Nonlocality of the optical potential and the adiabatic approximation

Abstract

The nonlocality property of the elastic channel optical potential is studied using a schematic coupled-channel system. It is explicitly shown that, consistent with the usual adiabatic approximation, the nonlocality is reduced as the scattering energy approaches the elastic threshold. The residual nonlocality found in the data may be partly due to the artificial truncation of the channels, and strong indications are found that a more complete treatment which includes a large number of channels would lead to better locality of the optical potential at low energy. For optical potentials corresponding to the inelastic channels, we find that the adiabaticity and the consequent locality is not well satisfied

Two causes of nonlocalities in nucleon-nucleus potentials and their effects in nucleon-nucleus scattering

“…where G (0) c is the free Green's function for each individual channel c. Historically, finding these solutions has been difficult. However the MCAS development allows the analogous definition [11,12],…”

“…The g-folding results are in much better agreement with data than are the tfolding ones. However, with this observable as well, there is little to choose between the results obtained using HO and WS bound states for the single-particle bound states of 12 in finding good predictions for both cross sections and analyzing powers. Further discussion is given in the next sub-section.…”

An algebraic solution of the multichannel problem applied to low energy nucleon–nucleus scattering

“…Formally, a set of coupled equations can be replaced by one for just the elastic channel alone from which one can define, in configuration space, the optical potential for elastic scattering. Of note is that, even assuming a local form for the elastic channel element of the potential matrix, the resulting optical potential will be energy dependent and nonlocal [4,5,6,13]. For completeness, a brief development of the optical potential resulting from the sturmian expansion method is given in Appendix B.…”

“…That is also the case with many applications of R-matrix theory of scattering [1], though at least one [2], for n- 12 C scattering, sought to specify the background scattering from an optical potential with partial widths of the resonances specified from (p-s-d) basis shell-model wave functions of the nuclei involved, i.e. 12,13 C.…”

“…Note that we use laboratory frame energies when dealing with the scattering domain as the data to be used is so specified. However, when considering the bound states (below the n- 12 C threshold) and/or spectra of 13 C we use energies in the center of mass system as such are used in tabulations of that spectra [12].…”