  The investigation into the pairing phase transition in the odd-A nucleus
161Dy utilizes a sophisticated blend of covariant density functional theory and
the shell-model-like approach. It is discerned 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 indication 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 161Dy, occurring around 0.7 to 1.0 MeV, is unequivocally
characterized as a first-order transition. Furthermore, an exploration into the
impact of varying strengths of pairing correlations on these transitions
reveals a nonlinear relationship, adding complexity to the transition dynamics.
