Lineshape of rotational spectrum of CO in 4He droplets

In a recent experiment the rovibrational spectrum of CO isotopomers in superfluid helium-4 droplets was measured, and a Lorentzian lineshape with a large line width of 0.024 K (half width at half maximum) was observed [von Haeften et al., Phys. Rev. B 73, 054502 (2006)]. In the accompanying theoretical analysis it was concluded that the broadening mechanism may be homogeneous and due to coupling to collective droplet excitations (phonons). Here we generalize the lineshape analysis to account for the statistical distribution of droplet sizes present in nozzle expansion experiments. These calculations suggest an alternative explanation for the spectral broadening, namely, that the coupling to phonons can give rise to an inhomogeneous broadening as a result of averaging isolated rotation-phonon resonances over a broad cluster size distribution. This is seen to result in Lorentzian lineshapes, with a width and peak position that depend weakly on the size distribution, showing oscillatory behavior for the narrower size distributions. These oscillations decrease with droplet size and for large enough droplets (~104) the line widths saturate at a value equal to the homogeneous line width calculated for the bulk limit.