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Physical Chemistry Chemical Physics

Collisional relaxation of MnH (X7Σ+) in a magnetic field: effect of the nuclear spin of Mn

Thierry Stoecklin, Philippe Halvick

Published Jan 1, 2011• 4 citations
Publisher

Abstract

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.

DOI
10.1039/c1cp21466g

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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 MnH (${}^{7}\ensuremath{\Sigma}$) 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 $\ensuremath{\Delta}{M}_{j}>2$ 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.
We investigate the effect of hyperfine interactions on ultracold molecular collisions in magnetic fields, using 24{}^{24}24Mg(1S)+14{}^{1}S){+}^{14}1S)+14NH(${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$) as a prototype system. We explore the energy and magnetic-field dependence of the cross sections, comparing the results with previous calculations that neglected hyperfine interactions [A.O.G. Wallis and J. M. Hutson, Phys. Rev. Lett. 103, 183201 (2009)]. The main effect of hyperfine interactions for spin relaxation cross sections is that the kinetic energy release of the dominant outgoing channels does not reduce to zero at low fields. This results in reduced centrifugal suppression of the cross sections and increased inelastic cross sections at low energy and low field. We also analyze state-to-state cross sections, for various initial states, and show that hyperfine interactions introduce additional mechanisms for spin relaxation. In particular, there are hyperfine-mediated collisions to outgoing channels that are not centrifugally suppressed. However, for Mg+NH\mathrm{Mg}+\mathit{NH}Mg+NH these unsuppressed channels make only small contributions to the total cross sections. We consider the implications of our results for sympathetic cooling of NH by Mg and conclude that the ratio of elastic to inelastic cross sections remains high enough for sympathetic cooling to proceed.
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.
We explore the quantum dynamics of nuclear spin relaxation in cold collisions of 1 Σ + molecules with structureless atoms in an external magnetic field. To this end, we develop a rigorous coupled-channel methodology, which accounts for rotational and nuclear spin degrees of freedom of 1 Σ + molecules and their interaction with an external magnetic field as well as anisotropic atom–molecule interactions. We apply the methodology to study the collisional relaxation of the nuclear spin sublevels of 13 CO molecules immersed in a cold buffer gas of 4 He atoms. We find that nuclear spin relaxation in the ground rotational manifold ( N = 0) of 13 CO occurs extremely slowly due to the absence of direct couplings between the nuclear spin sublevels. The rates of collisional transitions between the rotationally excited ( N = 1) nuclear spin states of 13 CO are generally much higher due to the direct nuclear spin–rotation coupling between the states. These transitions obey selection rules, which depend on the values of space-fixed projections of rotational and nuclear spin angular momenta ( M N and M I ) for the initial and final molecular states. For some initial states, we also observe a strong magnetic field dependence, which can be understood by using the first Born approximation. We use our calculated nuclear spin relaxation rates to investigate the thermalization of a single nuclear spin state of 13 CO( N = 0) immersed in a cold buffer gas of 4 He. The calculated nuclear spin relaxation times ( T 1 ≃ 1 s at T = 1 K at a He density of 10 –14 cm –3 ) display a steep temperature dependence decreasing rapidly at elevated temperatures due to the increased population of rotationally excited states, which undergo nuclear spin relaxation at a much faster rate. Thus, long relaxation times of N = 0 nuclear spin states in cold collisions with buffer gas atoms can be maintained only at sufficiently low temperatures ( k B T ≪ 2 B e ), where B e is the rotational constant.
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 measure and theoretically determine the effect of molecular rotational splitting on Zeeman relaxation rates in collisions of cold 3Sigma molecules with helium atoms in a magnetic field. All four stable isotopomers of the imidogen (NH) molecule are magnetically trapped and studied in collisions with 3He and 4He. The 4He data support the predicted 1/B_{e};{2} dependence of the collision-induced Zeeman relaxation rate coefficient on the molecular rotational constant B_{e}. The measured 3He rate coefficients are much larger than the 4He coefficients, depend less strongly on B_{e}, and theoretical analysis indicates they are strongly affected by a shape resonance. The results demonstrate the influence of molecular structure on collisional energy transfer at low temperatures.