The study of energy bands in nucleus 102Zr

Abstract

Theoretical calculations of the energy bands in nucleus 102 Zr are carried out by taking the projected shell model approach, which has reproduced the experimental data. In addition, by analyzing band-head energies, corresponding configurations of yrast band, quasi-particle rotational bands and side bands, we have worked out the microscopic formation mechanism of axially symmetric deformation bands: The low-excitation deformation bands are attributed to the high-j intruder states 1g 7/2 and 1h 11/2 in the N=4, 5 shells; the quasi-particles in the orbit v5/2- [532], v3/2+ [411] and v3/2+ [413] in particular play an important role in the deformation of 102 Zr.projected shell model, yrast band, quasi-particle rotational band, side bandThe nucleus 102 Zr (Z=40, N=62) is located in the A≈100 neutron-rich region, where the nuclei lie far from the β stability and where the valence nucleons begin to fill the g 9/2 proton and h 11/2 neutron orbitals. This region exhibits many important features, such as the shell-closure effects of Z=40, N=56 spherical subshells and a sudden onset of large ground-state deformation for N≥60.By the empirical measurement of prompt γ-rays of spontaneous fission or induced fission of heavy nuclei, much information about energy spectra of this nucleus has been obtained. For 102 Zr, the transition from the 2 + state to the ground state was first identified by Cheifetz et al. [1]. In β-decay work, two 0 2 + and 2 2 + states were also observed [2]. Subsequently, by Durell and Hamilton et al., the ground band [3] was extended up to 12 + and many new twoquasi-particle bands were identified [4] with the pair strength of 102 Zr nucleus calculated, G Q =0.19 MeV. In 2004, more high spin states were observed [5]. For example, the deformed ground band was extended up to 20 + . Led by Hamilton et al., research groups for the first time have identified a two-quasi-particle band with a band head energy of 2926.4 keV through measuring prompt γ-rays in the spontaneous fission of 252 Cf with the Gammasphere array at American Lawrence Berkeley National Laboratory [6] and identified also are two rotational collective bands, with band head energies of 1386.3 and 1652.7 keV.Theoretically, Federman and Pittel et al. made the first calculations that explained onset of large deformation at N=60 in Zr isotope. They also gave evidence that the neutron-proton interaction between the valence particles in the orbits (1g 9/2 ) π and (1g 7/2 ) v might be responsible for the large deformation [7][8][9][10][11], while the neutron-neutron or proton-proton effective interactions were mostly of spherifying nature [12][13][14][15][16][17]. Furthermore, the Zr isotope was calculated based on relativistic mean field theory [18-20] and on the phenomenological quadrupole-quadrupole plus pairing model [21][22][23] of two body interaction respectively. Both the theory and the mode assigned the large deformation in

A short revisit to Kuo-Brown effective interactions

“…A few examples could be found in refs. [20][21][22][23][24][25]. The monopole Hamiltonian is specified by the angular-momentum averaged two-body matrix elements, i.e., monopole matrix elements [18] …”