Electron scattering on ${\mathbf{A=3}}$ nuclei from quantum Monte Carlo based approaches

TL;DR

This paper presents first-principle quantum Monte Carlo calculations of electron scattering on helium-3 and tritium nuclei, benchmarking different theoretical approaches against experimental data to quantify uncertainties and highlight the importance of relativistic effects at high energies.

Contribution

It introduces a comprehensive comparison of three quantum Monte Carlo-based methods for electron-nucleus scattering, providing insights into their uncertainties and the role of relativistic effects.

Findings

Excellent agreement with experimental data at high momentum transfer.

Quantification of uncertainties in factorization schemes.

Relativistic effects are crucial at high energy transfers.

Abstract

We perform first-principle calculations of electron-nucleus scattering on $^3$He and $^3$H using the Green's function Monte Carlo method and two approaches based on the factorization of the final hadronic state: the spectral-function formalism and the short-time approximation. These three methods are benchmarked among each other and compared to the experimental data for the longitudinal and transverse electromagnetic response functions of $^3$He, and the inclusive cross sections of both $^3$He and $^3$H. Since these three approaches are based on the same description of nuclear dynamics of the initial target state, comparing their results enables a precise quantification of the uncertainties inherent to factorization schemes. At sufficiently large values of the momentum transfer, we find an excellent agreement of the Green's function Monte Carlo calculation with experimental data and with both the spectral-function formalism and the short-time approximation. We also analyze the relevance of relativistic effects, whose inclusion becomes crucial to explain data at high momentum and energy transfer.