Based on the spectator expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding cal
culations of the effective (optical) potential for nucleon-nucleus scattering for light nuclei.
Calculating microscopic optical potentials for elastic nucleon-nucleus scattering has already led to large body of work in the past. For folding first-order calculations the nucleon-nucleon (NN) interaction and the one-body density of the nucleus wer
e taken as input to rigorous calculations in a spectator expansion of the multiple scattering series. Based on the Watson expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for light nuclei. We calculate scattering observables, such as total, reaction, and differential cross sections as well as the analyzing power and the spin-rotation parameter, for elastic scattering of protons and neutrons from $^4$He, $^{6}$He, $^{12}$C, and $^{16}$O, in the energy regime between 100 and 200~MeV projectile kinetic energy, and compare to available data. Our calculations show that the effective nucleon-nucleus potential obtained from the first-order term in the spectator expansion of the multiple scattering expansion describes experiments very well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the NN amplitudes and the one-body nuclear density.
Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction $^6$He(p,p)$^6$He at projectile energies starting at 71 MeV/nucleon. The optical potential needed to describe the reaction is based on a m
icroscopic Watson first-order folding potential, which explicitly takes into account that the two neutrons outside the $^4$He-core occupy an open p-shell. The folding of the single-particle harmonic oscillator density matrix with the nucleon-nucleon t-matrix leads for this case to new terms not present in traditional folding optical potentials for closed shell nuclei. The effect of those new terms on the elastic scattering observables is investigated. Furthermore, the influence of an exponential tail of the p-shell wave functions on the scattering observables is studied, as well as the sensitivity of the observables to variations of matter and charge radius. Finally elastic scattering observables for the reaction $^8$He(p,p)$^8$He are presented at selected projectile energies.
The sensitivity of nucleon-nucleus elastic scattering observables to the off-shell structure of nucleon-nucleon t-matrices, derived from realistic NN potentials, is investigated within the context of a full-folding model based on the impulse approxim
ation. Our study uses recently developed NN potential models, which describe a subset of the NN data base with a $chi^2$ per datum $sim$1, which means that the NN t-matrices are essentially on-shell equivalent. We calculate proton-nucleus elastic scattering observables for $^{16}$O, $^{40}$Ca, and $^{208}$Pb between 100 and 200 MeV laboratory energy. We find that the elastic scattering observables are insensitive to off-shell differences of the employed NN t-matrices. A more detailed investigation of the scattering equation and the optical potential as given in a factorized approximation reveals that the elastic scattering observables do not sample the NN t-matrices very far off-shell where they exhibit differences.
The influence of the energy dependence of the free NN t-matrix on the optical potential of nucleon-nucleus elastic scattering is investigated within the context of a full-folding model based on the impulse approximation. The treatment of the pole str
ucture of the NN t-matrix, which has to be taken into account when integrating to negative energies is described in detail. We calculate proton-nucleus elastic scattering observables for $^{16}$O, $^{40}$Ca, and $^{208}$Pb between 65 and 200 MeV laboratory energy and study the effect of the energy dependence of the NN t-matrix. We compare this result with experiment and with calculations where the center-of-mass energy of the NN t-matrix is fixed at half the projectile energy. It is found that around 200 MeV the fixed energy approximation is a very good representation of the full calculation, however deviations occur when going to lower energies (65 MeV).
Optical model potentials for elastic nucleon nucleus scattering are calculated for a number of target nuclides from a full-folding integral of two different realistic target density matrices together with full off-shell nucleon-nucleon t-matrices der
ived from two different Bonn meson exchange models. Elastic proton and neutron scattering observables calculated from these full-folding optical potentials are compared to those obtained from `optimum factorized approximations in the energy regime between 65 and 400 MeV projectile energy. The optimum factorized form is found to provide a good approximation to elastic scattering observables obtained from the full-folding optical potentials, although the potentials differ somewhat in the structure of their nonlocality.
