Inelastic scattering of nucleons on single-hole-nuclei in the theory of finite Fermi systems

Abstract

The inelastic scattering of nucleons on magic nuclei with a single hole is considered in the framework of the theory of finite Fermi systems. It is shown that the amplitude for the reactionμ, k⇒v, k∼', where ¦ μ, v(A− 1)〉:=single hole states of the initial and final nuclei andk:=k, στ, is determined by the four pole vertexΓ of the two-particle Green function. The particle-hole equation forΓ is established and an approximate solution is discussed where the vertex is represented by a nonresonant and a sum of compound nucleus contributions. It is shown that the nonresonant part and the position and strengths of the compound nucleus contributions are determined by the same effective particle-hole interaction introduced byMigdal and coworkers¹⁻³ in their semi-phenomenological description of the static properties of nuclei adjacent to magic ones. It is pointed out briefly that the theory of inelastic scattering on magic nuclei with one additional nucleon proceeds along the same line. A new set of parameters has to be introduced, however, because in this case the particle-particle equation forΓ has to be considered.