Chemical-potential dependence of the pairing gap in a nuclear-matter slab

The equation for the pairing gap Δ in a slab of nuclear matter governed by the Paris nucleon-nucleon potential is solved for various values of the chemical potential µ in the range from ?8 MeV, which corresponds to stable nuclei, to ?0.1 MeV, which corresponds to nuclei in the vicinity of the nucleon drip line. The slab is placed in a one-dimensional Woods-Saxon potential whose parameters are set to values typical of nuclei. Two models are considered. In the first, the potential-well depth is fixed at U ₀ = ?50 MeV, the density within the slab growing as |µ| is reduced. In the second model, the density is fixed at the center of the slab, |U ₀| decreasing as |µ| is reduced. The behavior of the gap Δ as a function of µ is model-dependent. In the first model, Δ decreases with decreasing |µ|, while, in the second, it increases. At the same time, the effect of the surface enhancement of Δ becomes more pronounced with decreasing |µ| in both models.