A shell model calculation with reaction matrix

Abstract

While explaining the success of the shell model of the nucleus, the Brueckner theory of nuclear many body problem prescribes that the reaction matrix should be used in setting up the shell model Hamiltonian. The theory shows how the reaction matrix between two nucleons inside a nucleus can be calculated if the interaction potential between two free nucleons is known. So far no shell model calculation has been performed with such a reaction matrix, mainly because its evaluation in a finite nucleus is an extremely laborious task. In this paper an approximate form for the reaction matrix has been used to calculate the level spacings of Ca⁴². The reaction matrix has been parametrized with two quantities. One is the correlation length and the other is a quantity related to the effective mass. Reasonable agreement between the experimentally measured level spacings and the theoretical values are obtained for values of the two parameters which are consistent with the estimates of these quantities based on the studies of the properties of nuclear matter.