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Physical Review A

Strong isotope effect in ultracold collision of N2+ ( ν=1 , j=0 ) with He: A case study of virtual-state scattering

Thierry Stoecklin, A. Voronin

Published Oct 26, 2005• 34 citations
Publisher

Abstract

A comparative study of the vibrational deactivation of $^{14}\mathrm{N}_{2}^{+}$ ($\ensuremath{\nu}=1$, $j=0$) in collision with $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ 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 $^{3}\mathrm{He}$ is strongly enhanced by the presence of a virtual state associated with the van der Waals well. The change of mass from $^{3}\mathrm{He}$ to $^{4}\mathrm{He}$ 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.

DOI
10.1103/physreva.72.042714

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A comparative study of the vibrational deactivation of 14N2+^{14}\mathrm{N}_{2}^{+}14N2+​ (\ensuremathν=1\ensuremath{\nu}=1\ensuremathν=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\ensuremath-cm\ensuremath−1{10}^{\ensuremath{-}6}--2000\text{\ensuremath{-}}{\mathrm{cm}}^{\ensuremath{-}1}10\ensuremath−6−−2000\ensuremath-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×\else\texttimes\fi10\ensuremath−3cm\ensuremath−15\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}5\ifmmode×\else\texttimes\fi10\ensuremath−3cm\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.
A quantum-mechanical investigation of the vibrational deactivation of ${}^{14}{\mathrm{N}}_{2}(\ensuremath{\nu}=1,{j}_{\mathrm{rot}}=j)$ in the ultracold collisions with 3He{}^{3}\mathrm{He}3He atoms is presented. Ab initio potential-energy calculations are carried out at BCCD(T) level and a global three-dimensional potential-energy surface is obtained by fitting ab initio points within the reproducing kernel Hilbert space method. Close coupling scattering calculations are performed at collision energy ranging from ${10}^{\ensuremath{-}6}$ to 2000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. It is shown that the potential-energy surface supports a series of shape and Feshbach resonances. Their influence on the behavior of elastic and inelastic cross sections and quenching rate coefficients is discussed. It is demonstrated that, similar to the ${\mathrm{H}\mathrm{e}\ensuremath{-}\mathrm{O}}_{2}$ system, the rate coefficients exhibit three different regimes: Wigner regime at very low temperatures, van der Waals regime at intermediate temperatures due to series of resonances, and the usual rovibration--translation energy transfer regime at high temperatures.
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.
Helium dimer in its metastable triplet electronic state, He2(a 3Σu+)_2(a~^3Σ_u^+)2​(a 3Σu+​), is a promising candidate for direct laser cooling and precision measurements. Interactions and collisions involving He2(a 3Σu+)_2(a~^3Σ_u^+)2​(a 3Σu+​) remain unexplored in ultracold and cold energy domains. Here, we present the first theoretical investigation of intermolecular interactions and collision dynamics of He2(a 3Σu+)_2(a~^3Σ_u^+)2​(a 3Σu+​)+Ne van der Waals complex. For the ground electronic state, X 3A′X~^3\mathrm{A}'X 3A′, we employ a spin-restricted coupled cluster method with single, double, and noniterative triple excitations. The resulting interaction potential exhibits an extremely shallow well with a depth of 4.612 cm−1^{-1}−1. We construct a three-dimensional vibrationally averaged potential energy surface. Using this surface, we perform full close-coupling calculations including fine-structure levels of He2(a 3Σu+)_2(a~^3Σ_u^+)2​(a 3Σu+​) to investigate collisional excitation and quenching induced by Ne. We analyze the low-energy scattering dynamics and model resonant features associated with quasi-bound states supported by interaction potential. Propensity rule for fine-structure conserving transitions is established. We additionally consider He2_22​+Ar collisions and compare their energy dependence and resonance structure with those of He2_22​+Ne. The He2_22​+Ar system exhibits a richer resonance structure, highlighting the sensitivity of low-energy scattering to interaction potential and reduced mass. Calculated PES and scattering properties provide a reliable benchmark for description of He2_22​+Ne van der Waals complex and may be useful for interpretation of future experimental spectra and collision measurements.
We present results of quantum mechanical scattering calculations including full rovibrational coupling on the relaxation of vibrationally excited H2{\mathrm{H}}_{2}H2​ molecules in collision with ultracold 3He{}^{3}\mathrm{He}3He and 4He{}^{4}\mathrm{He}4He atoms. The exothermic vibrational deactivation cross sections exhibit minima at translational temperatures near 10 K and show an inverse velocity dependence in accordance with Wigner's threshold law in the limit of zero kinetic energy. The corresponding rate coefficients exhibit minima before attaining constant values below ${10}^{\ensuremath{-}3}$ K. The rate coefficients increase by 3 orders of magnitude when the initial vibrational level of the molecule is raised from v=1v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1v=1 to v=10v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10v=10. The results suggest that quasibound resonance states of 3HeH2{}^{3}{\mathrm{HeH}}_{2}3HeH2​ and 4HeH2{}^{4}{\mathrm{HeH}}_{2}4HeH2​ exist, associated with each excited vibrational state of H2{\mathrm{H}}_{2}H2​, and that both the triatomic species 3HeH2{}^{3}{\mathrm{HeH}}_{2}3HeH2​ and 4HeH2{}^{4}{\mathrm{HeH}}_{2}4HeH2​ have one bound vibrational state.
In a recent work we compared spin-free collisions of N2+\mathrm{N}_{2}{}^{+}N2​+ with 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He using a newly developed potential energy surface. We found that such collisions exhibit a strong isotope effect in the ultracold regime. In the present study we consider the role of the spin-rotation interaction in cold $\mathrm{He}\text{\ensuremath{-}}\mathrm{N}_{2}{}^{+}$ collisions. We find that our spin-free vibrational quenching cross sections are not affected. Conversely, the cross sections for rotational quenching are strongly modified in the ultracold regime and exhibit resonance structures which are analyzed. These structures, which are not observed when the spin-rotation interaction is omitted, are shown to be due to the Feshbach resonances associated with the nonconservation of parity.
Accurate quantum calculations have been carried out at ultralow energies (from ${10}^{\ensuremath{-}2}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}{10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) for the vibrational deexcitation of ${\mathrm{Li}}_{2}(^{1}\ensuremath{\Sigma}_{g}^{+})$ by collisions with He, starting from a broad range of initial highly excited vibrational levels. The results indicate the clear dominance of a few transitions with the smallest $\ensuremath{\Delta}\ensuremath{\nu}$ changes and show the overall deexcitation cross sections to markedly depend on the initial vibrational state of the molecule, in line with earlier results on H2+He{\mathrm{H}}_{2}+\mathrm{He}H2​+He [Balakrishan et al. Phys. Rev. Lett. 80, 3224 (1998)] vibrational quenching. A connection is made with very recent measurements on the vibrational quenching of ultracold Cs2{\mathrm{Cs}}_{2}Cs2​ molecules in optical traps that were instead found to behave in a very different manner. Numerical experiments on the present system as well as on the H3{\mathrm{H}}_{3}H3​ reaction strongly suggest a possible explanation for such differences.