  Short-lived radioactive nuclei (SLR) with mean lives below 100 Myr provide us
with unique insights into current galactic nucleosynthetic events, as well as
events that contributed to the material of our Solar System more that 4.6 Gyr
ago. Here we present a statistical analysis of the ratios of these radioactive
nuclei at the time of early Solar System (ESS) using both analytical
derivations and Monte Carlo methods. We aim to understand the interplay between
the production frequency and the mean lives of these isotopes, and its impact
on their theoretically predicted ratios in the interstellar medium (ISM). We
find that when the ratio of two SRLs, instead of the ratios of each single SLR
relative to its stable or long-lived isotope, is considered, not only the
uncertainties related to the galactic chemical evolution of the stable isotope
are completely eliminated, but also the statistical uncertainties are much
lower. We identify four ratios, 247Cm/129I, 107Pd/182Hf, 97Tc/98Tc, and
53Mn/97Tc, that have the potential to provide us with new insights into the r-,
s-, and p-process nucleosynthesis at the time of the formation of the Sun, and
need to be studied using variable stellar yields. Additionally, the latter two
ratios need to be better determined in the ESS to allow us to fully exploit
them to investigate the galactic sites of the p process.
