We consider pairing in a dilute system of Fermions with a short-range interaction. While the theory is ill-defined for a contact interaction, the BCS equations can be solved in the leading order of low–energy effective field theory. The integrals are evaluated with the dimensional regularization technique, giving analytic formulas relating the pairing gap, the density, and the energy density to...

3 P 2 pairing in neutron matter is investigated using the Bonn potential models. We find pairing energy gaps in pure neutron matter comparable to the results of previous investigators when the attractive tensor coupling is included. However, taking into account that in a neutron star we have matter at β equilibrium, we find that the 3 P 2-3 F 2 energy gap is reduced considerably.

Cryptographic pairing (bilinear mapping) is a core algorithm for various cryptography protocols. It is computationally expensive and inefficiently computed with general purpose processors. Although there has been previous work looking into efficient hardware designs for pairing, most of these systems use small characteristic curves which are incompatible with practical software designs. In this...

We consider pairing in a dilute system of Fermions with a short-range interaction. While the theory is ill-defined for a contact interaction, the BCS equations can be solved in the leading order of low–energy effective field theory. The integrals are evaluated with the dimensional regularization technique, giving analytic formulas relating the pairing gap, the density, and the energy density to...

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is reexamined in the context of the Quantum Inverse Scattering Method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators i...

The inhomogeneous nuclear matter forms the inner crust of neutron stars at densities ranging from 10 fm to 10 fm. The nuclear matter is thus diluted and the nucleons are strongly paired through the attraction in the s-wave channel. Since the proton fraction does not exceed a few percent in this density region the main contribution to the pairing energy comes from neutrons. The dependence of the...

We calculate the neutrino energy emission rate due to singlet-state pairing of protons in the neutron star cores taking into account the relativistic correction to the non-relativistic rate. The non-relativistic rate is numerically small, and the relativistic correction appears to be about 10 – 50 times larger. It plays thus the leading role, reducing great difference between the neutrino emiss...

We investigate the BCS treatment of neutron-proton pairing involving timereversed orbits. We conclude that an isospin-symmetric hamiltonian, treated with the help of the generalized Bogolyubov transformation, fails to describe the ground state pairing properties correctly. In order for the np isovector pairs to coexist with the like-particle pairs, one has to break the isospin symmetry of the h...