Ground state phase transition in the Nilsson mean-field plus standard pairing model

Abstract

The ground state phase transition in Nd, Sm and Gd isotopes is investigated by using the Nilsson mean-field plus standard pairing model based on the exact solutions obtained from the extended Heine-Stieltjes correspondence. The results of the model calculations successfully reproduce the critical phenomena observed experimentally in the odd-even mass differences, odd-even differences of two-neutron separation energy, α-decay and double β − -decay energy of these isotopes. Since the odd-even effects are the most important signatures of pairing interactions in nuclei, the model calculations gain microscopic insight into the nature of the ground state phase transition manifested by the standard pairing interaction.

Resolution of the spin paradox in the Nilsson model

“…The use of asymptotic quantum numbers for deformed nuclei is just an example of choosing a basis as close as possible to the dynamics of the physical system under study [32,33]. It should be noted that the Nilsson model is still in wide use, 65 years after its introduction [11], either in the framework of Nilsson mean-field plus pairing calculations [34,35], cranking shell model calculations based on the Nilsson potential with pairing correlations [36], or in relation to approximate SU(3) symmetries [37] like the pseudo-SU(3) symmetry [38][39][40][41][42][43][44][45][46][47], the quasi-SU(3) symmetry [48,49], the proxy-SU(3) symmetry [50][51][52][53][54][55][56][57], and the recovery of SU(3) symmetry at superdeformation [58].…”