Reaction Rate Sensitivity of the Production of $\gamma$-ray Emitting Isotopes in Core-Collapse Supernova

Radioactive isotopes produced in core-collapse supernovae (CCSNe) provide useful insights into the underlying processes driving the collapse mechanism and the origins of elemental abundances. Their study generates a confluence of major physics research, including experimental measurements of nuclear reaction rates, astrophysical modeling, and $\gamma$-ray observations. Here we identify the key nuclear reaction rates to the nucleosynthesis of observable radioactive isotopes in explosive silicon-burning during CCSNe. Using the nuclear reaction network calculator SkyNet and current REACLIB reaction rates, we evolve temperature-density-time profiles of the innermost $0.45~M_\odot$ ejecta from the core collapse and explosion of a $12~M_\odot$ star. Individually varying 3403 reaction rates by factors of 100, we identify 141 reactions which cause significant differences in the isotopes of interest, namely, $^{43}$K, $^{47}$Ca, $^{44,47}$Sc, $^{44}$Ti, $^{48,51}$Cr, $^{48,49}$V, $^{52,53}$Mn, $^{55,59}$Fe, $^{56,57}$Co, and $^{56,57,59}$Ni. For each of these reactions, we present a novel method to extract the temperature range pertinent to the nucleosynthesis of the relevant isotope; the resulting temperatures lie within the range $T = 0.47$ to $6.15~$GK. Limiting the variations to within $1\sigma$ of STARLIB reaction rate uncertainties further reduces the identified reactions to 48 key rates, which can be used to guide future experimental research. Complete results are presented in tabular form.