Longitudinal Response Function of $^{3}$H from Chiral Potentials

In the electron scattering off a nucleus, the cross section is proportional to the longitudinal response function \begin{equation} R_{L}(\omega,\mathbf{q})=\sum_{f}\hspace{-13pt}\int\left|\langle\Psi_{f}|\rho(\mathbf{q})|\Psi_{0}\rangle\right|^{2}\delta\left(E_{f}-E_{0}-\omega\right), \end{equation} where $\rho(\mathbf{q})$ is the current operator. We aim at calculating it for the $^{3}$H nucleus using Chiral Effective Field Theory (EFT) potentials. Electron scattering observables are sensitive to three-nucleon forces [1], and thus, it is relevant to test EFT on reactions in the continuum. We use the Lorentz Integral Transform (LIT) to reduce the continuum problem to the solution of a bound state like equation [2] which is solved by expanding wave functions in terms of hyperspherical harmonics [3]. The response is obtained by a numerical inversion of the (LIT). Preliminary results are presented for low energies at q = 174 MeV/c, along with a comparison with experimental data and previous calculations [4].\\[0pt] [1] Bacca {\it et al.} Phys. Rev. Lett. 102, 162501 (2009)\\[0pt] [2] Efros {\it et al.} Phys. Lett. B, 338 130 (1994)\\[0pt] [3] Barnea {\it et al.} Phys. Rev. C 61, 054001 (2000)\\[0pt] [4] Efros {\it et al.} Phys. Rev. C 69, 044001 (2004)