Charge, proton and neutron systems and matter radii of N ≈ Z odd-mass nuclei using a particle-number projection approach in the T = 1 pairing case

Abstract

The charge radii, the proton and neutron systems radii, as well as the matter radii of [Formula: see text] odd-mass nuclei are studied using a particle-number projection approach in the neutron–proton (np) isovector ([Formula: see text]) pairing case. Expressions of the proton and neutron systems quadratic radii are first established within a projection after variation method (i.e., of PBCS type) using a recently proposed wave function for odd-mass nuclei. It is checked that they reduce to the ones obtained in the like-particles pairing case. The new expressions are then used to study numerically the various radii of nuclei such as [Formula: see text] and [Formula: see text], using the single-particle energies of a Woods–Saxon mean-field. It is shown that the few available experimental data are satisfactorily described by means of the present work approach. Furthermore, it appears that the np pairing and projection effects on the various radii are small on average in the case of odd-mass nuclei. However, the relative discrepancies with the values when only the pairing between like-particles is taken into account or the values obtained before the projection may reach up to 3% or 4% for some nuclei.

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].…”

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.…”