Prediction of band-head spin of triaxial super-deformed bands using the modified VMI model

Abstract

The band-head spin $ (I_{0})$ of triaxial super-deformed (TSD) bands recently available in the rare-earth region are evaluated by using the modified variable moment of inertia (VMI) model. Quantitatively good results of the $ \gamma$ -ray energies and the spins of the TSD bands for Tm, Lu and Hf isotopes are obtained. The ratio of transition energies over spin $ E_{\gamma}/2I$ is used to evaluate the correct spin of the band-head by the VMI equation. The calculated and observed transition energies agree quite well when the correct band-head spin $ (I_{0})$ is obtained. This method provides consistently good spin assignment of TSD bands which could help in designing future experiments for these bands. In the present paper, we have reported the band-head spin for 20 triaxial super-deformed bands known experimentally. Out of 20 bands, the band-head spin is assigned correctly for 16 TSD bands which match with the suggested values and for the rest of the 4 TSD cases the spin predicted is either higher or lower than the experimentally suggested value.