Large scale shell model calculation for collectivity in nuclei beyond 78Ni

TL;DR

This work develops a tailored effective interaction for nuclei above the doubly magic $^{78}$Ni and applies large-scale shell-model calculations to map single-particle evolution in $N=51$ isotones and collectivity in $N=52$ isotones. Using a valence space of protons in $\\{1p_{3/2},1p_{1/2},0f_{5/2},0g_{9/2}\\}$ and neutrons in $\\{1d_{3/2},1d_{5/2},2s_{1/2},0g_{7/2},0h_{11/2}\\}$, the effective interaction $V_{\rm eff}$ is derived from CD-Bonn via $V_{low-k}$ with $\Lambda = 2.6$ fm$^{-1}$, including up to third-order $\hat{Q}$-box components and folded-diagram summation, with monopole tweaks and a $0.7e$ polarization charge. The calculations reproduce the $N=51$ and $N=52$ trends in excitation energies $E(2_1^+)$ and $B(E2; 2^+ \to 0^+)$, notably predicting the maximum collectivity at $^{84}$Ge and revealing pseudo-SU(3) structure in proton configurations. The study also explores low-lying spectra and band structures in neutron-rich Ge and Se isotopes, indicating $\gamma$-softness and potential triaxial deformation, and provides predictions for unobserved states to guide future experiments on shell evolution and nuclear collectivity near $^{78}$Ni.

Abstract

A shell model effective interaction for nuclei beyond the double magic nucleus 78Ni is constructed. First, the single-particle evolutions for valence neutrons above the double magic 78Ni are systematically explored in the N = 51 isotones using the large scale shell model (LSSM) calculations based on the constructed effective interaction. Subsequently, we calculate the excitation energies of 2+1 states and reduced electric quadrupole transition probabilities B(E2; 2+ to 0+) for N = 52 isotones. Notably, our calculation gives the result most consistent with the trend of the B(E2) values observed in the N = 52 isotones, especially for 84Ge, a result that poses a serious challenge to the theoretical model. Furthermore, the collectivity in N = 52 isotones, as well as the roles of pseudo-SU(3) symmetry, are investigated via the calculated primary configurations of their ground states and the first excited states. Additionally, the low-lying structures and band characteristics of neutron-rich Ge and Se isotopes are investigated. The ground state and the γ-soft band are constructed in our LSSM calculations, aligning well with available experimental evidence. Finally, we present the calculated evolutions of low-lying states in neutron-rich Ge and Se isotopes. The predictions for the as-yet unobserved low-lying states in these nuclei provide a comprehensive dataset to guide and inform future experimental efforts to decipher the evolution of shell structures and collectivity.

Figures (4)

• Figure 1: Calculated excitation energy of $1/2^+$ and $3/2^+$ states for the light $N=51$ odd isotones from $Z=30$ to 40 using LSSM, along with available experimental data ensdf.
• Figure 2: Calculated excitation energy of $2_1^+$ and $B(E2;2^+\to0^+)$ systematics of the $N = 52$ even-even isotones from $Z = 30$ to $Z = 38$ with LSSM, along with experimental data PhysRevLett.121.192502 and theoretical calculations presented in Ref. PhysRevLett.121.192502.
• Figure 3: Excitation energies and reduced transition rates $B(E2)$ (in ${\rm e^2fm^4}$) for Ge and Se isotopes, calculated in the shell model framework, along with the experimental data for comparison ensdf.
• Figure 4: Comparison of experimental and theoretical excitation energy evolution for isotopic chains of Ge ($Z = 32$) and Se ($Z = 34$).