The polarisation labelling spectroscopy method is applied to study the C^1Σ^+← X^1 Σ^+ band system of the KLi molecule. Rotationally resolved polarisation spectra are observed in the spectral range of 17150-20350 cm^{-1}. A set of Dunham coefficients describes the C^1Σ^+ state to 95% of its potential well depth, and the potential curve is constructed by the Rydberg-Klein-Rees procedure. The molecular parameters deduced from this work are compared with theoretical calculations.
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