Ab Initio Study of $^7$Li with Coupled $^6$Li + $n$ and $^6$He + $p$ Mass Partitions

Background: Lithium plays an important role in nuclear astrophysics, fusion energy generation, and nuclear technology. From a theoretical point of view, the nucleus $^7$Li presents a remarkable challenge, as its bound states and resonances can be understood as being formed by a $^4$He and $^3$H pair, or simultaneously, a single neutron/proton coupled to a $^6$Li/$^6$He core. In light of this complexity, a consistent description of $^7$Li bound-state and continuum properties in a unified model presents a significant advancement towards a predictive theory of nuclear structure and reactions. Purpose: Towards achieving such a predictive description, we carry out calculations for $^7$Li within an ab initio framework, taking into account the mass/charge partitions $^6$Li + $n$ and $^6$He + $p$ in a single coupled-channel calculation. This approach allows us to both investigate the effects of the coupling between partitions on the spectrum of $^7$Li, and calculate the cross sections for the $^6$Li($n,p)^6$He and $^6$He($p,n)^6$Li reactions. Method: We use the no-core shell model with continuum, which is capable of describing both bound and scattering states in a unified framework. Results: Our calculation reproduces all the experimentally observed states of $^7$Li in the correct order and predicts new resonances. We also calculated the cross section of the reaction $^6$He($p,n)^6$Li and differential cross sections of the elastic scattering of protons on $^6$He to provide theoretical results for comparison with planned experiments. Conclusions: The overall shape of the cross section of the reaction $^6$Li$(n,p)^6$He as a function of energy is reproduced, although the absolute magnitude is overestimated due to omission of the ($n,\alpha$) reaction channel. A more accurate description of the cross section is achieved by phenomenological adjustmenting the energies of resonances.