Evaporative Cooling of Helium Nanodroplets with Angular Momentum Conservation

Abstract

Evaporative cooling of helium nanodroplets is studied with a statistical rate model that includes, for the first time, angular momentum conservation as a constraint on the accessible droplet states. It is found that while the final temperature of the droplets is almost identical to that previously predicted and later observed, the distribution of total droplet energy and angular momentum states is vastly more excited than a canonical distribution at the same temperature. It is found that the final angular momentum of the droplets is highly correlated with the initial direction, and that a significant fraction of the alignment of the total angular momentum should be transferred to the rotational angular momentum of an embedded molecule.The study of helium nanodroplets has received considerable attention in the past decade. 1,2,3 Such droplets rapidly cool by helium atom evaporation while they travel inside a vacuum chamber. Brink and Stringari 4 used a statistical evaporation model and predicted a terminal temperature of 4 He nanodroplets of 0.4 K, in excellent agreement with the value of 0.38 K later deduced from the rotational structure in vibrational spectra of SF 6 and other molecules. 5,6 Despite the obvious success of this theoretical work, the model used is clearly incomplete in that the constraint of angular momentum conservation was not imposed. The need for a more complete evaporative cooling study was made evident by the recent observation of a polarization anisotropy in the absorption spectrum of pentacene in helium droplets. 7 The authors of this work suggested that the total angular momentum deposited in the droplets by the pickup of a heavy molecule is aligned perpendicular to the droplet velocity, and that this droplet alignment survives the evaporative cooling and is transferred to the embedded molecule. The present study was undertaken to test the reasonableness of this conjecture.We model the evaporative cooling with a statistical rate approach, analogous to phase space theory in unimolecular dissociation, which explicitly includes the constraints of angular momentum conservation. 8 We use Monte Carlo sampling to follow cooling 'trajectories' as the droplets lose much of their initial energy and angular momentum by helium atom evaporation. It is found that the droplets cool to final temperatures close to those predicted without angular momentum constraints. 4 However, the distribution of terminal droplet states (where the evaporative cooling lifetime becomes longer than typical flight times in experiments) cover a vastly broader range of energy (E) and total angular momentum (J) than was previously expected. Further, it is found that the final angular momentum vector of the droplet is highly correlated with the initial value, such that much of the alignment remains, and that a sizable fraction of this alignment is transfered to an embedded rotor.Evaporative Cooling Model -Consider a helium nanodroplet, D, with initial values of the conserved quantities n (number of helium atoms), E ′ (total int...

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“…In that case, the deformation of the droplet might result in an anisotropic potential and alignment of the molecule. Later, evaporative cooling of droplets were revisited with a statistical model including the angular momentum conservation, and it was concluded that a significant fraction of the alignment of the total angular momentum should be transferred to the rotational angular momentum of an embedded molecule [29].…”

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“…It has been shown 36 that some of the angular momentum deposited in the droplet during the pick-up process may be kept in the impurity atom, resulting in a different angular momentum distribution from the Boltzmann one. This could yield that some Mg atoms are actually closer to the drop surface.…”

Spectroscopy and dynamics in helium nanodroplets

“…If we assume the droplets statistically distribute this energy, the temperature of the droplets will raise to several K, typically above the λ transition of bulk helium. Following this temperature jump, the droplets will rapidly cool by helium evaporation [83,101].…”

“…However, the evaporative cooling calculations predict that for droplet in the size range studied in most experiments, the spread of final energies for a given droplet size is determined by the evaporation energy, not the energy fluctuations of a canonical ensemble. Perhaps more importantly, an isolated droplet must also conserve total angular momentum, J, and thus should be described by an ensemble that has both E and J as good quantum numbers [101].…”