Impact of $\textit{T}$- and $\rho$-dependent decay rates and new (n,$\gamma$) cross sections on the $\textit{s}$ process in low-mass AGB stars

We study the impact of nuclear input related to weak-decay rates and neutron-capture reactions on predictions for the $s$ process in AGB stars. We provide the first database of surface abundances and stellar yields of the isotopes heavier than iron from the $Monash$ models. We run nucleosynthesis calculations with the $Monash$ post-processing code for 7 stellar structure evolution models of low-mass AGB stars with 3 different sets of nuclear input. The reference set has constant decay rates and represents the set used in the previous $Monash$ publications. The second set contains the temperature and density dependence of $\beta$ decays and electron captures based on the default rates of NETGEN. In the third set, we update 92 neutron-capture rates based on reevaluated experimental cross sections from the ASTRAL. We compare and discuss the predictions of each set relative to each other in terms of isotopic surface abundances and total stellar yields. We also compare results to isotopic ratios measured in presolar stardust SiC grains from AGB stars. The new sets of models resulted in a $\sim$66% solar $s$-process contribution to the $p$-nucleus $\mathrm{^{152}Gd}$, confirming that this isotope is predominantly made by the $s$ process. The nuclear input updates resulted in predictions for the $\mathrm{^{80}Kr/^{82}Kr}$ ratio in the He intershell and surface $\mathrm{^{64}Ni/^{58}Ni}, \mathrm{^{94}Mo/^{96}Mo}$ and $\mathrm{^{137}Ba/^{136}Ba}$ ratios more consistent with the corresponding ratios measured in stardust, however, the new predicted $\mathrm{^{138}Ba/^{136}Ba}$ ratios are higher than the typical values of the stardust SiC grain data. The W isotopic anomalies are in agreement with data from analysis of other meteoritic inclusions. We confirm that the production of $\mathrm{^{176}Lu}$ and $\mathrm{^{205}Pb}$ is affected by too large uncertainties in their decay rates from NETGEN.