Partial-wave contributions to pairing in nuclei

Abstract

We present a detailed study of partial-wave contributions of nuclear forces to pairing in nuclei. For T=1, J=0 pairing, partial waves beyond the standard 1S0 channel play an interesting role for the pair formation in nuclei. The additional contributions are dominated by the repulsive 3P1 partial wave. Their effects, and generally spin-triplet nuclear forces between paired nucleons, are influenced by the interplay of spin-orbit partners. We explore the impact of including partial waves beyond the 1S0 channel on neutron-neutron pairing gaps in semi-magic isotopic chains. In addition, we show that nuclear forces favor T=1, J=0 over T=0, J=1 pairing, except in low-j orbitals. This is in contrast to the free-space motivation that suggests the formation of deuteron-like T=0 pairs in N=Z nuclei. The suppression of T=0 pairing is because the 3S1 strength is distributed on spin-orbit partners and because of the effects of the repulsive 1P1 channel and of D waves.Comment: 10 pages, 16 figure

Overview of neutron–proton pairing

“…Only the contour is shown that separates the isoscalar condensate from isoscalar pair vibration regime. The two boundaries delineate four phases: weak pairing, only T = 0 and T = 1 pair vibrations exist (ISPV+IVPV), T = 1 con- Figure 10: Energies of the lowest states for N = 4, 6, 8 in a single j shell as a function of the relative mixture parameter x of the isovector and isoscalar parts in the interaction (15). This is the equivalent to Fig.…”

“…The anomalously large ratio for the p 2 1/2 -p 2 1/2 matrix element beyond S waves is due to the small T = 1, J = 0 pairing matrix element in this case. From [15].…”

A new statistical method for the structure of the inner crust of neutron stars

“…These values have been tuned in Ref. [65] to reproduce the density dependence of the 1 S 0 [66] pairing gap in pure neutron matter with a realistic interaction at the BCS level. To avoid the ultraviolet divergency [67], we use a sharp cut-off of E cut = 60 MeV in the quasi-particle space.…”

Superfluid properties of the inner crust of neutron stars

“…Here we use the standard notation 2S+1 J rel , with the Cooper-pair total spin S, the relative orbital angular momentum and the relative total angular momentum J rel = + S. Higher partial waves can also contribute to the superfluidity in finite nuclei, with P waves giving a ≈15% quenching of the S-wave pairing gaps [7]. This contribution could be even smaller in the inner crust of neutron stars, where the states close to the Fermi surface are in the continuum and the center of mass of the Cooper pairs plays a less important role.…”

“…Recently, independent studies have been carried out by different groups [6][7][8][9] to improve the connection of EDF theories to basic nuclear forces. Particular attention has been paid to the pairing correlations that are responsible for the superfluid properties of the nucleus.…”