Phase transitions in N = 40, 60 and 90 nuclei

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 new 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 to the experimental data for ${}^{74}$Se, ${}^{102}$Mo and ${}^{150}$Nd, considered to be the best candidates for the critical point nuclei.