Ground State Shape (Phase) Crossover In Er And Yb Isotopes

Abstract:In this thesis,ground-state shape?phase?crossover in Er and Yb isotopes is mani-fested in the axially deformed Nilsson mean-field plus extended pairing model.It is found that variation of the pairing interaction strengthand the deformation parameter ?₂ in the model alters the energy ratio R_02⁺/21⁺ and the ground-state occupation probabilities of valence nucleon pairs with different angular momenta.Whenis small,the Nilsson mean-field is dominan-t,the system is in the axially deformed?rotational?shape?phase?with R_02⁺/21⁺?35.With the increasing of,R_02⁺/21⁺ changes non-monotonically for all the given ?₂ values considered.Furthermore,whenis sufficiently large,the system is dominated by the pairing interaction with R_02⁺/21⁺?2 corresponding to the spherical?vibrational??shape?phase.It is observed that a critical region of the shape?phase?evolution exists as shown in the energy ratio R_02⁺/21⁺ and the ground-state occupation probabilities of nucleon pairs with different angular momen-ta for any value of the quadrupole deformation parameter,which is justified from the analysis of the ground-state information entropy of the model.The energy ratio R_02⁺/21⁺,the odd-even mass differences,the ground-state occupation probabilities of valence nucleon pairs with dif-ferent angular momenta,are calculated under the present model,reproduce the shape?phase?crossover behaviors of these quantities in^155-163Er and^157-165Yb isotopes.It is shown from these quantities as functions of the quadrupole deformation parameter ?₂ and the overall pair-ing interaction strengththat the ground-state shape?phase?crossover is mainly driven by the pairing interaction and less affected by the quadrupole deformation,which thus provides a possible origin of the ground-state shape?phase?axially of these isotopes.