Lower limits on the nucleosynthezis of $^{44}$Ti and $^{60}$Fe in the dynamic spiral-arms model
We have previously focused on studying the electron-capture isotopes within the dynamic spiral-arms model and empirically derived the energy dependence of the electron attachment rate using the observation of $^{49}$Ti/$^{49}$V and $^{51}$V/$^{51}$Cr ratios in cosmic rays (Benyamin et al. 2017). We have also shown how this relation recovers the energy dependence seen in the lab measurements (Letaw et al. 1985). In this work we use this relation to construct the $^{44}$Ca/$^{44}$Ti ratio and place a lower limit on the amount of $^{44}$Ti that is required to be nucleosynthesized at the source. The results also imply that the acceleration process of the radioisotopes cannot be much longer than a century time scale (or else the required nucleosynthesized amount has to be correspondingly larger). We also provide a similar lower limit on the source $^{60}$Fe by comparing to the recently observed $^{60}$Fe/$^{56}$Fe (Binns et al. 2016).