Separable Multichannel Momentum Space Potentials for Nuclear Reactions

Many nuclei are deformed and their properties can be described using a rotational model. This involves defining a deformed surface of the nucleus and constructing the nucleon-nucleus interaction as a function of distance to the surface. Such a potential has non-zero matrix elements between different nuclear rotational states which are characterized by the spin-parity $I^\pi$, leading to channel couplings. For specific reaction calculations, it is advantageous to have separable representations of the interaction matrix elements available. We develop separable representations following a scheme suggested by Ernst, Shakin, and Thaler (EST). Since optical potentials are complex and energy-dependent, the multichannel EST scheme is generalized to complex, energy-dependent separable potentials. In the case of proton-nucleus interactions the EST scheme is further extended to include charged particles. The multichannel EST scheme is applied to nucleon scattering off $^{12}$C, where the first two excited states $(I^\pi=2^+ ,4^+)$ are taken into account.