Ab initio Leading Order Effective Potentials for Elastic Nucleon-Nucleus Scattering

Abstract

Background: Calculating microscopic effective interactions (optical potentials) for elastic nucleon-nucleus scattering has already in the past led to a large body of work. For first-order calculations a nucleon-nucleon (NN ) interaction and a one-body density of the nucleus were taken as input to rigorous calculations of microscopic full-folding calculations.Purpose: Based on the spectator expansion of the multiple scattering series we employ a chiral next-to-next-toleading order (NNLO) nucleon-nucleon interaction on the same footing in the structure as well as in the reaction calculation to obtain an in leading-order consistent effective potential for nucleon-nucleus elastic scattering, which includes the spin of the struck target nucleon. Methods:The first order effective folding potential is computed by first deriving a nonlocal scalar density as well as a spin-projected momentum distribution. Those are then integrated with the off-shell Wolfenstein amplitudes A, C, and M . The resulting nonlocal potential serves as input to a momentum-space Lippmann-Schwinger equation, whose solutions are summed to obtain the nucleon-nucleus scattering observables.Results: We calculate elastic scattering observables for 4 He, 6 He, 8 He, 12 C, and 16 O in the energy regime between 100 and 200 MeV projectile kinetic energy, and compare to available data. We also explore the extension down to about 70 MeV, and study the effect of ignoring the spin of the struck nucleon in the nucleus. Conclusions:In our calculations we contrast elastic scattering off closed-shell and open-shell nuclei. We find that for closed-shell nuclei the approximation of ignoring the spin of the struck target nucleon is excellent. We only see effects of the spin of the struck target nucleon when considering 6 He and 8 He, which are nuclei with a N/Z ratio larger than 1.

Ab initio nucleon-nucleus elastic scattering with chiral effective field theory uncertainties

“…We also see a deterioration of the agreement of our central values with experiment for those energies. This is somewhat in contrast to previous studies and experiences using different interactions [19,33,34] which described N N observables about equally well at energies up to 200 MeV. The systematic study of chiral truncation uncertainties, carried out here for the first time, seems to indicate that ab initio effective N A interactions derived from certain chiral EFTs allows for a good description of experiment at energies lower than previously assumed, provided we focus on regions of momentum transfer where the analysis of the EFT truncation uncertainty is valid.…”

“…Details of the derivation of the leading order term and how the spin structure of the N N interaction is consistently taken into account in the reaction process are given in Refs. [19,20,27] and shall not be repeated here. Since the leading order in the spectator expansion considers two nucleons being active in the scattering process, we do not include three-nucleon forces which naturally occur in the chiral expansion starting at next-to-next-to-leading order (N2LO).…”

“…multiple scattering effects resulting from first solving the integral equation to obtain the Watson potential [29] and then second from solving the Lippmann-Schwinger integral equation do not influence the analysis. Our calculations are based on an ab initio effective interaction calculated in the leading of the spectator expansion of a multiple scattering theory [19], in which a one-body nuclear density matrix is folded with N N amplitudes calculated from the same N N force. In the elastic scattering of a proton (neutron) from a spin-0 nucleus the effective interaction contains only two contributions, a spin-independent central potential and a spin-orbit potential.…”

“…As shown in detail in Refs. [19,27], the central potential is built by folding the N N Wolfenstein [30] amplitudes A and C with the nuclear density matrix, while the spin-orbit potential contains contributions from the N N Wolfenstein amplitudes C and M . Furthermore, one should note that the amplitude C is zero for zero-momentum transfer, and very small for momentum transfers q ≤ 1 fm −1 .…”

“…elastic scattering of nucleon from nuclei in the framework based on the spectator expansion [18] of multiple scattering theory. Recently the leading order term in the spectator expansion has been successfully derived and calculated, treating the N N interaction consistently when deriving the effective interaction [19,20].…”