Ab Initio Computation of the Longitudinal Response Function in ${}^{40}\mathrm{Ca}$

We present a consistent ab initio computation of the longitudinal response function $R_L$ in ${}^{40}\mathrm{Ca}$ using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for $R_L$ in ${}^4\mathrm{He}$ and the Coulomb sum rule in ${}^{40}\mathrm{Ca}$ against experimental data and other calculations. For $R_L$ in ${}^{40}\mathrm{Ca}$ we obtain a very good agreement with experiment in the quasielastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a milestone towards ab initio computations of neutrino-nucleus cross sections relevant for experimental long-baseline neutrino programs.

Figure 1

Longitudinal response function for ${}^4\mathrm{He}$ at $q=300\mathrm{MeV}/\mathrm{c}$. HH results taken from Ref. [44], GFMC results from Ref. [43], and experimental data from Ref. [45].

Figure 2

${}^{40}\mathrm{Ca}$ results for Coulomb sum rule for ${\mathrm{NNLO}}_{\mathrm{sat}}$ and $\hslash \omega =22\mathrm{MeV}$ compared with CVMC results of Ref. [46] and experimental data taken from Ref. [47].

Figure 3

Longitudinal response of ${}^{40}\mathrm{Ca}$ for $q=300$, 350, $400\mathrm{MeV}/\mathrm{c}$ for ${\mathrm{NNLO}}_{\mathrm{sat}}$ and ${\mathrm{\Delta }\mathrm{NNLO}}_{\mathrm{GO}}(450)$ potentials. For $q=200\mathrm{MeV}/\mathrm{c}$ the strength of excited states was scaled by factor of $1/2$ for better visibility. Experimental data taken from Ref. [47].