Short-range effects on nuclear pairing

Abstract

We determine the influence of the three-body force and the medium modification of meson masses on pairing in nuclear and neutron matter. A reduction of the pairing gap is found and increases with density.The pairing interaction in electron superconductors has a natural cutoff determined by the lattice spacing. On the contrary, in nuclear matter there is no such sharp cutoff. The realistic bare nucleon-nucleon (NN) interactions have a smooth behavior which is determined by the fit of the experimental phase shifts of high-energy nucleon-nucleon scattering. However, medium effects strongly modify the NN interaction in nuclear and neutron matter, including its shortrange part ͓1͔. We have still a poor knowledge of these modifications. All predictions on the pairing gap in nuclear matter suffer from this drawback, as the solution of the gap equation is very sensitive to the value of the tail of the interaction in momentum space ͓2͔, i.e., to the short-range behavior of the coordinate-space potential.In this note we discuss the role played in neutron and nuclear matter superfluidity by some mechanisms which may affect the short-range behavior of the pairing force. The nucleon-nucleon correlations ͑ladder diagrams͒, which renormalize the short-range part of the interaction much the same as in the Brueckner G matrix, fix already a kind of cutoff in the gap equation ͓2͔. Other processes may have a strong influence, such as nucleonic excitations or N N exchange giving rise to three-body forces ͑TBF͒ ͓3͔. TBF have been proven to play a crucial role for the saturation properties of nuclear matter due to their short-range repulsive nature ͓4͔. In addition, a medium modification of the heavy meson masses, which has been addressed as manifestation of the chiral symmetry restoration in nuclear matter ͓5͔, can modify the range of the interaction. Experimental evidence for the latter is provided by dilepton production in high-energy heavy ion collisions ͓6͔.The magnitude of the pairing gap in nuclear matter is determined by the competition between the repulsive shortrange part and the attractive long-range part of the interaction. The medium modification of the long-range part was confidently obtained within the random-phase approximation or induced interaction model, and it was discussed elsewhere ͓1,7,8͔. The short-range part is partially incorporated by the gap equation itself with the bare interaction. A simple way ͓2͔ to illustrate this property is to split the gap equation into two coupled equationswhere E k ϭͱ(e k Ϫ) 2 ϩ⌬ k 2 . This shows that the effective interaction Ṽ , arising from the introduction of a cutoff k c in momentum space, sums up a series of ladder diagrams analogous to the Bethe-Goldstone equation. We want to stress that Ṽ and the cutoff are interrelated, so that one cannot use a phenomenological interaction in the gap equation and fix arbitrarily the cutoff. It is quite sensitive to the tail (kϾk c ) of the NN interaction, which reflects the short-range part of the nuclear force. A great deal of uncertainty...

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