical electric-quadrupole matrix elements are too small by a factor of 3-5, and the theoretical lifetimes too short by approximately a factor of 10. For three particles in the level () or three neutrons in the state, the eigenfunctions given by the generator formalism are found to be almost identical with those derived from a conventional shell-model calculation.
- Received 6 July 1961
- Published in the issue dated December 1961
© 1961 The American Physical Society