Shell-model calculations of isovector electromagnetic transitions and Gamow-Teller beta decays in the N

Abstract

Isovector E2 and M1 transitions from isobaric analog states of the N=29 isotones to low-lying states in the N=28 isotones are discussed by making use of the shell model. The ${f}_{7/2}^{n\mathrm{\ensuremath{-}}1}$j and the ${f}_{7/2}^{n}$+${f}_{7/2}^{n\mathrm{\ensuremath{-}}1}$j configurations are assumed for the N=29 and N=28 isotones, respectively, where j denotes one of the ${p}_{3/2}$, ${p}_{1/2}$, and ${f}_{5/2}$ orbits. First, the model space is restricted to j=${p}_{3/2}$ only, and it is extended to include all the ${p}_{3/2}$, ${p}_{1/2}$, and ${f}_{5/2}$ orbits, in order to study stepwise the role of the various wave function components. For the isovector E2 transitions, it is confirmed that the major components of the wave functions play a decisive role for the allowed transitions in the single-particle shell model and the use of the good isospin wave functions is indispensable for the forbidden ones. For the isovector M1 transitions, it is shown that the spin-nonflip ${f}_{7/2}$\ensuremath{\rightarrow}${f}_{7/2}$ transition, which is introduced by the neutron-excited components in the wave functions of the N=28 isotones, plays a very significant role: It gives rise to the important cancellation which is responsible for the strong suppression of the M1 transition strength in comparison with the simple shell-model prediction, and it becomes the leading term in the l- and j-forbidden M1 transitions. Similar discussion holds for the Gamow-Teller beta decays between the levels of the N=28 and N=29 nuclei.