Microscopic analysis of shape evolution and triaxiality in germanium isotopes

Abstract

Background: The motivation for this study is the experimental evidence for rigid triaxial deformation at low energy in ${}^{76}\mathrm{Ge}$ that was recently observed.Purpose: Quadrupole shapes and low-energy spectra of the isotopes $^{72--82}\mathrm{Ge}$ are analyzed using a theoretical framework based on nuclear density functional theory.Method: The relativistic functional DD-PC1, supplemented by a finite-range pairing force, is used to perform constrained triaxial mean-field calculations of energy surfaces as functions of quadrupole deformation parameters. The corresponding collective Hamiltonian, based on DD-PC1, is employed in the calculation of excitation spectra and transition rates.Results: Model calculations reproduce the empirical trend of collective observables and predict the evolution of shapes from weakly triaxial in $^{74}\mathrm{Ge}$ to $\ensuremath{\gamma}$ soft in $^{78,80}\mathrm{Ge}$. For ${}^{76}\mathrm{Ge}$, in particular, the theoretical excitation spectrum is in good agreement with available data, the experimental ratio $E({2}_{2}^{+})/E({2}_{1}^{+})$ is reproduced, as well as the pattern and amplitude of the staggering in energy between odd- and even-spin states in the $\ensuremath{\gamma}$ band.Conclusions: The mean-field potential of ${}^{76}\mathrm{Ge}$ appears to be $\ensuremath{\gamma}$ soft. Collective correlations drive the nucleus toward triaxiality but do not stabilize a rigid triaxial shape. Both the experimental and theoretical staggering of levels in the $\ensuremath{\gamma}$ band display a pattern consistent with triaxial shapes but the amplitudes are negligible and do not present evidence for rigid triaxiality.