The Particle-Vibrotor Coupling Model For Deformed Odd-A Nuclei

The nuclear collective model is one of successful models in effective description of medium and heavy mass nuclei.The particle-rotor model based on the triaxial rotor model in adopting deformed shell model approximation for the particle has long been an important model in description of low excitation spectra of odd-A nuclei.To avoid the approximation appearing in the core-particle coupling in the particle-rotor model,the particle-rotor coupling model has been proposed recently.However,there is the level-missing problem in the particle-rotor coupling model due to the ignorance of possible vibration excitations.In order to provide a better description of low excitation properties of odd-A nuclei,it is necessary to take both vibration excitations and the quarupole-quarupole interaction of an even-even core with a single particle into account simultaneously.Based on the vibrotor model,the particle-vibrotor coupling model for deformed odd-A nuclei is established by introducing the quarupole-quarupole coupling of an even-even core with a single particle,of which a Mathematica code for numerical computation is complied.As a primary application,the model is applied in fitting low level energies,reduced E2 transition probabilities,and electric quarupole moments of¹³⁵Ba and¹³¹Xe with a detailed comparison of the model results to those of other models.It is shown that the particle-vibrotor coupling model obviously overcomes the level-missing problem in the particle-rotor coupling model.Except for the reduced E2 transition probabilities of¹³¹Xe,the fitting results of¹³⁵Ba and the low-lying level energies of¹³¹Xe are better than those of other models.Therefore,the particle-vibrotor coupling model is one of suitable models to describe low excitation properties of transitional odd-A nuclei.The comparatively larger deviation occurring in fitting the reduced E2 transition probabil-ities of¹³¹Xe is mainly due to the fact that triaxial deformation is likely to occur in transitional nuclei,while only axial deformation is taken into account in the present model.Anyway,this thesis provides the formalisms and the computation procedure of the particle-vibrotor coupling model,which is necessary for further application of the particle-vibrotor coupling model to well-deformed nuclei in rare-earth and actinide regions,which will be a part of our follow-on work.