Measuring differential cross sections using the Doppler shift

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Abstract
We discuss two methods, one of them new, for recovering level-specific differential cross sections in crossed molecular beams experiments from the Doppler profiles of line shapes observed by laser induced fluorescence. The angular resolutions of the two methods are compared and shown to be complementary. An experiment using both methods can have moderately good angular resolution at all scattering angles. In the first method, which has previously been demonstrated experimentally, the Dopper profile is taken with the laser beam parallel to the relative velocity of the collision system. Good angular resolution is obtained between π/4 and 3π/4. In the second method, which is proposed here, the Doppler profile is taken with the laser beam perpendicular to this relative velocity, and the best angular resolution is obtained in the regions 0 to π/4 and 3π/4 to π. This method requires an integral transform to recover the cross section from the Doppler profile. A practical implementation of this transform is presented along with a numerical example showing its relative insensitivity to noise in the profile.