Electron scattering on $A=3$ nuclei from quantum Monte Carlo based approaches

We perform first-principle calculations of electron-nucleus scattering on ${}^3\mathrm{He}$ and ${}^3\mathrm{H}$ 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 ${}^3\mathrm{He}$, and the inclusive cross sections of both ${}^3\mathrm{He}$ and ${}^3\mathrm{H}$. 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.

Figure 1

${}^3\mathrm{H}$ elastic contribution to the total longitudinal response density at $q=300$ MeV/$c$.

Figure 2

${}^3\mathrm{H}$ total longitudinal response density at $q=300$ MeV/$c$, as a function of relative energy and center-of-mass energy.

Figure 3

Single proton momentum distribution of ${}^3\mathrm{He}$.

Figure 4

Longitudinal and transverse response functions of ${}^3\mathrm{He}$.

Figure 5

Longitudinal and transverse response functions of ${}^3\mathrm{H}$.

Figure 6

STA Longitudinal and transverse response functions of ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ and contribution of different pairs. Solid lines are full responses, dashed lines are $np$ pairs, and dashed-dotted lines are $nn$ and $pp$ pairs respectively.

Figure 7

Inclusive double-differential cross sections for electron scattering on ${}^3\mathrm{He}$.

Figure 8

Inclusive double-differential cross sections for electron scattering on ${}^3\mathrm{H}$.