# Quantum Theory of Molecular Collisions in a Magnetic Field: Efficient Calculations Based on the Total Angular Momentum Representation

 Title: Quantum Theory of Molecular Collisions in a Magnetic Field: Efficient Calculations Based on the Total Angular Momentum Representation Author: Dalgarno, Alexander; Tscherbul, Timur V. Note: Order does not necessarily reflect citation order of authors. Citation: Tscherbul, Timur V. and Alexander Dalgarno. 2010. Quantum theory of molecular collisions in a magnetic field: Efficient calculations based on the total angular momentum representation. Journal of Chemical Physics 133(18): 184104. Full Text & Related Files: Dalgarno_Quantum.pdf (348.2Kb; PDF) Abstract: An efficient method is presented for rigorous quantum calculations of atom-molecule and molecule-molecule collisions in a magnetic field. The method is based on the expansion of the wavefunction of the collision complex in basis functions with well-defined total angular momentum in the body-fixed coordinate frame. We outline the general theory of the method for collisions of diatomic molecules in the $$^{2}\Sigma$$ and $$^{3}\Sigma$$ electronic states with structureless atoms and with unlike $$^{2}\Sigma$$ and $$^{3}\Sigma$$ molecules. The cross sections for elastic scattering and Zeeman relaxation in low-temperature collisions of CaH($$^{2}\Sigma^{+}$$) and NH($$^{3}\Sigma^{-}$$) molecules with $$^{3}$$He atoms converge quickly with respect to the number of total angular momentum states included in the basis set, leading to a dramatic >10-fold enhancement in computational efficiency compared to the previously used methods [A. Volpi and J. L. Bohn, Phys. Rev. A 65, 052712 (2002); R. V. Krems and A. Dalgarno, J. Chem. Phys. 120, 2296 (2004)]. Our approach is thus well suited for theoretical studies of strongly anisotropic molecular collisions in the presence of external electromagnetic fields. Published Version: doi:10.1063/1.3503500 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:5141368

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