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

Abstract

Abstract 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 U2-. 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 24Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U3 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.