Local approximations in the microscopic treatment of heavy ion reactions

Although the interaction between nuclei is nonlocal, certain models using local potentials are quite successful. It is a challenge for the unified theory of nuclear reactions to investigate how local approximations follow from a microscopic description. These ideas are examined with respect to quasi-identical scattering, the elastic scattering of a heavy projectile A on a target nucleus B = (A + c). Inspection of the resonating-group kernel reveals that the core--core exchange term is sharply peaked and has the longest range compared with the other exchange terms. As a result, only the direct and core--core exchange terms need be considered for surface reactions. When only zero-order moments are retained, an equation is derived that has a form similar to that of the LCNO model. By including higher-order terms, one can account for higher-order recoil effects