Comparison of quasar absorption line spectra with laboratory spectra provides a precise probe for variability of the fine structure constant, alpha, over cosmological time-scales. We constrain variation in alpha in 21 Keck/HIRES Si IV absorption systems using the alkali doublet (AD) method in which changes in alpha are related to changes in the doublet spacing. The precision obtained with the AD method has been increased by a factor of 3: da/a = (-0.5 +/- 1.3) * 10^{-5}. We also analyse potential systematic errors in this result. Finally, we compare the AD method with the many-multiplet method which has achieved an order of magnitude greater precision and we discuss the future of the AD method.
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