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We investigate the effects of a magnetic field on the dynamics ofrotationally inelastic collisions of open-shell molecules ($^2\Sigma$,$^3\Sigma$, and $^2\Pi$) with closed-shell atoms. Our treatment makes use ofthe Fraunhofer model of matter wave scattering and its recent extension tocollisions 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 themolecule in the space-fixed frame and thereby alters the effective shape of thediffraction target. This significantly affects the differential and integralscattering cross sections. We exemplify our treatment by evaluating themagnetic-field-dependent scattering characteristics of the He -- CaH ($X^2\Sigma^+$), He -- O$_2$ ($X ^3\Sigma^-$) and He -- OH ($X ^2\Pi_{\Omega}$)systems at thermal collision energies. Since the cross sections can be obtainedfor different orientations of the magnetic field with respect to the relativevelocity vector, the model also offers predictions about thefrontal-versus-lateral steric asymmetry of the collisions. The steric asymmetryis 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 $\Delta M$transitions dominate the He -- OH $(J=3/2,f \to J', e/f)$ integral crosssections in a magnetic field parallel to the relative velocity vector, even$\Delta M$ transitions prevail in the case of the He -- CaH ($X ^2\Sigma^+$)and He -- O$_2$ ($X ^3\Sigma^-$) collision systems. For the latter system, themagnetic field opens inelastic channels that are closed in the absence of thefield. These involve the transitions $N=1, J=0 \to N', J' $ with $J'=N'$.

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