Investigating the $^{38}$K($p$,$\gamma$)$^{39}$Ca reaction rate in novae via the energy levels of $^{39}$Ca

While it is known that the endpoint of nucleosynthesis in nova explosions is around $^{40}$Ca, discrepancies exist between the modeled and observed abundances of nuclei near the endpoint. Uncertainties in the $^{38}$K($p$,$\gamma$)$^{39}$Ca reaction rate could be one source of the discrepancy. Accurate calculation of the rate depends on knowledge of three $\ell=0$ resonances, which correspond to $J^\pi=5/2^+$ excited states in $^{39}$Ca above the $^{38}$K+$p$ threshold. Gammasphere ORRUBA: Dual Detectors for Experimental Structure Studies (GODDESS) was used to study these excited states via the $^{40}$Ca($^3$He,$\alpha$)$^{39}$Ca reaction at Argonne National Laboratory. Three excited states with energies of 6156.2(16), 6268.8(22), and 6470.8(19) keV were found by studying the $\gamma$-$\alpha$ coincidences in the measurement, corresponding to three suspected $J^\pi=5/2^+$ states. Their impact on the $^{38}$K($p$,$\gamma$)$^{39}$Ca reaction rate was investigated and these results will be discussed.