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arXiv:1101.2159 · Physical Review A

Zeeman relaxation of MnH ( X7Σ+ ) in collisions with He3 : Mechanism and comparison with experiment

Florence Turpin, Thierry Stoecklin, Philippe Halvick

Published Mar 28, 2011• 6 citations
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Abstract

We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of MnH (${}^{7}\ensuremath{\Sigma}$) in collisions with $^{3}\mathrm{He}$. We analyze the collisional Zeeman transition mechanism as a function of the final diatomic state and its variation as a function of an applied magnetic field. We show that as a result of this mechanism the levels with $\ensuremath{\Delta}{M}_{j}>2$ give negligible contributions to the Zeemam relaxation cross section. We also compare our results to the experimental cross sections obtained from the buffer-gas cooling and magnetic trapping of this molecule and investigate the dependence of the Zeeman relaxation cross section on the accuracy of the three-body interaction at ultralow energies.

DOI
10.1103/physreva.83.032717

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We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of MnH (7\ensuremathΣ{}^{7}\ensuremath{\Sigma}7\ensuremathΣ) in collisions with 3He^{3}\mathrm{He}3He. We analyze the collisional Zeeman transition mechanism as a function of the final diatomic state and its variation as a function of an applied magnetic field. We show that as a result of this mechanism the levels with \ensuremathΔMj>2\ensuremath{\Delta}{M}_{j}>2\ensuremathΔMj​>2 give negligible contributions to the Zeemam relaxation cross section. We also compare our results to the experimental cross sections obtained from the buffer-gas cooling and magnetic trapping of this molecule and investigate the dependence of the Zeeman relaxation cross section on the accuracy of the three-body interaction at ultralow energies.
In the present study we investigate the role played by the hyperfine structure of manganese in the cooling and magnetic trapping of MnH((7)Σ(+)). The effect of the hyperfine structure of Mn on the relaxation of the magnetically trappable maximally stretched low-field seeking state of MnH((7)Σ(+)) in collisions with (3)He is deduced from comparison between the results of the present approach and our previous nuclear spin free calculations. We show that our previous results are unchanged at the temperature of the buffer gas cooling experiment but find a new resonance at very low collision energy. The role played by the different contributions to the hyperfine diatomic Hamiltonian considered in this work as well as the effect of an applied magnetic field on this resonance are also analyzed.
We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of CrH(X6Σ+) in collisions with 3He. A two dimensional potential energy surface (PES) was calculated with the partially spin-restricted coupled cluster singles, doubles, and non-iterative triples [RCCSD(T)] method. The global minimum was found for the collinear He⋯Cr–H geometry with the well depth of 1143.84 cm−1 at Re = 4.15 a0. Since the RCCSD(T) calculations revealed a multireference character in the region of the global minimum, we performed additional calculations with the internally contracted multireference configuration interaction with the Davidson correction (ic-MRCISD+Q) method. The resulting PES is similar to the RCCSD(T) PES except for the region of the global minimum, where the well depth is 3032 cm−1 at Re = 3.8 a0. An insight into the character of the complex was gained by means of symmetry-adapted perturbation theory based on unrestricted Kohn-Sham description of the monomers. Close coupling calculations of the Zeeman relaxation show that although the ΔMJ=MJ′−MJ = −1 and −2 transitions are the dominant contributions to the collisional Zeeman relaxation, ΔMJ<−2 transitions cannot be neglected due to the large value of CrH spin-spin constant. The calculated elastic to inelastic cross section ratio is 1600 for the RCCSD(T) PES and 500 for the MRCISD+Q PES, while the estimate from the buffer-gas cooling and magnetic trapping experiment is 9000.
We report on the buffer-gas cooling and trapping of CrH and MnH molecules in a magnetic quadrupole trap with densities on the order of ${10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ at a temperature of 650mK650\phantom{\rule{0.3em}{0ex}}\mathrm{mK}650mK. Storage times of up to 180ms180\phantom{\rule{0.3em}{0ex}}\mathrm{ms}180ms have been observed, corresponding to a 20-fold lifetime enhancement with respect to the field-free diffusion through the 3He^{3}\mathrm{He}3He buffer-gas. Using Monte Carlo trajectory simulations, inelastic molecule-3He^{3}\mathrm{He}3He collision cross sections of $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ and $3.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$ are extracted for CrH and MnH, respectively. Furthermore, elastic molecule-3He^{3}\mathrm{He}3He collision cross sections of $1.4(\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$ are determined for both species. We conclude that the confinement time of these molecules in a magnetic trapping field is limited by inelastic collisions with the helium atoms leading to Zeeman relaxation.
A detailed analysis of the He-NH((3)Sigma(-)) van der Waals complex is presented. We discuss ab initio calculations of the potential energy surface and fitting procedures with relevance to cold collisions, and we present accurate calculations of bound energy levels of the triatomic complex as well as collisional properties of NH molecules in a buffer gas of (3)He. The influence of the external magnetic field used to trap the NH molecules and the effect of the atom-molecule interaction potential on the collisionally induced Zeeman relaxation are explored. It is shown that minute variations of the interaction potential due to different fitting procedures may alter the Zeeman relaxation rate at ultralow temperatures by as much as 50%.
Ab initio calculations of cross sections and rate constants for elastic scattering and Zeeman relaxation in collisions of $\mathrm{NH}(X{}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}})$ molecules with 3He{}^{3}\mathrm{He}3He atoms in a magnetic field are presented and the mechanism for Zeeman transitions in ground-state ${}^{3}\ensuremath{\Sigma}$ molecules is established. The potential surface for He-NH interaction is obtained using all-electron coupled-cluster calculations with single, double, and noniterative triple excitations in a basis set augmented by bond functions. The ratio of the rates for elastic energy transfer and Zeeman relaxation in NH-3He{}^{3}\mathrm{He}3He collisions exceeds 105{10}^{5}105 at temperatures between 0.50.50.5 and 1 K.
NH radicals are magnetically trapped and their Zeeman relaxation and energy transport collision cross sections with helium are measured. Continuous buffer-gas loading of the trap is direct from a room-temperature molecular beam. The Zeeman relaxation (inelastic) cross section of magnetically trapped electronic, vibrational, and rotational ground state NH molecules in collisions with 3He^{3}\mathrm{He}3He is measured to be $3.8\ifmmode\pm\else\textpm\fi{}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}\text{ }\text{ }{\mathrm{cm}}^{2}$ at 710 mK. The NH-He energy transport cross section is also measured, indicating a ratio of diffusive to inelastic cross sections of $\ensuremath{\gamma}=7\ifmmode\times\else\texttimes\fi{}{10}^{4}$, in agreement with recent theory [R. V. Krems, H. R. Sadeghpour, A. Dalgarno, D. Zgid, J. K\l{}os, and G. Cha\l{}asi\ifmmode \acute{n}\else \'{n}\fi{}ski, Phys. Rev. A 68, 051401 (2003)].