Study of the $^{150}$Sm(t,$^{3}$He) and $^{150}$Nd($^{3}$He,t) reactions with applications for the 0$\nu\beta\beta$ decay of $^{150}$Nd

The NSCL charge-exchange group has ongoing programs to measure the spin-isospin response of nuclei. This talk will focus on measurements of the $^{150}$Sm(t,$^{3}$He)$^{150}$Pm* and $^{150}$Nd($^{3}$He,t)$^{150}$Pm* reactions, which are essential for studies of the neutrinoless double beta ($0\nu\beta\beta$) decay of $^{150}$Nd. $^{150}$Nd is one of the main candidates for $0\nu\beta\beta$ decay detection experiments. To design detectors for $0\nu\beta\beta$ decay and to extract information about the neutrino mass scale and hierarchy from resulting experimental data, accurate nuclear matrix elements are needed. Nuclear charge-exchange experiments can constrain theories used to predict these matrix elements by providing Gamow-Teller and higher order multipole transition strengths in the virtual intermediate nucleus. In addition to its applications for $0\nu\beta\beta$ decay, investigation of the spin-isospin response of heavy, deformed nuclei is important for future work on rare isotopes.