Many-Body Theory of Nuclear Reactions

Abstract

The localization of composite projectiles in the many-body theory of nuclear reactions is studied within the single-particle shell model with configuration mixing. Difficulties are pointed out in extending the existing theory of nucleon-heavy-nucleus scattering to more general reaction processes, and it is shown that an improved treatment of the collective variables corresponding to the c.m. motion of clusters is necessary in order to generalize the theory. Multiple, deformed single-particle (shell-model) potentials, modified to incorporate the c.m. motion, are introduced to spatially localize the composite particles in the continuum. The total c.m. motion gives rise to a physically trivial degeneracy, while the relative motion of clusters is the very scattering process being solved. Double sets of redundant variables are introduced to describe the reactions involving two-cluster channels, and the correct scattering functions are obtained by the double-projection method of Peierls and Thouless.