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 .