Description of $^{178}$Hf$^{m2}$ in the constrained relativistic mean field theory

TL;DR

This paper uses the relativistic mean field theory to analyze the properties and excitation energy of the isomeric state $^{178}$Hf$^{m2}$, achieving results close to experimental data by including time-odd fields.

Contribution

It introduces a self-consistent RMF approach with time-odd fields to accurately predict the excitation energy of $^{178}$Hf$^{m2}$, improving upon previous models.

Findings

RMF calculations reproduce ground state properties of $^{178}$Hf.

Calculated excitation energy of $^{178}$Hf$^{m2}$ is 2.801 MeV, close to experimental 2.446 MeV.

Time-odd fields are crucial for accurate excitation energy predictions.

Abstract

The properties of the ground state of $^{178}$Hf and the isomeric state $^{178}$Hf$^{m2}$ are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of $^{178}$Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with $K^\pi=16^+$ is found to be $\nu(7/2^-[514])^{-1}(9/2^+[624])^{1}$ $\pi(7/2^+[404])^{-1}(9/2^-[514])^{1}$. Its excitation energy calculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the $^{178}$Hf$^{m2}$ experimental excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.