Abstract
A scheme to solve the Hamiltonian in the interacting boson-fermion model in terms of the SU(3) coupling basis is introduced, through which the effects of an odd particle on shape phase transitions (SPTs) in odd-A nuclei are examined by comparing the critical behaviors of some selected quantities in odd-even and even-even systems. The results indicate that the spherical to prolate (U(5)-SU(3)) SPT and spherical to -soft (U(5)-O(6)) SPT may clearly occur in the odd-even system with the SPT signatures revealed by various quantities including the excitation energies, energy ratio, ratio, quadrupole moments, and one-particle-transfer spectroscopic intensities. In particular, the results indicate that the spherical to prolate SPT in the odd-even system can even be strengthened by the effects of the odd particle with the large fluctuations of the quadrupole deformations appearing near the critical point.
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