Solution of the microscopic gap equation for a slab of nuclear matter with the Paris NN-potential

Abstract

The gap equation in the ${}^1{S}_0$-channel is solved for a nuclear slab with the separable form of the Paris potential. The gap equation is considered in the model space in terms of the effective pairing interaction which is found in the complementary subspace. The absolute value of the gap $\Delta$ turned out to be very sensitive to the cutoff $K_{max}$ in the momentum space in the equation for the effective interaction. It is necessary to take $K_{max}=160-180f{m}^{-1}$ to guarantee 1% accuracy for $\Delta$. The gap equation itself is solved directly, without any additional approximations. The solution reveals the surface enhancement of the gap $\Delta$ which was earlier found with an approximate consideration. A strong surface-volume interplay was found also implying a kind of the proximity effect. The diagonal matrix elements of $\Delta$ turned out to be rather close to the empirical values for heavy atomic nuclei.

17 pages, 12 figures

References in corpus (6)

• Many-body effects in nuclear structure
• Low Momentum Nucleon-Nucleon Interaction and Fermi Liquid Theory
• Dispersive effects in neutron matter superfluidity
• Screening of nuclear pairing in nuclear and neutron matter
• On the mechanisms of superfluidity in atomic nuclei
• Surface behaviour of the pairing gap in a slab of nuclear matter

Cited by in corpus (6)

• Properties of the nuclear medium
• Effect of pairing correlations on incompressibility and symmetry energy in nuclear matter and finite nuclei
• Interaction of the single-particle and collective degrees of freedom in non-magic nuclei: the role of phonon tadpole terms
• Microscopic evaluation of the pairing gap
• Spatial correlation properties of the anomalous density matrix in a slab of nuclear matter with realistic NN-forces
• The microscopic pairing gap in a slab of nuclear matter for the Argonne v18 NN-potential