Infinitesimal cranking for triaxial angular-momentum-projected configuration-mixing calculation and its application to the gamma vibrational band

TL;DR

This paper introduces an infinitesimal cranking method for triaxial nuclei to improve rotational motion descriptions, applying it to gamma vibrational bands in 164Er, and finds significant spectrum modifications and reasonable agreement with experimental data.

Contribution

The paper develops and applies an infinitesimal cranking approach for triaxial nuclei, enhancing angular-momentum-projected configuration-mixing calculations with novel insights into gamma vibrational bands.

Findings

Cranking about three axes differently affects the energy spectrum.

Inclusion of all three axes modifies the spectrum significantly.

The method reproduces gamma vibrational bands with anharmonicity and good spectral agreement.

Abstract

Inclusion of time-odd components into the wave function is important for reliable description of rotational motion by the angular-momentum-projection method; the cranking procedure with infinitesimal rotational frequency is an efficient way to realize it. In the present work we investigate the effect of this infinitesimal cranking for triaxially deformed nucleus, where there are three independent cranking axes. It is found that the effects of cranking about three axes on the triaxial energy spectrum are quite different and inclusion of all of them considerably modify the resultant spectrum from the one obtained without cranking. Employing the Gogny D1S force as an effective interaction, we apply the method to the calculation of the multiple gamma vibrational bands in $^{164}$Er as a typical example, where the angular-momentum-projected configuration-mixing with respect to the triaxial shape degree of freedom is performed. With this method, both the $K=0$ and $K=4$ two-phonon gamma vibrational bands are obtained with considerable anharmonicity. Reasonably good agreement, though not perfect, is obtained for both the spectrum and transition probabilities with rather small average triaxial deformation $\gamma\approx 9^\circ$ for the ground state rotational band. The relation to the wobbling motion at high-spin states is also briefly discussed.