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arXiv:cond-mat/0502198 · Physical Review B

Suppression of inelastic bound-state resonance effects by the dimensionality of an atom-surface scattering event

Antonio Šiber, B. Gumhalter

Published Feb 8, 2005• 13 citations
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Abstract

We develop a multidimensional coupled-channel method suitable for studying the interplay of bound-state resonance and phonon-assisted scattering of inert gas atoms from solid surfaces in one, two, and three dimensions. This enables us to get insight into the features that depend on the dimensionality of inelastic resonant processes typically encountered in low-energy He atom scattering from surfaces, in general, and to elaborate on the observability of recently conjectured near threshold resonances in scattering from Einstein phonons, in particular.

DOI
10.1103/physrevb.71.081401

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We develop a multidimensional coupled-channel method suitable for studying the interplay of bound-state resonance and phonon-assisted scattering of inert gas atoms from solid surfaces in one, two, and three dimensions. This enables us to get insight into the features that depend on the dimensionality of inelastic resonant processes typically encountered in low-energy He atom scattering from surfaces, in general, and to elaborate on the observability of recently conjectured near threshold resonances in scattering from Einstein phonons, in particular.
We present a detailed study of the bound-state phonon-mediated resonances in atom-surface scattering that extends our earlier work [\ifmmode \check{S}\else \v{S}\fi{}iber and Gumhalter, Phys. Rev. B 71, 081401 (2005)]. Previous results obtained within the restricted Fock space coupled-channel algorithm are reconsidered in view of the enlargement and refinement of the basis of quantum states used in the calculation. The convergence demonstrated in this procedure reinforces the usefulness of the developed algorithm.
The bound-state-plus-two-phonon resonances in scattering of atoms by surface phonons are considered in detail. We compute the dependence of single phonon transition probabilities on the initial energy performing large-scale coupled channel calculations. It turns out that the resonances in this case are relatively strong and sharp. Furthermore, due to a new implementation we are able to consider two- and three-phonon resonances in the scattering in full detail. It turns out the two phonon resonances should be observable but three phonon resonances not.
We present a comparative assessment of the features of inelastic atom-surface scattering spectra that are produced by different forms of linear and nonlinear phonon coupling to the projectile atom. Starting from a simple theoretical model of atom-surface scattering and employing recently developed exact numerical and approximate analytical methods we calculate and compare the scattering probabilities ensuing from each form of interaction. This enables us to demonstrate that in the regime of thermal energy atom scattering from surfaces the dominant contributions to the zero-, one-, and multiphonon excitation probabilities arise from linear coupling treated to all orders in the interaction.
The role of shape resonances and many-body effects on universal quantum sticking of ultracold atoms onto solid surfaces is examined analytically and computationally using an exactly solvable representation of the Dyson equation. We derive the self-energy renormalization of the transition amplitude between an ultracold scattering atom and the bound states on the surface in order to elucidate the role of virtual phonon exchanges in the limiting behavior of the sticking probability. We demonstrate that, to first order in the interactions for finite ranged atom–surface potentials, virtual phonons can only rescale the strength of the atom–surface coupling and do not rescale the range of the coupling. Thus, universal sticking behavior at ultralow energies is to be expected for all finite ranged potentials. We demonstrate that the onset of the universal sticking behavior depends greatly on the position of the shape resonance of the renormalized potential and for sufficiently low energy shape resonances, deviations from the universal s(E)∝√E can occur near these energies. We believe that this accounts for many of the low energy sticking trends observed in the scattering of submillikelvin H atoms from superfluid 4He films.
The zero energy scattering limit of inelastic molecule–surface scattering is studied within the context of a multiphonon expansion of the molecule–bath wave function. By assuming that at low scattering energies the expansion may be truncated at first order in the phonon operators, we derived a closed form solution to the Lippmann Schwinger equation for the scattering wave function which includes a nonlocal and energy dependent self-energy term which correctly incorporates virtual phonon transitions in the elastic channel. The closure relation results from the use of a discrete spectral (ℒ2) form of the inelastic channel Greens functions. We compute the zero energy limit of these wave functions and discuss the trapping and reflection of cold atoms from ultracold surfaces. Our results indicate that for realistic atom surface interactions the low energy limit of the sticking coefficient, s, can deviate markedly from the expected s∝E1/2 behavior and is shown to approach a constant nonzero limiting value. This trend is consistent with recent experimental work involving the sticking of spin polarized hydrogen atoms on liquid He films.
We present a semianalytical treatment of both the elastic and inelastic collisional properties near a ppp-wave Feshbach resonance. Our model is based on a simple three-channel system that reproduces more elaborate coupled-channel calculations. We stress the main differences between sss-wave and ppp-wave scattering. We show in particular that, for elastic and inelastic scattering close to a ppp-wave Feshbach resonance, resonant processes dominate over the low-energy behavior.