Energy levels of light nuclei. III Z = 11 to Z = 20

Collective motion in the nuclear shell model III. The calculation of spectra

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

Collective motion in the nuclear shell model IV. Odd-mass nuclei in the sd shell

The U 3 coupling scheme is used as the basis for a survey of the odd nuclei in the sd shell. Energy levels and electromagnetic properties are compared with experiment. In the first half of the shell, A < 28, there is agreement, but in the second half the data suggest some­thing much closer to jj coupling. The need for an effective charge also disappears beyond A = 28.