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Simple microscopic model for the scalar-isoscalar component of the Landau-Migdal amplitude
Authors:M Baldo  U Lombardo  E E Saperstein  M V Zverev
Institution:(1) Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182, Russia;(2) Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Corso Italia 57, I-95129 Catania, Italy;(3) Moscow State Engineering Physics Institute (Technical University), Kashirskoe sh. 31, Moscow, 115409, Russia
Abstract:A simple microscopic model is proposed that describes the coordinate dependence of the zeroth harmonic f 0(r) of the scalar-isoscalar component of the Landau-Migdal amplitude. In the theory of finite Fermi systems due to Migdal, such a dependence was introduced phenomenologically. The model presented in this study is based on a previous analysis of the Brueckner G matrix for a planar slab of nuclear matter; it expresses the function f 0(r) in terms of the off-mass-shell T matrix for free nucleon-nucleon scattering. The result involves the T matrix taken at the negative energy value equal to the doubled chemical potential μ of the nucleus being considered. The amplitude f 0(r) found in this way is substituted into the condition that, in the theory of finite Fermi systems, ensures consistency of the self-energy operator, effective quasiparticle interaction, and the density distribution. The calculated isoscalar component of the mean nuclear field V(r) agrees fairly well with a phenomenological nuclear potential. Owing to a strong E dependence of the T matrix at low energies, the potential-well depth V(0) depends sharply on μ, increasing as |μ| is reduced. This effect must additionally stabilize nuclei near the nucleon drip line, where μ vanishes.
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