Lower Limits on the Nucleosynthesis of ⁴⁴Ti and ⁶⁰Fe in the Dynamic Spiral-arm Cosmic-Ray Propagation Model

We have previously focused on studying the electron-capture isotopes within the dynamic spiral-arms cosmic-rays propagation model and empirically derived the energy dependence of the electron attachment rate using the observation of ⁴⁹Ti/⁴⁹V and ⁵¹V/⁵¹Cr ratios in cosmic rays. We have also shown how this relation recovers the energy dependence seen in the lab measurements. In this work, we use this relation to construct the ⁴⁴Ti/⁴⁴Ca ratio and place a lower limit on the amount of ⁴⁴Ti that is required for it to be nucleosynthesized at the source. The results also imply that the acceleration process of the radioisotopes cannot be much longer than a century timescale (or else the required nucleosynthesized amount has to be correspondingly larger). We also provide a similar lower limit on the source ⁶⁰Fe by comparing to the recently observed ⁶⁰Fe/⁵⁶Fe.