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Physical Review A

Energy transfer in atom-dimer collisions

Slobodan Danko Bosanac

Published Apr 1, 1988• 0 citations
Publisher

Abstract

Energy transfer in atom-dimer collisions is analyzed using a model of loosely bound hard spheres. The results are compared with calculations for a real system. It is found that large energy transfer at a particular scattering angle is sensitive to the initial internal state of the dimer. A quantum theory of atom-dimer collisions is developed and it is found that resonances in the dissociation channel of the dimer are expected. The final rotational states of the dimer are also investigated. It is found that large energy transfer occurs with no change in the rotational state of the dimer.

DOI
10.1103/physreva.37.2335

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Energy transfer in atom-dimer collisions is analyzed using a model of loosely bound hard spheres. The results are compared with calculations for a real system. It is found that large energy transfer at a particular scattering angle is sensitive to the initial internal state of the dimer. A quantum theory of atom-dimer collisions is developed and it is found that resonances in the dissociation channel of the dimer are expected. The final rotational states of the dimer are also investigated. It is found that large energy transfer occurs with no change in the rotational state of the dimer.
Three further types of collision between atomic systems in which no change of internal energy takes place are considered. These are collisions in which transfer of excitation occurs between two similar atoms, spin exchange collisions, and collisions in which the direction but not the magnitude of the orbital angular momentum of an excited atom is changed on impact. An account is given of the theory of these processes in relation to that for other processes, elastic scattering and symmetrical charge exchange, discussed in the earlier articles, in which no change of internal energy occurs. Methods for measuring the relevant cross sections are described. These make use of optical pumping and nuclear magnetic resonance techniques. Comparison is made between observed and calculated cross sections.
We consider a dimer formed by two particles with an attractive contact interaction in one dimension, colliding with a hard wall. We compute the scattering phase shifts and the reflection coefficients for various collision energies and various mass ratios of the two particles. For low-energy collisions (with dimer kinetic energies much smaller than the binding energy) our results are consistent with those of D. Lee and M. Pine, The European Physical Journal A 47, 41 (2011). For mass ratios much greater than 1 we use the Born-Oppenheimer approximation to show that the scattering length and the effective range of the dimer-wall collision both depend logarithmically on the mass ratio. For collision energies much greater than the binding energy, the dissociation probability is inversely proportional to the square of the incident momentum of the dimer and we find the constant of proportionality analytically, and we use a semiclassical analysis to approximately derive the ``angular distribution" of the dissociated pair, where the ``angle" θθθ depends on the ratio of the velocities of the two outgoing unbound particles.
We consider weakly bound diatomic molecules (dimers) formed in a two-component atomic Fermi gas with a large positive scattering length for the interspecies interaction. We develop a theoretical approach for calculating atom-dimer and dimer-dimer elastic scattering and for analyzing the inelastic collisional relaxation of the molecules into deep bound states. This approach is based on the single-channel zero-range approximation, and we find that it is applicable in the vicinity of a wide two-body Feshbach resonance. Our results draw prospects for various interesting manipulations of weakly bound dimers of fermionic atoms.
Resonant energy transfer collisions, those in which one atom or molecule transfers only internal energy, as oppposed to translational energy, to its collision partner require a precise match of the energy intervals in the two collision partners. Because of this energy specificity, resonant collisional energy transfer plays an important role in many laser applications, the He–Ne and CO 2 lasers being perhaps the best known examples. It is interesting to imagine an experiment in which we can tune the energy of the excited state of atom B through the energy of the excited state of atom A, as shown in Fig. 14.1. At resonance we would expect the cross section for collisionally transferring the energy from an excited A atom to a ground state B atom to increase sharply as shown in Fig. 14.1. In general, atomic and molecular energy levels are fixed, and the situation of Fig. 14.1 is impossible to realize. Nonetheless systematic studies of resonant energy transfer have been carried out by altering the collision partner, showing the importance of resonance in collisional energy transfer. The use of atomic Rydberg states, which have series of closely spaced levels, presents a natural opportunity for the study of resonant collisional energy transfer. One of the earliest experiments was the observation of resonant rotational to electronic energy transfer from NH 3 to Xe Rydberg atoms by Smith et al .
Quantum and classical quasiresonant vibration-rotation energy transfer is investigated for ultracold $\mathrm{He}\ensuremath{-}{\mathrm{H}}_{2}$ collisions. Classical trajectory computations show that extremely strong correlations between $\ensuremath{\Delta}j$ and $\ensuremath{\Delta}v$ persist at low energies, though the changes themselves are less than one quantum. Quantum computations show that quasiresonant transitions occur in the limit of zero collision energy but that threshold effects become important and that some quasiresonant channels close. The qualitative similarity between classical and quantum results suggests that they share a common mechanism.
Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near two-dimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. As the scattering length is ramped to the large final value at which the atom loss rate is measured, the time-dependent scattering length generates a small condensate of shallow dimers coherently from the atom condensate. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near two-dimer resonances due to inelastic dimer collisions.