Collisions of paramagnetic molecules in magnetic fields: an analytic model based on Fraunhofer diffraction of matter waves

Abstract

We investigate the effects of a magnetic field on the dynamics of rotationally inelastic collisions of open-shell molecules ($^2Σ$, $^3Σ$, and $^2Π$) with closed-shell atoms. Our treatment makes use of the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric [M. Lemeshko and B. Friedrich, J. Chem. Phys. \textbf{129}, 024301 (2008)] and radiative fields [M. Lemeshko and B. Friedrich, Int. J. Mass. Spec. in press (2008)]. A magnetic field aligns the molecule in the space-fixed frame and thereby alters the effective shape of the diffraction target. This significantly affects the differential and integral scattering cross sections. We exemplify our treatment by evaluating the magnetic-field-dependent scattering characteristics of the He -- CaH ($X ^2Σ^+$), He -- O$_2$ ($X ^3Σ^-$) and He -- OH ($X ^2Π_Ω$) systems at thermal collision energies. Since the cross sections can be obtained for different orientations of the magnetic field with respect to the relative velocity vector, the model also offers predictions about the frontal-versus-lateral steric asymmetry of the collisions. The steric asymmetry is found to be almost negligible for the He -- OH system, weak for the He -- CaH collisions, and strong for the He -- O$_2$. While odd $ΔM$ transitions dominate the He -- OH $(J=3/2,f \to J', e/f)$ integral cross sections in a magnetic field parallel to the relative velocity vector, even $ΔM$ transitions prevail in the case of the He -- CaH ($X ^2Σ^+$) and He -- O$_2$ ($X ^3Σ^-$) collision systems. For the latter system, the magnetic field opens inelastic channels that are closed in the absence of the field. These involve the transitions $N=1, J=0 \to N', J' $ with $J'=N'$.