Formal Theory of Nuclear Models

Abstract

The formal theory of nuclear model operators discussed by Eden and Francis is presented from a some-what different point of view. Our way of approach is, first, to introduce the model space $\mathfrak{M}$ of arbitrary dimension which is composed of simple known wave functions; second, to transform the original Schr\"odinger equation into that in the model space, the model wave function and the model Hamiltonian being defined in an unambiguous way; third, to obtain the integral equation for the model operator which also determines the model Hamiltonian. This equation no longer contains the exact eigenvalues as in the work of Eden and Francis and is shown to have a unique solution in some cases. The formal relation of this theory to the nuclear scattering problem is discussed.