The mass systematics of the 2s-1d shell analysed by the average energy method

Abstract

It is well known that the average two-body interaction energy of all states with the same seniority, reduced isospin and isospin in the j n configuration can easily be calculated by a device of group theory, which will be called the average method in this paper. This method is generalized in the direction that it is applicable to an m-body operator ( m is an arbitrary number) and to any type of coupling schemes specified by the group chains as well as the seniority-reduced-isospin scheme. The mass systematics of the 2s-1d shell is analysed by the least mean square method, in terms of the formulae derived by the generalized average energy method for the jj- and the LS-coupling pairing scheme. All of the sd-shell nuclei cannot be systematized by only one coupling scheme. Very good agreement with the experimental values is obtained in the region 14–16 ≦ N, Z ≦ 20 by the jj-coupling pairing scheme in the ( s 1 2 , d 3 2 ) n or ( d 3 2 ) n configuration, while outside of this region, only the even-odd nuclei can be systematized by the simple formula for the LS- or the jj-coupling pairing scheme in the ( d 5 2 s 1 2 d 3 2 ) n configuration. It is conjectured from this fact that the doubly even and even-odd nuclei in the first half of the sd-shell obey the different coupling schemes.