Pseudo-SU(4) Model and Beta Decay of pf-shell Nuclei

The pf-shell (i.e. the 2p 1 2 -2p 3 2 -1f 5 2 shell) is important for a variety of problems in nuclear structure, however, the study of this shell has been hindered by the huge size of the shell model space. In recent years there have been studies by using the Monte-Carlo shell model [1] and that based on the pseudo-SU(4) symmetry model [2]. The original Wigner Supermultiplet SU(4) model[3] is based on the spin-isospin symmetry of the nucleon-nucleon interaction. But the symmetry is broken by the l-s coupling and the breaking increases with the nucleon number. It has been established that the SU(4) symmetry works well in the p-shell [4, 5], but for the ds-shell the SU(4) symmetry is good only for nuclei with N ∼= Z [6, 7]. For nuclei beyond ds-shell the SU(4) symmetry is heavily broken due to large l-s coupling. There have been efforts to restore symmetry for the nuclei which have large l-s coupling by introducing the concept of pseudo-spin and pseudo-orbit[8]. The pseudo-SU(4) model [2] was proposed to deal with the pf-shell by combining the pseudo-spin and the isospin. Since the pseudospin-pseudo-orbit splitting (between 1f 5 2 and 2p 3 2 ) is substantially smaller than the normal spin-orbit splitting (i.e. between 2p 1 2 and 2p 3 2 ), the breaking of the pseudo-SU(4) symmetry is correspondingly smaller. The advantage of the pseudo-SU(4) symmetry is that it keeps all the algebraic features of the SU(4) model while incorporating large l-s coupling. A brief analysis in ref.[2] indicates that the pseudoSU(4) model is promising for describing the pf-shell nuclei. This work intends to check the validity of the pseudoSU(4) model by a comprehensive analysis of the spectra and the beta decays of the Ni-Cu-Zn isotopes with A=58, 59 and 60.