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arXiv:1308.0771 · Physical Review A

Elastic and inelastic collisions of 2Σ molecules in a magnetic field

Jie Cui, Roman V. Krems

Published Oct 11, 2013• 6 citations
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Abstract

We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the rovibrational ground state of a ${}^{2}\ensuremath{\Sigma}$ electronic state and the Zeeman state with the electron spin projection ${M}_{S}=\frac{1}{2}$ on the magnetic field axis. This is the lowest-energy state of ${}^{2}\ensuremath{\Sigma}$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule-molecule interaction potentials, which yield the expectation intervals for the cross sections and the elastic-to-inelastic cross-section ratios. We find that the elastic-to-inelastic cross-section ratios under conditions corresponding to trapped molecular ensembles at $T\ensuremath{\sim}{10}^{\ensuremath{-}3}$ K exceed 100 for the majority of ${}^{2}\ensuremath{\Sigma}$ molecules. The range of ${}^{2}\ensuremath{\Sigma}$ molecules expected to be collisionally unstable in magnetic traps at $T<{10}^{\ensuremath{-}3}$ K is limited to molecules with the spin-rotation interaction constant ${\ensuremath{\gamma}}_{\mathrm{SR}}>0.5$ cm${}^{\ensuremath{-}1}$ and the rotational constant ${B}_{e}<4$ cm${}^{\ensuremath{-}1}$.

DOI
10.1103/physreva.88.042705

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We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the rovibrational ground state of a 2\ensuremathΣ{}^{2}\ensuremath{\Sigma}2\ensuremathΣ electronic state and the Zeeman state with the electron spin projection MS=12{M}_{S}=\frac{1}{2}MS​=21​ on the magnetic field axis. This is the lowest-energy state of 2\ensuremathΣ{}^{2}\ensuremath{\Sigma}2\ensuremathΣ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule-molecule interaction potentials, which yield the expectation intervals for the cross sections and the elastic-to-inelastic cross-section ratios. We find that the elastic-to-inelastic cross-section ratios under conditions corresponding to trapped molecular ensembles at T\ensuremath∼10\ensuremath−3T\ensuremath{\sim}{10}^{\ensuremath{-}3}T\ensuremath∼10\ensuremath−3 K exceed 100 for the majority of 2\ensuremathΣ{}^{2}\ensuremath{\Sigma}2\ensuremathΣ molecules. The range of 2\ensuremathΣ{}^{2}\ensuremath{\Sigma}2\ensuremathΣ molecules expected to be collisionally unstable in magnetic traps at T<10\ensuremath−3T<{10}^{\ensuremath{-}3}T<10\ensuremath−3 K is limited to molecules with the spin-rotation interaction constant \ensuremathγSR>0.5{\ensuremath{\gamma}}_{\mathrm{SR}}>0.5\ensuremathγSR​>0.5 cm\ensuremath−1{}^{\ensuremath{-}1}\ensuremath−1 and the rotational constant Be<4{B}_{e}<4Be​<4 cm\ensuremath−1{}^{\ensuremath{-}1}\ensuremath−1.
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.
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The binary collision dynamics of 2Dg,3/2{}^{2}{D}_{g,3/2}2Dg,3/2​ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.
We describe calculations of elastic and inelastic scattering of neutral molecules and cold ions in a magnetic field. The molecule is assumed to have a magnetic and electric dipole moment. The external magnetic field splits the ground rovibrational energy levels of the molecule. The highest energy state within the ground rovibrational manifold increases in energy as the distance to the ion decreases leading to a repelling potential. At low energy, inelastic collisions are strongly suppressed due to the large distance of closest approach. Thus, a collision between a neutral molecule and a cold ion will lead to a decrease in the molecule's kinetic energy with no change in internal energy. We present results for the specific case of OH molecules cooled by Be+{\mathrm{Be}}^{+}Be+, Mg+{\mathrm{Mg}}^{+}Mg+, or Ca+{\mathrm{Ca}}^{+}Ca+ ions. Also, we perform molecular dynamics simulations of ions and molecules in a combined Paul trap and time-averaged orbiting potential trap. Our results suggest that sympathetic cooling of neutral molecules by ions would be possible if cold ions and molecules could be simultaneously trapped.
We show that the integral cross sections for state-to-state quantum scattering of cold molecules in a magnetic field can be efficiently computed using the total angular momentum representation despite the presence of unphysical Zeeman states in the eigenspectrum of the asymptotic Hamiltonian. We demonstrate that the unphysical states arise due to the incompleteness of the space-fixed total angular momentum basis caused by using a fixed cutoff value Jmax for the total angular momentum of the collision complex J. As a result, certain orbital angular momentum (l) basis states lack the full range of J values required by the angular momentum addition rules, resulting in the appearance of unphysical states. We find that by augmenting the basis with a full range of J-states for every l, it is possible to completely eliminate the unphysical states from quantum scattering calculations on molecular collisions in external magnetic fields. To illustrate the procedure, we use the augmented basis sets to calculate the state-to-state cross sections for rotational and spin relaxation in cold collisions of 40CaH(X2Σ+, v = 0, N = 1, MN = 1, MS = 1/2) molecules with 4He atoms in a magnetic field. We find excellent agreement with benchmark calculations, validating our proposed procedure. We find that N-conserving spin relaxation from the highest-energy to the lowest-energy Zeeman state of the N = 1 manifold, |1112〉→|1−1−12〉 is nearly completely suppressed due to the lack of spin–rotation coupling between the fully spin-stretched Zeeman states. Our results demonstrate the possibility of rigorous, computationally efficient, and unphysical state-free quantum calculations on cold molecular collisions and on near-threshold energy levels of strongly anisotropic atom-molecule collision complexes in an external magnetic field.