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arXiv:2110.05681 · The Journal of Chemical Physics

Total angular momentum representation for state-to-state quantum scattering of cold molecules in a magnetic field

Suyesh Koyu, Rebekah Hermsmeier, Timur V. Tscherbul

Published Jan 19, 2022• 5 citations
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Abstract

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.

DOI
10.1063/5.0074844

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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.
Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta J of the collision complex. We show that by restricting the total angular momentum basis to include only the states with helicities K ≤ Kmax, it is possible to obtain accurate elastic and inelastic cross sections for low-temperature He + CaH, Li + CaH, and Li + SrOH collisions in the presence of an external magnetic field at a small fraction of the computational cost of the full coupled-channel calculations (where K is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field, with the minimal basis set (Kmax = 0) producing quantitatively accurate results for, e.g., ultracold Li + CaH and Li + SrOH scattering at low magnetic fields, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in the magnetic field dependence of Li + CaH and Li + SrOH inelastic cross sections in the few partial wave-regime as well as indirect spin relaxation in He + CaH collisions. Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different K and the couplings between the rotational states of the same K induced by the anisotropy of the interaction potential.
We show that the cross sections for molecule-molecule collisions in the presence of an external field can be computed efficiently using a total angular momentum basis, defined either in the body-fixed frame or in the space-fixed coordinate system. This method allows for computations with much larger basis sets than previously possible. We present calculations for (15)NH-(15)NH collisions in a magnetic field. Our results support the conclusion of the previous study that the evaporative cooling of rotationally ground (15)NH molecules in a magnetic trap has a prospect of success.
Cold collisions of polyatomic molecular radicals with S-state atoms in a magnetic field: An ab initio study of He + CH2(X~){\rm CH}_2(\tilde{X})CH2​(X~) CH 2(X) collisions
We develop a rigorous quantum mechanical theory for collisions of polyatomic molecular radicals with S-state atoms in the presence of an external magnetic field. The theory is based on a fully uncoupled space-fixed basis set representation of the multichannel scattering wave function. Explicit expressions are presented for the matrix elements of the scattering Hamiltonian for spin-1/2 and spin-1 polyatomic molecular radicals interacting with structureless targets. The theory is applied to calculate the cross sections and thermal rate constants for spin relaxation in low-temperature collisions of the prototypical organic molecule methylene [CH(2)(X(3)B(1))] with He atoms. To this end, two accurate three-dimensional potential energy surfaces (PESs) of the He-CH(2)(X(3)B(1)) complex are developed using the state-of-the-art coupled-cluster method including single and double excitations along with a perturbative correction for triple excitations and large basis sets. Both PESs exhibit shallow minima and are weakly anisotropic. Our calculations show that spin relaxation in collisions of CH(2), CHD, and CD(2) molecules with He atoms occurs at a much slower rate than elastic scattering over a large range of temperatures (1 μK-1 K) and magnetic fields (0.01-1 T), suggesting excellent prospects for cryogenic helium buffer-gas cooling of ground-state ortho-CH(2)(X(3)B(1)) molecules in a magnetic trap. Furthermore, we find that ortho-CH(2) undergoes collision-induced spin relaxation much more slowly than para-CH(2), which indicates that magnetic trapping can be used to separate nuclear spin isomers of open-shell polyatomic molecules.
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 MS=12{M}_{S}=\frac{1}{2}MS​=21​ 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 Be<4{B}_{e}<4Be​<4 cm${}^{\ensuremath{-}1}$.
We present an accurate quantum mechanical study of molecule–molecule collisions in the presence of a magnetic field. The work focuses on the analysis of elastic scattering and spin relaxation in collisions of O 2 ( 3 Σ g – ) molecules at cold (∼0.1 K) and ultracold (∼10 –6 K) temperatures. Our calculations show that magnetic spin relaxation in molecule–molecule collisions is extremely efficient except at magnetic fields below 1 mT. The rate constant for spin relaxation at T =0.1 K and a magnetic field of 0.1 T is found to be as large as 6.1 × 10 –11 cm –3 s –1 . The magnetic field dependence of elastic and inelastic scattering cross sections at ultracold temperatures is dominated by a manifold of Feshbach resonances with the density of ∼100 resonances per Tesla for collisions of molecules in the absolute ground state. This suggests that the scattering length of ultracold molecules in the absolute ground state can be effectively tuned in a very wide range of magnetic fields. Our calculations demonstrate that the number and properties of the magnetic Feshbach resonances are dramatically different for molecules in the absolute ground and excited spin states. The density of Feshbach resonances for molecule–molecule scattering in the low-field-seeking Zeeman state is reduced by a factor of 10.