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Physical Review A

Isotope effects in complex scattering lengths for He collisions with molecular hydrogen

J. L. Nolte, Benhui Yang, Phillip C. Stancil, Teck-Ghee Lee, N. Balakrishnan, Robert C. Forrey, A. Dalgarno

Published Jan 8, 2010• 12 citations
Publisher

Abstract

We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic ``hydrogen'' masses less than 1 u or a ``helium'' mass of $1.95$ u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ with ${\mathrm{H}}_{2}$, HD, HT, and DT should be feasible in the near future.

DOI
10.1103/physreva.81.014701

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Physical Review A•Nov 30, 2010•6 citations
We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic hydrogen'' masses less than 1 u or a helium'' mass of 1.951.951.95 u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He with H2{\mathrm{H}}_{2}H2​, HD, HT, and DT should be feasible in the near future.
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 present a treatment of cold hydrogen-antihydrogen collisions based on the asymptotic properties of atom-antiatom interactions. We derive general formulas for the elastic and inelastic cross sections and for the scattering lengths and analyze their sensitivity to the parameters characterizing the inelasticity of the collision process. Given the inelasticity, we obtain bounds for the complex scattering length. We investigate the influence of strong nuclear forces and the isotope effects in HH‾\text{H}\overline{\text{H}}HH and DH‾\text{D}\overline{\text{H}}DH collisions and demonstrate enhancement of these effects due to the presence of the near-threshold narrow HH‾\text{H}\overline{\text{H}}HH (DH‾)(\text{D}\overline{\text{H}})(DH) states. The values of the elastic and inelastic cross sections with simultaneous account of rearrangement and strong forces are presented. General expressions for the (complex) energies of the near-threshold HH‾\text{H}\overline{\text{H}}HH states are obtained.
Abstract Motivated by the needs of atomic tritium sources for neutrino mass experiments and Doppler-free two-photon 1 S–2 S spectroscopy in atomic deuterium and tritium, we present calculations of energy-dependent elastic scattering cross sections of hydrogen isotopes (H, D, and T) on helium isotopes ( 3 He and 4 He) in the temperature range 1 mK to 300 K. The tritium-on-helium cross sections are found to be enhanced over their hydrogen-on-helium counterparts by a near-threshold resonant s -wave bound state at low energy, similar to one that has been predicted in the triplet T–T system. While the energy-dependent cross sections span a wide range at low energy due to this s -wave enhancement, they tend toward a common value at high energy where the scattering becomes effectively geometric in nature.
Inducing low-energy p -wave resonances by an additional external electric field has been shown recently to be a possible way of controlling ultra-low energy atomic collisions (Krems R. V., Phys. Rev. Lett. , 96 (2006) 123202). We show here by calculation that also in molecular systems with long-range interactions there exist internal states for which a low energy p -wave resonance is clearly contributing to the scattering even at ultra-low energies, and that for this collisional regime the scattering length turns out to be positive. We thus present results for the vibrational relaxation cross-sections of H 2 , prepared in different vibrational states, in collision with Li + in that energy regime and examine the changes in scattering attributes, both in the elastic and inelastic channels, when the internal vibrational state of H 2 is modified.
Theoretical results for ultracold atom-molecule collisions involving exoergic reactions are presented. Systems with a reaction barrier are considered; specifically, we report the results of extensive computations for D + H 2 and Cl + H2. We analyzed the extreme situation of translationally cold collisions between an atom and an internally hot molecule; namely, for D + H2 we explored the role played by the internal vibrational excitation of the diatomic target for initial states H2(υ) with υ = 0,1,2,…, 8. The υ-dependence of the zero-temperature limit of the reaction rate coefficient shows two distinct regimes: a barrier dominated regime for υ < 4, and a barrierless regime for υ > 4. Also, for highly excited initial states, the distribution over the final states of the products shows an approximate conservation of the internal vibrational energy. For Cl + H2 we studied in detail the isotopic effect by varying continuously the mass of H, which allowed us to find resonance effects in the threshold behavior of cross sections. These resonances are caused by long-lived van der Waals complexes (Cl···H2) which have vanishingly small binding energy, or by virtual states of the Cl···H 2 complex. ^
The translational and internal level cooling of atoms and molecules in ultracold gases results from a combination of elastic and inelastic collisional processes. While elastic collisions lead to rapid thermalization, exoergic inelastic collisions may lead to heating and trap loss. To date, most collisional studies have targeted low-lying levels of diatomic molecules. Here we investigate inelastic quenching and elastic scattering of rotationally excited linear (H2{}_{2}2​, HD, CO, O2{\mathrm{O}}_{2}O2​, and CO2{}_{2}2​) and nonlinear (H2{}_{2}2​O and NH3{}_{3}3​) molecules in ultracold collisions with He and report the corresponding complex scattering lengths. It has been found that the ratio of the imaginary component $\ensuremath{\beta}$ to the real component $\ensuremath{\alpha}$ of the scattering length generally increases with decreasing rotational constant for linear molecules. With the exception of CO, $\ensuremath{\beta}$ becomes significantly smaller than $\ensuremath{\alpha}$ as the energy gap for rotational transitions increases. In all cases, $\ensuremath{\beta}$ decreases with rotational energy gap for relatively large rotational excitation, allowing for convenient fits to an exponential energy gap formula. Excited rotational levels of H2{\mathrm{H}}_{2}H2​ and HD appear to be collisionally stable due to the very low values of $\ensuremath{\beta}/\ensuremath{\alpha}$. Rotationally excited H2{\mathrm{H}}_{2}H2​O also appears to be a viable candidate for He buffer gas cooling due to relatively small values of $\ensuremath{\beta}$.