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Physical Review A

Quantum enhancement of vibrational predissociation near the dissociation threshold

Robin Côté, E. I. Dashevskaya, E. E. Nikitin, Juergen H. Troe

Published Jan 15, 2004• 10 citations
Publisher

Abstract

We discuss quantum enhancement of the quasiclassical vibrational predissociation (VP) rate of an atom (A)-diatom (BC) van der Waals (vdW) complex $A\ensuremath{-}\mathrm{BC}$ from a state lying close to the dissociation threshold. The enhancement is due to the accumulation of a noticeable fraction of the state population near the outer turning point of the $A\ensuremath{-}\mathrm{BC}$ bond. For potentials behaving as power-laws at large separations, the enhancement manifests itself in the variation of the energy dependence of the VP frequency factor from the classical frequency to its quantum counterpart. We show that it is related to the complex scattering length associated with the vibrational relaxation of BC in collisions with A. We also discuss the corrected quasiclassical quantization condition for energy levels of a diatom lying very close to the dissociation threshold. Our results generalize those of J. Trost, C. Eltshka, and H. Friedrich [J. Phys. B 31, 361 (1998)] and C. Boisseau et al. [Eur. Phys. J. D 12, 199 (2000)] for the calculation of complex energy levels of an anharmonic oscillator that dissociates from highly excited states under the action of a weak high-frequency perturbation.

DOI
10.1103/physreva.69.012704

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We discuss quantum enhancement of the quasiclassical vibrational predissociation (VP) rate of an atom (A)-diatom (BC) van der Waals (vdW) complex A\ensuremath−BCA\ensuremath{-}\mathrm{BC}A\ensuremath−BC from a state lying close to the dissociation threshold. The enhancement is due to the accumulation of a noticeable fraction of the state population near the outer turning point of the A\ensuremath−BCA\ensuremath{-}\mathrm{BC}A\ensuremath−BC bond. For potentials behaving as power-laws at large separations, the enhancement manifests itself in the variation of the energy dependence of the VP frequency factor from the classical frequency to its quantum counterpart. We show that it is related to the complex scattering length associated with the vibrational relaxation of BC in collisions with A. We also discuss the corrected quasiclassical quantization condition for energy levels of a diatom lying very close to the dissociation threshold. Our results generalize those of J. Trost, C. Eltshka, and H. Friedrich [J. Phys. B 31, 361 (1998)] and C. Boisseau et al. [Eur. Phys. J. D 12, 199 (2000)] for the calculation of complex energy levels of an anharmonic oscillator that dissociates from highly excited states under the action of a weak high-frequency perturbation.
Vibrational relaxation of trapped molecules due to collisions with cold atoms is investigated using the results of quantum-mechanical scattering calculations. Trap loss is analyzed using an exactly solvable kinetic model that includes direct collisional quenching and an indirect process of vibrational predissociation. At low atom density, the relaxation is due primarily to collisional quenching. At high atom density, the relaxation involves additional time scales due to the formation and decay of van der Waals complexes. It is shown that the most weakly bound state of the van der Waals complex for a given diatomic vibrational level controls the relaxation at all atom densities. Possible experiments using trapped molecules are discussed.
Quantum-mechanical scattering calculations of Feshbach resonances arising from van der Waals molecule formation are used to determine vibrational and rotational predissociation lifetimes. A multichannel effective range theory is used to establish the relationship between predissociation and the zero-temperature limit of collisional quenching for resonances lying close to the thresholds for dissociation. The elastic scattering Feshbach resonances may be measurable in ultracold atom-molecule experiments.
A comparative study of the vibrational deactivation of 14N2+^{14}\mathrm{N}_{2}^{+}14N2+​ ($\ensuremath{\nu}=1$, j=0j=0j=0) in collision with 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He atoms is investigated. Close-coupling calculations are carried out in the ${10}^{\ensuremath{-}6}--2000\text{\ensuremath{-}}{\mathrm{cm}}^{\ensuremath{-}1}$ kinetic energy range. At very low kinetic energy, it is found that the cross sections for the collision involving 3He^{3}\mathrm{He}3He is strongly enhanced by the presence of a virtual state associated with the van der Waals well. The change of mass from 3He^{3}\mathrm{He}3He to 4He^{4}\mathrm{He}4He also erases a strong shape resonance at $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ supported by the van der Waals well. As a result, the law of variation of the associated vibrational quenching rate coefficient is found to be very different for these two systems. This behavior is further analyzed by drawing the real part of the scattering length as a function of the variable mass of a fictitious He atom. Two zero energy resonances are identified for a mass of, respectively, about 3.18 and 3.85 atomic mass units.
We analyse the influence of the attractive tail of the p–H two-body potential on the energy progression of the near-threshold rotationless bound states of the H molecular ion. For the 1sσ g configuration we study different definitions of the reference potential describing the potential tail. In each case, the scattering length consistent with the energies of the highly excited vibrational states, as calculated by Hilico et al. [Eur. Phys. J. D 12, 449 (2000)], is found to lie in the range between −30.5 and −31 au. In the 2pσ u configuration, for which there is an extremely weakly bound v = 1 vibrational state [Carbonell et al., Europhys. Lett. 64, 316 (2003)], we obtain a scattering length near 762.8 au. In contrast to previously conveyed impressions, the weakly bound v = 1 state can be satisfactorily described as the excited state in a distant shallow potential well of the p–H two-body potential, provided that a sufficient number of terms is included in the representation of the large-distance behaviour of this potential.
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A quantum control mechanism is proposed for molecular fragmentation processes within a scenario grounded on the quantum Zeno effect. In particular, we focus on the van der Waals Ne-Br(2) complex, which displays two competing dissociation channels via vibrational and electronic predissociation. Accordingly, realistic three-dimensional wave packet simulations are carried out by using ab initio interaction potentials recently obtained to reproduce available experimental data. Two numerical models to simulate the repeated measurements are reported and analyzed. It is found that the otherwise fast vibrational predissociation is slowed down in favor of the slow electronic (double fragmentation) predissociation, which is enhanced by several orders of magnitude. Based on these theoretical predictions, some hints to experimentalists to confirm their validity are also proposed.