Systematic Cranked Shell Model Calculations for $^{87, 89, 91}$Br

Abstract

A systematic investigation of the odd-mass neutron-rich bromine isotopes $^{87-91}$Br has been carried out within the configuration-constrained cranked shell model (CSM) framework. The calculated kinematic moments of inertia and angular-momentum alignments reproduce the experimental trends with excellent agreement for the proposed quasiparticle configurations, thereby supporting the assigned band structures. The total Routhian surface calculations reveal pronounced $γ$-softness in $^{87}$Br, shape coexistence in $^{89-93}$Br, and a gradual prolate-to-oblate transition approaching $N=56$. These results demonstrate that the CSM provides a reliable description of rotational behavior and shape evolution in this mass region, achieving a better level of accuracy, while offering a transparent interpretation of quasiparticle configurations and shape-driving effects.

Figures (6)

• Figure 1: Total Routhian surface plots at four different rotational frequencies, $\omega$ = 0.0, 0.2, 0.4 & 0.6 (MeV/$\hbar$), in vacuum configuration for $^{85,87,89,91,93}$Br isotopes, respectively. The red-filled circle represents deformation at TRS minimum, and the contour line spacing is $0.2$ MeV.
• Figure 2: Neutron and proton single-particle levels in $^{87}$Br as a function of the quadrupole deformation $\beta_2$ calculated using the Woods-Saxon potential. Positive (negative) parity lines are represented with solid (dashed) lines. The Fermi level is marked with filled circles. The subshells are indicated for each orbital, together with important asymptotic Nilsson quantum numbers.
• Figure 3: Single-particle Routhians (Left) and quasiparticle Routhians (Right) for neutrons $(\nu)$ and protons $(\pi)$ close to the Fermi level of $^{87}$Br as a function of rotational frequency for $\beta_2 =0.1668$. Parity and signature $(\pi,\alpha)$ are represented by solid $(+,+1/2)$, dotted $(+,-1/2)$, dot-dash $(-,+1/2)$ and dashed $(-,-1/2)$ lines.
• Figure 4: Aligned angular momentum $\langle J_x \rangle$ and kinematic moment of inertia $\mathcal{J}^{(1)}$ for Band 1 in $^{87,89,91}\mathrm{Br}$, calculated using the CSM (solid line). The dashed and dash--dotted lines denote the proton and neutron contributions, respectively. Experimental data are shown by blue-filled circles.
• Figure 5: A comparison of the experimentally deduced positive parity band 1 in $^{87,89,91}$Br isotopes J.Dudouet.