The ($^{6}$Li,$^{6}$Li$'$[3.56 MeV]) reaction as a novel probe for studying the inelastic neutrino-nucleus response in astrophysical scenarios

We have proposed to perform a $({}^{6}\mathrm{Li},{}^{6}\mathrm{Li}'[3.56 \, \mathrm{MeV}])$ experiment at $E _{{}^{6}\mathrm{Li}} = 100 \, \mathrm{MeV}/u$ at $0 ^\circ$ with CAGRA and GRAND RAIDEN. In this reaction the ejectile is in the 3.56-MeV excited state which decays directly to the ground state by $\gamma$ emission, allowing the reaction channel to be identified via the detection of the 3.56-MeV $\gamma$ rays with CAGRA. This reaction exclusively excites $\mathrm{GT}_0$ transitions, namely the pure spin- and isospin-flip transitions in the inelastic channel ($\Delta S = 1, \Delta T = 1, \Delta T_ z = 0)$, whose transition strength [$B(\mathrm{GT}_0)$] is directly connected to, e.g., the inelastic neutrino-nucleus scattering (INNS) cross sections. We plan to measure five targets, ${}^{12}\mathrm{C}$, ${}^{24}\mathrm{Mg}$, ${}^{56}\mathrm{Fe}$, ${}^{93}\mathrm{Nb}$, and ${}^{124}\mathrm{Sn}$, with the aim to establish this new technique as well as address various astrophysical topics including nucleosynthesis ($r$- and $\nu$-processes), supernova neutrino detection, supernova evolution and modeling. In addition, many astrophysical models rely on neutral-current and charged-current neutrino interactions with heavy nuclei for which very little data exists, therefore this experiment and the ${}^{6}\mathrm{Li}$ reaction probe are of high scientific importance. The success of this project could lead to future plans that employ the $({}^{6}\mathrm{Li},{}^{6}\mathrm{Li}')$ reaction in inverse kinematics to study GT$_0$ responses of rare isotopes.