Marrying {\it ab initio} calculations and Halo-EFT: the case of ${}^7{\rm Li} + n \rightarrow {}^8{\rm Li} + \gamma$

Abstract

We report a leading-order calculation of radiative ${}^{7}\mathrm{Li}$ neutron captures to both the ground and first excited state of ${}^{8}\mathrm{Li}$ in the framework of a low-energy effective field theory (Halo-EFT). Each of the possible final states is treated as a shallow bound state composed of both $n+{}^{7}\mathrm{Li}$ and $n+{}^{7}\mathrm{Li}^{*}$ (core excitation) configurations. The {\it ab initio} variational Monte Carlo method is used to compute the asymptotic normalization coefficients of these bound states, which are then used to fix couplings in our EFT. We calculate the total and partial cross sections in the radiative capture process using this calibrated EFT. Fair agreement with measured total cross sections is achieved and excellent agreement with the measured branching ratio between the two final states is found. In contrast,a previous Halo-EFT calculation [G. Rupak and R. Higa, Phys. Rev. Lett {\bf 106}, 222501 (2011)] assumes that the $n$-${}^{7}\mathrm{Li}$ couplings in different spin channels are equal, fits the $P$-wave "effective-range" parameter to the threshold cross section for ${}^7{\rm Li} + n \rightarrow {}^8{\rm Li} + \gamma$, and assumes the core excitation is at high enough energy scale that it can be integrated out.