Pairing phase transition in the odd-A nuclei: identification and classification*

Research on the pairing phase transition in the odd- A nucleus is based on a sophisticated blend of the covariant density functional theory and the shell-model-like approach. It has been observed that variations in thermodynamic quantities at the critical temperature do not exclusively align with pairing phase transitions. The presence of an S -shaped heat capacity curve, often interpreted as an indicator of such transitions, does not offer a definitive confirmation. Additional factors, including the blocking effect, can modify the heat capacity curve and impede the transition process. The pairing phase transition in , which occurs approximately from 0.7 to 1.0 MeV, is unequivocally characterized as a first-order transition. Furthermore, the analysis of the impact of varying strengths of pairing correlations on these transitions reveals a nonlinear relationship, thereby adding complexity to the transition dynamics.