Moment of inertia of even–even proton-rich nuclei using a particle-number conserving approach in the isovector neutron–proton pairing case

Abstract

An expression of the particle-number projected nuclear moment of inertia (MOI) has been established in the neutron–proton (np) isovector pairing case within the cranking model. It generalizes the one obtained in the like-particles pairing case. The formalism has been, as a first step, applied to the picket-fence model. As a second step, it has been applied to deformed even–even nuclei such as [Formula: see text] and of which the experimentally deduced values of the pairing gap parameters [Formula: see text], [Formula: see text], are known. The single-particle energies and eigenstates used are those of a deformed Woods–Saxon mean-field. It was shown, in both models, that the np pairing effect and the projection one are non-negligible. In realistic cases, it also appears that the np pairing effect strongly depends on [Formula: see text], whereas the projection effect is practically independent from the same quantity.

Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

“…However, it is well known that the BCS approach breaks particle-number conservation symmetry [29,30], either in the case of pairing between like-particles, or in the np pairing case. The particle-number fluctuations may affect predictions dealing with several observables, such as the moment of inertia [31][32][33], the two-neutron [34] or two-proton [35] separation energies, the nuclear radii [36,37], the electromagnetic moments [38,39], the pairing energy [40][41][42] or the beta transition probabilities [43,44].…”

Number-projected nuclear moment of inertia in the isovector pairing case within the Richardson model

“…It is however given in Ref. [26]. As it was the case for the ground-state, the projection effect on the two-qp state energy is an additional term.…”

“…(24) does generalize the conventional BCS one. Indeed, when Gnp=0 (and hence np=0), one has: u 0 u np 2 n 1 np 2 n 1 2 n np 2 n 2 2 n np 2 n 2 np 2 p 2 np 2 p 2 2 p np 2 p 1 2 p np 2 p 1 (26) where v t and u t (t=n,p) respectively represent the occupation and inoccupation probability amplitudes in the conventional BCS theory.…”

Isovector pairing and particle-number fluctuation effects on the spectroscopic factors of one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei

“…The particlenumber fluctuations affect several nuclear observables, when one takes into account either the like-particle pairing or the np pairing. Among others, let us cite the energy of the system [46][47][48][49][50][51], the two-particle separation energy [52,53], the moment of inertia [54][55][56][57], the nuclear radii [58,59], the electric moments [60,61] and statistical quantities [62]. The restoration of the particle-number is therefore essential for an accurate determination of the nuclear wave-function.…”