Particle - Core Coupling around 68

The single-particle spectrum of nuclei with large neutron excess is predicted by some approaches [1] to become similar to that of a harmonic oscillator with a spin-orbit term (no additional~l2 term) and thus reinforce some of the harmonic oscillator magic numbers. This is the case of N=40, and indeed experimental results accumulating in the past few years [2,3] indicate the presence of a subshell closure in Ni. Although Ni is only modestly far from stability (the last stable Ni isotope has A=64), understanding the properties of the nuclei around Ni is one important step towards understanding the structure of the more exotic Ni. In addition, the existence of a good subshell closure at N=40 is expected to have a significant impact on the properties of the nuclei in the region. Furthermore, a good subshell closure at N=40 in Ni might develop into a real shell closure for nuclei with smaller proton numbers and larger neutron excess. Pursuing the evolution of the N=40 subshell gap in the very neutron-rich nuclei towards Ca, while being a very difficult experimental task, would give rich information about the evolution of the nuclear spin-orbit term for large neutron excess. We studied the influence of the subshell closure at N=40 on nuclei adjacent to Ni in the framework of the Particle-Core Coupling Model (PCM). A detailed description of the model can be found in Refs. [4,5]; calculations on nuclei in the region of Ni have been reported in Ref. [6]. The aim of the particle-core coupling study is to (i) investigate ifNi is a good core for the adjacent nuclei; and (ii) extract information about the neutron and proton single-particle energies around N=40, Z=28 and their behavior with increasing neutron excess. The model space for the odd-mass Ni and Cu nuclei aroundNi, described herein, consists of single-hole or -particle states coupled to collective quadrupole and octupole vibrational excitations of the underlying even-even core. It is assumed that the core does not change whether a proton or a neutron particle or hole is coupled to it. In addition to the ‘‘natural’’ configuration space consisting of collective excitations in Ni coupled to single-hole or single-particle excitations, an additional subspace has been included, which accounts for neutron or proton excitations of the type two-particle one-hole (2p-1h) or one-particle two-hole (1p-2h). This latter part of the model space can be approximated by hole or particle excitations coupled to the collective excitations of Ni for the odd-neutron Ni isotopes, or of the corresponding Zn isotopes for the odd-proton Cu isotopes.