Phenomenological local single-particle potentials and their relationship to non-local potentials

Abstract

Abstract The single-particle potential for bound nucleons is probably complex and non-local, whereas in phenomenological calculations it is assumed to be real and local. We demonstrate that in practice the neglect of the imaginary part of the potential is a good approximation. By its inclusion the binding energy is hardly changed and the wave function is enhanced in the nuclear interior by less than 5%. The non-locality is often included by assuming an energy-dependent local potential and applying the Perey correction to the wave function. We show that the Perey-Buck approximation yields only one possible local potentials equivalent to a non-local one and that the Perey correction to the wave function is only valid if the assumed local potential happens to be the Perey-Buck potential. Thus the use of the Perey correction with phenomenological local potentials is open to question. We discuss the Perey-Buck approximation in detail and show that the method can be applied to a wider class of potentials than is usually considered. We show that for this class of potentials the Perey correction can always be expressed solely in terms of the energy variation of the Perey-Buck equivalent potential. Thus if we could restrict the phenomenological potential to the Perey-Buck one, the method could be widely used with confidence. We suggest criteria by which this can be done and give an example. Our discussion is in terms of bound states, but similar comments apply to scattering states including those involving heavy ions where explicit non-local calculations present problems.