Inclusive electron-nucleus cross section within the self-consistent Green's function approach

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.

Lepton scattering fromAr40andTi48in the quasielastic peak region

“…O[13] and nuclear radii up to isotopes near 48 Ca[34][35][36]. The quality of these predictions is demonstrated byFig.…”

“…In spite of being a relatively soft interaction, with a cutoff of 450 MeV/c, NNLO sat still predicts the presence of larger momentum components. Nevertheless, such components are clearly weaker than the ones obtained from high-accuracy (and high-cutoff) phenomenological forces such as AV18 [13].…”

“…In this regards, very promising results have been obtained combining the impulse approximation (IA) with a realistic spectral function that embeds many-body nuclear correlation effects. This formalism has been extensively tested in the electromagnetic sector and recently generalized to include one-and two-body current processes for both electron-and neutrino-nucleus scattering processes [11][12][13][14].…”

“…For the case of quasielastic processes at moderate values of the momentum transfer (|q| > ∼ 500 MeV), the impulse approximation allows to factorize |Ψ A f → |p ⊗|Ψ A−1 n into the outgoing nucleon of momentum p and the residual nucleus in a state |Ψ A−1 n . This leads to [13,14]:…”

Short-range correlations and the charge density

“…A possible way for calculating the point-proton density from the experimental charge density is described in Ref. [42]. Calculating the point density of 40 Ca based on Eqs.…”