J.-P. Dedonder

Scattering in PT-symmetric quantum mechanics

Abstract A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P , T or PT invariance of the Hamiltonian. Applications to some solvable PT -symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance.

Unitarity constraints in the construction of optical potentials

Abstract We first review the unitarity properties of the first order optical potential theory which arise from the one-body nature of both the single scattering approximation and of the single particle model for the nucleus. We construct optical potentials relaxing either the independent particle model assumption for the nucleus or the single scattering approximation. Our construction is guided by the requirement of incorporating the minimal unitarity of the first order theory and extending it to more complex situations. Our investigation of the effects of nucleon-nucleon residual interaction results in a description of the quasifree mechanism modified by final state interaction effects on the struck target nucleon. In the treatment of the projectile rescatterings, unitarity requires the inclusion of all possible scattering processes on a given pair of target nucleons. This naturally leads to a formulation of the optical potential in terms of three-body rather than two-body amplitudes. We discuss various approximations which make, in combination with phenomenological ingredients, an evaluation of these optical potentials feasible.

Optical potentials for charged-hadron-nucleus scattering: Role of Coulomb excitations.

For hadron-nucleus scattering, the projectiles Coulomb interaction induces, in optical potential approximations to multiple-scattering theories, an effective shift in the local energy at which the optical potential is evaluated. In addition, it gives rise to a contribution related to the Coulomb excitation (or deexcitation) of the target accompanied by the corresponding deexcitation (or excitation) by the strong interaction. The first effect is often referred to as the Coulomb shift of the reaction energy. We investigate more specifically the second one, which is usually neglected. The relative importance of both effects is studied for {pi}{sup {plus minus}}-nucleus scattering at intermediate energies.