The longitudinal and transverse spin response functions which Alberico, et al. [AEM82] predicted would be modified by an enhancement in the nuclear pion field, are given by [Bro95]
respectively, where and are the initial (final) wavefunctions and energy of the nucleons, respectively. The spin response functions describe the response of the nucleus to the various spin operators,
where is the spin of the nucleon and is the momentum transfer. In terms of these response functions the nucleon-nucleus (nA) cross section can be written as
where are the free nn partial differential cross sections and 0, i, j, and k are a complete basis for describing the nucleon polarization. Equation illustrates the meaning of the nuclear response function as a quantitative measure of the effect that the collective action of the nucleus has on scattering. The response functions describe how the free nn scattering is altered in nA scattering.
To obtain these response functions experimentally it is necessary to make a polarization transfer measurement of a target, which requires knowing the polarization of both the incident and ejected nucleon to determine how the spin is affected by interaction with the nucleus. Once the polarization transfer observables are measured it is possible to use them to determine the spin-response functions [IcK92]. This procedure will be elaborated upon in chapter .