Evidence of U(12/10) supersymmetry in the 1f2p shell

Abstract

The graded Lie group U(12/10) is proposed to deal with distinguishable proton and neutron bosons as opposed to the group U(6/10), which does not make the distinction. The group chain and the nuclear Hamiltonian for the excitation spectrum in the vibrational limit are given and the implications of the existence of the higher symmetry are discussed. The excitation spectra of 64,65Zn and 68,69Ge are analysed in terms of the UB+F(5)*SUF(2) limit of the group U(6/10). It is also found that the nuclei approximately obey U(12/10) symmetry. A simple symmetry-breaking calculation is performed to investigate the possible reasons for the departure from the U(12/10) symmetry.