Possible chiral symmetry in $^{138}$Nd

TL;DR

This paper explores the possibility of chiral symmetry in the nucleus $^{138}$Nd by extending a phenomenological model to include complex interactions, predicting four chiral bands and comparing results with experimental data.

Contribution

The study introduces a modified Generalized Coherent State Model Hamiltonian incorporating many-body interactions and chiral transformations, revealing the existence of four chiral bands in $^{138}$Nd.

Findings

Identification of four chiral bands, two degenerate.

Electromagnetic properties consistent with experimental data.

Evidence supporting chiral symmetry in $^{138}$Nd.

Abstract

The pheomenological Generalized Coherent State Model Hamiltonian is amended with a many body term describing a set of nucleons moving in a shell model mean-field and interacting among themselves with paring, as well as with a particle-core interaction involving a quadrupole-quadrupole and a hexadecapole-hexdecapole force and a spin-spin interaction. The model Hamiltonian is treated in a restricted space consisting of the core projected states associated to the bands ground, $\beta, \gamma,\widetilde{\gamma}, 1^+$ and $\widetilde{1^+}$ and two proton aligned quasiparticles coupled to the states of the ground band. The chirally transformed particle-core states are also included. The Hamiltonian contains two terms which are not invariant to the chiral transformations relating the right handed trihedral $({\bf J_F}, {\bf J_p}, {\bf J_n})$ and the left handed ones $(-{\bf J_F}, {\bf J_p}, {\bf J_n})$, $({\bf J_F}, -{\bf J_p}, {\bf J_n})$, $({\bf J_F}, {\bf J_p}, -{\bf J_n})$ where ${\bf J_F}, {\bf J_p}, {\bf J_n}$ are the angular momenta carried by fermions, proton and neutron bosons, respectively. The energies defined with the particle-core states form four chiral bands, two of them being degenerate. Electromagnetic properties of the chiral bands are investigated. Results are compared with the experimental data on $^{138}$Nd.