The Weak S-Process in Massive Stars

The weak $s-$process occurs in massive stars with $M \geq 8 M_{\odot}$ during convective core He burning and shell C burning, and synthesizes stable isotopes up to a mass of A $\approx$ 100. Computing the weak $s$ contributions to the solar abundances is more sensitive to cross-section uncertainties compared to the main component, and previous stellar models have difficulty obtaining the needed weak $s$-only isotopic abundances without also overproducing others. In this work, we calculate the weak component of the $s$-process. The weak $s$ solar abundances are taken as residuals from previous computations for the main $s$ component. To investigate possible differences in neutron exposures between both the main and weak components and the He-core and C-shell sites within the weak component itself, we complete the calculations using different neutron exposure distribution models: a linear combination of exponential distributions, a superposition of exponential distributions, a Gaussian distribution, and a Planck distribution. The solutions to the differential equation are assessed by tuning the fraction $f$ of $^{56}{Fe}$ seed nuclei and characteristic neutron exposure $\tau_{0}$ as fit parameters.