Abstract
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 ( approximately 10(4)) the line widths saturate at a value equal to the homogeneous line width calculated for the bulk limit.
Highlights
The reduction of the rotational excitation energies of molecules in superfluid helium-4 has been observed in many experimentssee table in Ref. 1͒ and has been studied extensively by quantum Monte Carlo simulations,[2,3,4,5] by phenomenological approaches based on the two-fluid picture[6,7] or hydrodynamics of ideal fluids,[8] and by quantum many-body theory.[9,10] In principle, this is a well-understood phenomenon: The molecule aquires an increased effective moment of inertia by coupling to excitations of the 4He environment that may be local or collective, depending on the nature of the molecule and its interaction with helium
It is important to understand how this result of an inhomogeneous absorption with Lorentzian lineshape relates to the line width calculation that was based on the bulk CBF theory in Ref. 15
Such a bulk theory necessarily results in a homogeneous line and the conclusion there was that the R0͒ line is homogeneously broadened by the relaxation of the rotational J = 1 excitation of the molecule coupling to a bulk phonon from the continuum of available phonon states and molecule translation states
Summary
The reduction of the rotational excitation energies of molecules in superfluid helium-4 has been observed in many experimentssee table in Ref. 1͒ and has been studied extensively by quantum Monte Carlo simulations,[2,3,4,5] by phenomenological approaches based on the two-fluid picture[6,7] or hydrodynamics of ideal fluids,[8] and by quantum many-body theory.[9,10] In principle, this is a well-understood phenomenon: The molecule aquires an increased effective moment of inertia by coupling to excitations of the 4He environment that may be local or collective, depending on the nature of the molecule and its interaction with helium. In this work we present CBF calculations which suggest an alternative explanation of the measured Lorentzian lineshape for the R0͒ rotational transition state of CO in 4He droplets coupled to the discrete phonon spectrum, namely, an inhomogeneous Lorentzian broadening of rotation/phonon resonances that results from the droplet size distribution in the experimental preparation of the He droplets.[27]. III we present calculations made assuming the log-normal distribution established for helium droplets.[27] These calculations show that the resulting inhomogeneous spectrum for the R0͒ rotational absorption of CO has a Lorentzian lineshape just like the homogeneous bulk spectrum. Both the width and peak position of the spectral line show variations with Nthat are oscillatory for a range of droplet size distributions. In addition to accounting for the inhomogenous Lorentzian lineshapes, the CBF theory accounts for the size dependence of the lineshape features and provides a microscopic description of the coupling of the molecule to the bath levels
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