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

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.

Comments: 12 pages(preprint), 2 figures, 1 table