Attractive and repulsive contributions of medium fluctuations to nuclear superfluidity

Abstract

Oscillations of mainly surface character (S = 0 modes) give rise, in atomic nuclei, to an attractive (induced) pairing interaction, while spin (S = 1) modes of mainly volume character generate a repulsive interaction, the net effect being an attraction which accounts for a sizeable fraction of the experimental pairing gap. Suppressing the particle-vibration coupling mediated by the proton degrees of freedom, i.e., mimicking neutron matter, the total surface plus spin-induced pairing interaction becomes repulsive. [2,3], strong force and spin and density modes exchange in the case of atomic nuclei and of neutron stars [4,5,6].While broad consensus exists concerning the mechanism of electron-electron and electron-phonon interaction leading to superconductivity in metals, the situation is much less clear in the case of strongly interacting particles in the different scenarios found in nature. In particular, it has been found that medium polarization effects associated with the exchange of vibrations lead to a quenching of the bare pairing interaction in the 1 S 0 channel in the inner crust of neutron stars [7] while, at the same time, account for a sizeable fraction of the pairing gap in open shell nuclei [8,9,10]. In the present paper we present, for the first time, evidence which allows to understand these seemingly contradictory results.We address the question at hand within the scenario provided by the paradigmatic (superfluid) open shell nucleus 120 Sn. The starting point corresponds to the calculation of the mean field potential and associated quasiparticle properties within the framework of Hartree-Fock plus BCS theory [11] using the SkM * force [12]. The polarization quanta were worked out within the framework of the quasi-particle random phase approximation (QRPA). The particle-hole residual interaction is derived in a self-consistent way from the Skyrme energy functional, with the exception of the spin-orbit and of the FIG. 1: Generalized Landau parameters associated with the interaction SkM * defining the strength of the particle-hole interaction in the isoscalar (F0), isovector (F ′ 0 ), spin isoscalar (G0) and spin isovector (G ′ 0 ) channels. In the inset the func-Coulomb part (cf.[13] for more details). On the other hand, we neglect the momentum-dependent part of the interaction in the calculation of the particle-vibration coupling discussed below [14]. The relevant part of the the particle-hole interaction can then be writtenWe shall only consider the τ z ·τ z term, in keeping with the fact that we are here interested in the neutron-neutron pairing interaction. Off-diagonal terms are associated with charge-exchange modes. Thus, in lowest order, they do not contribute to the neutron-neutron interaction, but are expected to be of relevance in the discussion of the proton-neutron pairing interaction.

Pairing matrix elements and pairing gaps with bare, effective, and induced interactions

“…This difference is removed and eventually overwhelmed by including the attractive contribution coming from the induced interaction v ind arising from the exchange of surface vibrations, which acts only on a rather small energy range around e F . We note that the pairing gap in 120 Sn is not much changed, including also the effect of spin fluctuations [23], which instead give the dominant (repulsive) contribution to the induced interaction in neutron matter.…”

Superfluid properties of the inner crust of neutron stars. II. Wigner-Seitz cells at finite temperature

“…It has been observed by some authors [41][42][43][44], that the inclusion of higher order diagrams, i.e particle-vibration coupling, can strongly affect the shell structure and the superfluid properties of the system. Such kind of calculations are still not available for WS cells, mainly because of the computational time requested.…”

Spatial structure of neutron Cooper pair in low density uniform matter

“…A recent Monte Carlo study [77] using the realistic bare force suggests the gap close to the BCS result. The higher order effects in symmetric nuclear matter [75] and in finite nuclei [78,79,80] are estimated to increase the gap. Keeping in mind these ambiguities, we consider that the BCS approximation provides a meaningful zero-th order reference.…”