Properties of the Inelastic Form Factors of the Nucleus

Abstract

Based on an inversion formula for the energy-weighted sum rules, a study is made of the properties of the inelastic form factors of the nucleus. The inversion formula is derived by using a simple representation of the identity operator for a restricted set of non-orthogonal states and it is applicable to both isoscalar and isovector transitions. As a result, it is shown that the longitudinal form factor for a particular multipolarity cannot be explicitly factorized into a product of a function of momentum transfer and a function of excitation energy over the entire range of momentum transfer. Further, the ambiguity arising out of the use of the hydrodynamical model to assign spins of giant resonances is illustrated, taking the isovector electric dipole form factor as an example.