Atomic Transition Probabilities for Transitions of Si I and Si II and the Silicon Abundances of Several Very Metal-Poor Stars

We report new measurements of branching fractions for 20 UV and blue lines in the spectrum of neutral silicon (Si I) originating in the 3$s^{2}$3$p$4$s$ $^{3}$P$^{\rm o}_{1,2}$, $^{1}$P$^{\rm o}_{1}$ and 3$s$3$p^{3}$ $^{1}$D$^{\rm o}_{1,2}$ upper levels. Transitions studied include both strong, nearly pure LS multiplets as well as very weak spin-forbidden transitions connected to these upper levels. We also report a new branching fraction measurement of the $^{4}$P$_{1/2}$ - $^{2}$P$^{\rm o}_{1/2,3/2}$ intercombination lines in the spectrum of singly-ionized silicon (Si II). The weak spin-forbidden lines of Si I and Si II provide a stringent test on recent theoretical calculations, to which we make comparison. The branching fractions from this study are combined with previously reported radiative lifetimes to yield transition probabilities and log($gf$)s for these lines. We apply these new measurements to abundance determinations in five metal-poor stars.