Recent atomic physics calculations for Si II are employed within the Cloudy modelling code to analyse Hubble Space Telescope (HST) STIS ultraviolet spectra of three cool stars, Beta-Geminorum, Alpha-Centauri A and B, as well as previously published HST/GHRS observations of Alpha-Tau, plus solar quiet Sun data from the High Resolution Telescope and Spectrograph. Discrepancies found previously between theory and observation for line intensity ratios involving the 3s$^{2}$3p $^{2}$P$_{J}$--3s3p$^{2}$ $^{4}$P$_{J^{prime}}$ intercombination multiplet of Si II at 2335 Angs are significantly reduced, as are those for ratios containing the 3s$^{2}$3p $^{2}$P$_{J}$--3s3p$^{2}$ $^{2}$D$_{J^{prime}}$ transitions at 1816 Angs. This is primarily due to the effect of the new Si II transition probabilities. However, these atomic data are not only very different from previous calculations, but also show large disagreements with measurements, specifically those of Calamai et. al. (1993) for the intercombination lines. New measurements of transition probabilities for Si II are hence urgently required to confirm (or otherwise) the accuracy of the recently calculated values. If the new calculations are confirmed, then a long-standing discrepancy between theory and observation will have finally been resolved. However, if the older measurements are found to be correct, then the agreement between theory and observation is simply a coincidence and the existing discrepancies remain.
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