A New Algorithm Of The Interaction Boson-Fermion Model And Its Application

As an algebraic model,the interacting boson-fermion model(IBFM)is regarded as one of the standard models for the description of odd-A nuclei.In this thesis,a new algorithm of solv-ing a general IBFM Hamiltonian has been developed in terms of the weak-coupling SU(3)basis and the corresponding computing code is further compiled using the Mathematica software.With the new algorithm,the influences of the three types of boson-fermion interaction includ-ing the monopole term,quadrupole term and exchange term have been individually checked for the three typical collective mode including the spherical vibratior(U(5)),the axially-symmetric rotor(SU(3))and the γ-unstable rotor(O(6)).The results indicate that the different type of interactional term may affect these collective modes in the different way.In particular,it is shown that the new code can run with a good calculation efficiency and high accuracy.The effects of the odd particle on three types of shape phase transitions(SPTs)have been further analyzed in the framework of the IBFM.Specifically,we have compared the critical behaviors of some physical quantities,which include the energy levels,typical energy ratio and B(E2)ration,quadrupole moment and single-particle transfer spectroscopic intensities,in between the even-even and odd-even systems.The results indicate that the SPTs including the spherical to prolate(U(5)-SU(3)),spherical to γ-unstable(U(5)-O(6))and prolate to oblate(SU(3)-SU(3))can appear not only in the even-even systems but also in the odd-even systems,where the crit-ical features of the 1st-order SPT can be even strengthened by the effects of the odd particle.This may in turn justify the previously theoretical analysis of the SPTs using the mean-field method and also suggest some observable signatures of SPTs.In addition,it is shown that there exist relatively large fluctuations in quadrupole moments appearing near the critical point of the U(5)-SU(3)SPT in the odd-even systems,which hints the possibilities of phase coexistence in odd-A nuclei.At last,the comparison between the dynamical structure near the critical point of the U(5)-SU(3)SPT and the low-lying spectrum in 153Eu is made,by which it is prelimi-nary proved that the critical features predicted by the present analysis can indeed be partially reflected in this nucleus.