Bethe-Goldstone equation in finite nuclei

Abstract

Following Brandow's suggestion of setting Q∪Q=0, where ∪ is the single-particle potential, the Bethe-Goldstone equation becomes Ψ =Φ-[Q/(QTQ-ω]vΨ . This equation has been approximated by replacing Q with the Eden-Emery Pauli operator and by neglecting Tχ , where T is the off-diagonal part of the c.m. kinetic energy operator in the oscillator representation. Care has been taken to retain TΦ, which is a large term. The approximate equation has been solved iteratively. It yields defect functions with the bulk of the effect of Q built in. Correction terms to our approximate results have been estimated. A very satisfactory feature of the present approach is that there is considerable cancellation between the so-called spectral and Pauli correction terms. The biggest correction term is <χ|T|χ>, which can be as large as 0.5 MeV in the triplet even case.