Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2005-09-12
Nucl.Phys. A765 (2006) 61-74
Physics
Nuclear Physics
Nuclear Theory
17 pages, 12 figures
Scientific paper
10.1016/j.nuclphysa.2005.10.010
The gap equation in the $^1S_0$-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 $K_{max}=160-180 fm^{-1}$ 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.
Baldo Marcello
Lombardo Umberto
Pankratov S. S.
Saperstein Eduard
Zverev M. V.
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