LIPPMANN-SCHWINGER EQUATION FOR NUCLEAR SCATTERING

The scattering of one particle by a target of A nucleons is treated in the frame of the shell-model. The bound states of the complete Hamiltonian for A particles are expanded into anti-symmetrized products of bound and unbound one-particle shell-model functions. From these exact target states a basis for the description of the scattering problem is constructed. As the elements of this basis we take all bound shell-model states of the (A+1)-particle system and all antisymmetrized products of the exact bound states of the target with an unbound one-particle state. Because of the antisymmetrization, the elements of this basis are not orthogonal. Under suitable assumptions they can, however, be shown to be linearly independent. That is why a dual basis exists. This basis is constructed explicitly. With its help the Lippmann-Schwinger equation is derived. It is proved that the integral operator in this equation has finite Hilbert-Schmidt norm for complex energies. © 1969.