On a Symmetry Property of the Inelastic Scattering Amplitude in the Adiabatic Approximation

A symmetry property of the exact T matrix for the inelastic scattering of particles with arbitrary spin is derived, in the adiabatic limit, using time reversal invariance properties of the elastic scattering amplitude and neglecting interaction terms that involve spins or velocities of the target nucleons. The symmetry property is used to show the equality of the generalized polarization and asymmetry tensors for inelastic scattering and to derive the symmetry properties, with respect to the adiabatic recoil axis, of the angular correlation function and the circular polarization of the deexcitation gamma rays. It is also shown that the nuclear excited state is aligned along the axis normal to the scattering plane. A brief discussion of the symmetry properties of the adiabatic DWBA amplitude is given. When interaction terms involving spins or velocities of the target nucleons are taken into account, it is shown that the inelastic scattering T matrix can be divided into two parts; one that satisfies the abo...