Time Dependent Channel Packet Calculation of Two Nucleon Scattering Matrix Elements

摘要

A new approach to calculating nucleon-nucleon scattering matrix elements using a proven atomic time-dependent wave packet technique is investigated. Wave packets containing centripetal barrier information are prepared in close proximity to nuclear well. This is accomplished by first using an analytic equation to determine the wave packets in a suitable intermediate asymptotic state where the centripetal barrier is negligible. Then, the split operator technique is used to propagate the wave packets back to their original positions under the full Hamiltonian. Here, one wave packet is held stationary while the other is allowed to evolve and explore the nuclear well. Scattering matrix elements are computed from the correlation function between the stationary wave packet and the evolving wave-packet after it has interacted with the nuclear potential. Determination of nucleon-nucleon phase shifts follows directly from computation of the scattering matrix elements. This technique is ideally suited for determining nuclear scattering matrix elements and phase shifts as it provides a high degree of energy resolution with lower computational effort than traditional time independent methods. These advantages will lead to a greater understanding of reactions involving nucleons with other elementary particles.