In this paper we focus on three mass regions where first-order phase transitions occur, namely, for $N=40$, 60, and 90. We investigate four isotopic chains (Se, Zr, Mo, and Nd) in the framework of microscopic Skyrme-Hartree-Fock$+$Bardeen-Cooper-Schrieffer calculations for 15 different parametrizations. The microscopic calculations show the typical behavior expected for first-order phase transitions. To find the best candidate for the critical point phase transition we propose different microscopic position and occupation indices calculated for positive-parity and negative-parity proton and neutron single-quasiparticle states around the Fermi level. The microscopic calculations are completed by macroscopic calculations within the algebraic collective model (ACM), and compared with the experimental data for ${}^{74}\mathrm{Se}$, ${}^{102}\mathrm{Mo}$, and ${}^{150}\mathrm{Nd}$, considered to be the best candidates for the critical-point nuclei.

• Received 20 April 2024
• Accepted 9 July 2024

DOI:https://doi.org/10.1103/PhysRevC.110.024317