Inclusive electron-nucleus cross section within the Self Consistent Green's Function approach

TL;DR

This paper uses the Self Consistent Green's Function approach to compute inclusive electron-nucleus cross sections and related nuclear properties, achieving good agreement with data and addressing center of mass effects in light nuclei.

Contribution

It introduces a novel application of the Self Consistent Green's Function method to inclusive electron scattering and develops a Monte Carlo technique to subtract center of mass effects in light nuclei.

Findings

Accurate description of electron-$^{16}$O cross sections with relativistic effects.

Development of a Monte Carlo method to remove center of mass contributions.

Significant impact of center of mass subtraction on light nuclei distributions.

Abstract

We compute inclusive electron-nucleus cross sections using ab initio spectral functions of $^4$He and $^{16}$O obtained within the Self Consistent Green's Function approach. The formalism adopted is based on the factorization of the spectral function and the nuclear transition matrix elements. This allows to provide an accurate description of nuclear dynamics and to account for relativistic effects in the interaction vertex. Our calculations use a saturating chiral Hamiltonian in order reproduce the correct nuclear sizes. When final state interactions for the struck particle are accounted for, we find nice agreement between the data and the theory for the inclusive electron-$^{16}$O cross section. The results lay the foundations for future applications of the Self Consistent Green's Function method, in both closed and open shell nuclei, to neutrino data analysis. This work also presents results for the point-proton, charge and single-nucleon momentum distribution of the same two nuclei. The center of mass can affect these quantities for light nuclei and cannot be separated cleanly in most ab initio post-Hartree-Fock methods. In order to address this, we developed a Metropolis Monte Carlo calculation in which the center of mass coordinate can be subtracted exactly from the trial wave function and the expectation values. We gauged this effect for $^4$He by removing the center of mass effect from the Optimal Reference State wave function that is generated during the Self Consistent Green's Function calculations. Our findings clearly indicate that the residual center of mass contribution strongly modifies calculated matter distributions with respect to those obtained in the intrinsic frame. Hence, its subtraction is crucial for a correct description of light nuclei.