Compound Levels and the Shell Model*>

A formalism of nuclear reactions is presented which clarifies the meaning of applying the usual shell model calculations to the resonance states as well as the bound states. The main point is the introduction of the internal region in the wave function space. An effective Hamiltonian is defined in this subspace, the diagonalization of which gives the energies and the wavefunctions for the resonance states as well as the bound states. As an application of the theory, calculations of the level widths are carried out for 5He nucleus. § l. ln1troduction When we speak of the energy levels of nuclei, we usually consider them as including unstable levels as well as stable ones. In fact, if we look at the ex-perimental data such as the energy spectra of particles inelastically scattered by a target nucleus, we are naturally led to the concept of "levels " irrespectively of whether they are stable or not. In the following, we call them compound levels. The compound levels in a more restrictive sense were first introduced by N. Bohr1l for the purpose of explaining many sharp peaks observed in neu-tron scattering and radiative capture cross sections. Though the concept o