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.

介绍了一种求解相互作用玻色子-费米子模型中基于SU (3)耦合基的哈密顿量的方案，通过比较奇数粒子对奇A核形状相变(SPT)的影响奇偶和偶偶系统中某些选定量的临界行为。结果表明，在具有 SPT 特征的奇偶系统中，球面向延长 ( U (5)- SU (3)) SPT 和球面向软 ( U (5)- O (6)) SPT 可能明显发生由激发能、能量比、比、四极矩和单粒子转移光谱强度。特别是，结果表明，奇偶系统中的球面扩展 SPT 甚至可以通过奇粒子的影响得到加强，在临界点附近出现四极变形的大波动。