Particle Model of Scattering from Collective States of Nuclei

Abstract

The differential cross sections for the excitation of the vibrational levels of nuclei are derived using the direct interaction between the projectile and the shell-model particles via a two-body force. The nuclear collective states are approximate solutions to the Hamiltonian consisting of a pairing plus a quadrupole interaction in a quasi-particle representation. The results obtained by this method are compared to those which follow from an interaction using collective coordinates for states of one and two phonons. Numerical results are given for the plane-wave first Born approximation scattering of alpha particles with a deltafunction interaction between the projectiles and the nuclear particle and for the plane-wave Born approximation scattering of electrons, assuming a Coulomb interaction.