Nonlocal Description of the Nucleus-Nucleus Interaction

Abstract

The mean field interaction between complex quantum many-body systems (nucleus-nucleus, cluster-cluster, etc.) is still an open question in current physics research. The study of this matter is a fundamental step in the understanding of many-body dynamics. In the nucleus-nucleus case, significant progress has been achieved concerning this question during the last decade [1], as a consequence of the measurement of accurate and extensive elastic scattering data at intermediate energies. Nuclear rainbow scattering, first observed in a systems [2 ‐4] and later in light heavy ions [5 ‐ 7], probes the nucleus-nucleus potential not only at the surface region but also at smaller distances, and ambiguities in the real part of the potentials have been removed. The resulting phenomenological interactions have significant dependence upon the bombarding energies. Some theoretical models have been developed to account for this energy dependence through realistic mean field potentials. Nowadays, the most successful models seem to be those based on the DDM3Y interaction [8 ‐ 10] which is an improvement of the originally energyindependent double-folding potential [11]. But, in order to fit the data, the density- and energy-dependent DDM3Y potential needs a renormalization factor which besides being system dependent [1,12] is still slightly energy dependent [1]. In this Letter we show, by an extensive description of elastic scattering data using an optical integro-differential equation, that the dependence on the bombarding energy of the real bare potential is mostly due to the intrinsically nonlocal nature of the effective one-body interaction. The real bare potential (by bare we mean the average, mean field, interaction with no coupled channels effects) is constructed using the folding model. It contains no adjustable parameters and is energy independent. The absorptive part is taken to be a three parameters WoodsSaxon interaction. We also supply a simple approach to obtain the local-equivalent energy-dependent potential. Before we set the stage for the analysis of elastic scattering data, we first describe our theoretical model. When dealing with nonlocal interactions, one is required to solve the integro-differential equation 2 ¯ h 2