Pairing in neutron matter: New uncertainty estimates and three-body forces

Abstract

We present solutions of the BCS gap equation in the channels 1 S0 and 3 P2− 3 F2 in neutron matter based on nuclear interactions derived within chiral effective field theory (EFT). Our studies are based on a representative set of nonlocal nucleon-nucleon (NN) plus three-nucleon (3N) interactions up to next-to-next-to-next-to-leading order (N 3 LO) as well as local and semilocal chiral NN interactions up to N 2 LO and N 4 LO, respectively. In particular, we investigate for the first time the impact of subleading 3N forces at N 3 LO on pairing gaps and also derive uncertainty estimates by taking into account results for pairing gaps at different orders in the chiral expansion. Finally, we discuss different methods for obtaining self-consistent solutions of the gap equation. Besides the widely-used quasi-linear method by Khodel et al. we demonstrate that the modified Broyden method is well applicable and exhibits a robust convergence behavior. In contrast to Khodel's method it is based on a direct iteration of the gap equation without imposing an auxiliary potential and is straightforward to implement.

Microscopic study of 1S0 superfluidity in dilute neutron matter

“…In our calculation, the contributions of the P -wave and higher partial-wave channels become important for the EOS, and indirectly to the 1 S 0 pairing gap, only for k F 0.8 fm −1 , as must also be the case in other studies of neutron matter in this density regime. Similarly, fundamental three-nucleon forces should have only modest impact on the EOS and 1 S 0 superfluid gap in this regime [8,9,49,50,51].…”

“…It is worth noting at this point that at similar densities, precise calculation of the EOS of pure neutron matter is less demanding than that for symmetrical nuclear matter, where large-scale cancellations occur between kinetic and potential contributions to E N . An additional consideration is that in the density regime of neutron matter of interest for 1 S 0 pairing, three-nucleon interactions are not expected to play a very significant role [8,9,49,50,51].…”

“…[1]). Among them we mention direct calculations based on the original Bardeen, Cooper, a e-mail: gepavlou@phys.uoa.gr Schrieffer (BCS) theory using bare two-nucleon potentials [6,7] and three-nucleon potentials [8,9], application of the polarization potential model of Pines and coworkers [10], inclusion of medium-polarization within a G-matrix formulation [11,12], application of Dirac-Brueckner-HartreeFock-Bogoliubov (DBHFB) theory [13], calculations using the Correlated Basis Function Method (CBF) [14,15,16], applications of the Self-Consistent Green's Function Method [17,18], a Renormalization Group (RG) treatment [7], and pursuit of various Monte Carlo techniques [19,20,21,22,23]. In spite of these many efforts, there is still ambiguity in the value of the 1 S 0 gap as a function of the density (or k F ), owing to the strong sensitivity of the gap to inputs for the pairing interaction and self-energies.…”

Neutron pairing with medium polarization beyond the Landau approximation

“…This system of equations has actually two decoupled blocks corresponding to the indices 1, 2, 6, 8, 10, 13, 16, 18, which have products of two time-even operators, and to the indices 3,4,5,7,9,11,12,14,15,17, which have products of two time-odd operators.…”

“…Hence, at the BCS level, phase-shift equivalence of the two-body interaction suffices to yield model independent results [16]. However, description of * urban@ipno.in2p3.fr † suna@physics.iitm.ac.in pairing in the triplet channel, which typically occurs at higher densities becomes challenging even at the BCS level, as the input free-space two-body interactions are no-longer phase shift equivalent and hence the gaps turn out to be model dependent [12][13][14][15]. As already noted, including the interaction of the neutrons with the medium is very important and can lead to crucial medium modifications such as screening of the free-space two-body interaction.…”