Moment Analysis of Atomic Spectral Lines

The moments of a spectral line are evaluated in a general way and compared with results which invoke standard assumptions of line-broadening theory. Cesium-rare-gas systems are analyzed for a variety of experimental conditions in the hope of extracting useful information about excited-state interactions. The computation uses atomic-beam results for the ground-state interaction and assumes that the excited-state potentials are represented to a first approximation by $V_f=\frac{G}{R^{12}}-\frac{D}{R^6}$. The calculation, which includes a comparison of line shapes, indicates that the following numbers (in cgs units) are reliable for the long-wavelength component of the resonance lines of cesium: with argon, $G=4.87\mathrm{}\times {10}^{-102\mathrm{}}$, $D=4.74\mathrm{}\times {10}^{-58\mathrm{}}$; with helium, $G=0.459\mathrm{}\times {10}^{-102\mathrm{}}$ and $D=-0.614\mathrm{}\times {10}^{-58\mathrm{}}$. Analysis of the cesium-xenon system yields results which illuminate the practical difficulties associated with an otherwise attractive technique.