Why does transverse wobbling occur in Lutetium isotopes?

Abstract

The evolutions of deformation and angular momentum orientation with rotational frequency in the \(\pi i_{13/2}\) bands of triaxial strongly deformed \(^{161, 163, 165, 167}{\textrm{Lu}}\) have been researched by the titled axis cranking model plus shell correction method. The potential energy surfaces corresponding to the deformation parameters (\(\varepsilon \), \(\gamma \)) and the angular momentum orientation (\(\theta , \phi \)) are presented for rotational frequency \(\hbar \omega \) varying from 0.0 to 0.6 MeV. It is found from the calculated potential energy surfaces that the nuclear shapes are very stable at a strong triaxial deformation for Lu isotopes and the total angular momentum is favorable to align on the short axis with increasing rotational frequency. The potential energy surfaces provide highly intuitive information that the transverse wobbling motion is favorable in Lu isotopes, and such kind of calculations will be helpful to clarify the debates in wobbling motions.