  We present an analytic model of thermal state-to-state rotationally inelastic
collisions of polar molecules in electric fields. The model is based on the
Fraunhofer scattering of matter waves and requires Legendre moments
characterizing the "shape" of the target in the body-fixed frame as its input.
The electric field orients the target in the space-fixed frame and thereby
effects a striking alteration of the dynamical observables: both the phase and
amplitude of the oscillations in the partial differential cross sections
undergo characteristic field-dependent changes that transgress into the partial
integral cross sections. As the cross sections can be evaluated for a field
applied parallel or perpendicular to the relative velocity, the model also
offers predictions about steric asymmetry. We exemplify the field-dependent
quantum collision dynamics with the behavior of the Ne-OCS($^{1}\Sigma$) and
Ar-NO($^2\Pi$) systems. A comparison with the close-coupling calculations
available for the latter system [Chem. Phys. Lett. \textbf{313}, 491 (1999)]
demonstrates the model's ability to qualitatively explain the field dependence
of all the scattering features observed.
