Collectivity and isomers in the Pb isotopes

TL;DR

Problem: The study investigates collectivity and isomerism in Pb isotopes near the $N=126$ shell closure. Approach: It uses shell-model calculations with the $KHH7B$ effective interaction in a 14-orbital space, implemented in KSHELL, for $^{196-206}$Pb, to compute energy spectra, $B(E2)$ values, magnetic and quadrupole moments, and isomer lifetimes. Key findings: Yrast $0^+$ and $2^+$ states are well reproduced across $^{196-206}$Pb; many negative-parity levels are compressed and several low-lying isomers emerge with maximum seniority $v=2$, with deformation trends shown by $eta_2$ from $Q(2_1^+)$. Significance: The results validate the KHH7B interaction in this region, provide detailed predictions to guide upcoming experiments, and indicate the necessity of extended model spaces across $Z=82$ and $N=126$ to improve predictive power near shell closures.

Abstract

In the present work, we aim to study collectivity in the Pb isotopes in the framework of nuclear shell model. We have performed shell-model calculations using KHH7B effective interaction. The model space of KHH7B interaction consists of 14 orbitals. We have reported results for even-even $^{196-206}$Pb isotopes for spectra and electromagnetic properties. The shell model results for isomeric states are also reported. Our results will be useful to compare upcoming experimental data.

Figures (5)

• Figure 1: Comparison between experimentalnndc and calculated energy levels for $^{196-200}$Pb isotopes.
• Figure 2: Comparison between experimentalnndc and calculated energy levels for $^{202-206}$Pb isotopes.
• Figure 3: Level-energy systematics of the neutron-deficient Pb isotopes with $A=196-206$.
• Figure 4: Comparison between calculated and experimentalnndcnudat B(E2;0$^+_1$$\rightarrow$ 2$^+_1$) for even-even $^{186-206}$Pb in the left panel. Calculated and experimental $E(2_1^+$) energy is also shown in the right panel.
• Figure 5: Shell-model results for deformation($\beta_2$).