Scattering Observables from One- and Two-Body Densities: Formalism and Application to $\gamma\,{}^3$He Scattering

TL;DR

The paper presents a new transition-density formalism for efficiently calculating scattering observables in light nuclei, enabling flexible and computationally efficient analysis of various reactions by decoupling nuclear structure from interaction kernels.

Contribution

Introduction of a general, efficient transition-density formalism that separates nuclear structure from interaction kernels, applicable to multiple reactions involving light nuclei.

Findings

The method converges well with partial waves in $^3$He scattering.

Results are consistent with previous Chiral EFT calculations.

Significantly improves computational efficiency for scattering calculations.

Abstract

We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. By choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on $^3$He. The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like $^4$He are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our $^3$He densities can be used to evaluate any $^3$He elastic-scattering observable with contributions from one- and two-body operators. They are available at https://datapub.fz-juelich.de/anogga.