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

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.