CORRELATED MEASUREMENTS IN LEAST SQUARES ANALYSIS OF HYPERFINE SPLITTINGS
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Date
1970
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Ohio State University
Abstract
In microwave spectroscopy, hyperfine coupling constants are often obtained by analysing the frequency splittings of a multiplet, rather than the absolute frequencies. In such a case, the errors in experimental observables are correlated, and the usual least squares technique should be modified. In practice, we find that the modification changes the constants by much less than their rms errors, thus validating previous work using the normal technique. In $CO(CN)_{2}$, the quadrupole coupling constants are $\chi_{aa} = -2.841 \pm 0.022$ MHz ($\chi_{bb}-\chi_{cc}) = -2.745 \pm 0.041$ MHz for the usual technique, and $\chi_{aa} = -2.846 \pm 0.033, (\chi_{bb}-\chi_{cc}) = -2.757 \pm 0.061$ for the correct technique.
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Author Institution: Physics Department, University of New Brunswick