Parametrizations of triaxial deformation and E2 transitions of the wobbling band

TL;DR

This paper discusses different parametrizations of triaxial deformation in nuclei, highlighting their differences and impact on E2 transition calculations, and shows that using appropriate deformation parameters improves theoretical predictions.

Contribution

It clarifies the relation between various gamma parametrizations and demonstrates how choosing suitable values enhances the accuracy of wobbling band calculations.

Findings

Different gamma parametrizations can differ by a factor of two for large deformations.

Using consistent triaxial deformation parameters improves B(E2) transition predictions.

Proper parametrization resolves previous underestimations in theoretical models.

Abstract

By the very definition the triaxial deformation parameter $\gamma$ is related to the expectation values of the K=0 and K=2 components of the intrinsic quadrupole tensor operator. On the other hand, using the same symbol "$\gamma$", various different parametrizations of triaxial deformation have been employed, which are suitable for various types of the mean-field potentials. It is pointed out that the values of various "$\gamma$" are quite different for the same actual triaxial deformation, especially for the large deformation; for example, the difference can be almost a factor two for the case of the triaxial superdeformed bands recently observed in the Hf and Lu nuclei. In our previous work, we have studied the wobbling band in Lu nuclei by using the microscopic framework of the cranked Nilsson mean-field and the random phase approximation, where the most serious problem is that the calculated B(E2) value is about factor two smaller. It is shown that the origin of this underestimation can be mainly attributed to the small triaxial deformation; if is used the same triaxial deformation as in the analysis of the particle-rotor model, the calculated B(E2) increases and gives correct magnitude compared with the experimental data.