Monte Carlo Investigation of the Ratios of Short-Lived Radioactive Isotopes in the Interstellar Medium

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.