Abstract
Electronically elastic, electron scattering cross sections are calculated for molecules in particular rotational states in order to establish the sensitivity of the scattering pattern to the quantum state. For the examples of diatomic molecules and symmetric tops considered here, the scattering pattern provides a unique fingerprint of the quantum state if one measures the scattered intensity for different orientations of the scattering vectors. The structure in the scattered intensity reflects the anisotropy of the square of the rotational wavefunction. Even for low angular momentum states which have diffuse rotational wavefunctions, very large differences in intensity are the result at certain scattering angles for states whose quantum numbers differ even by only one unit.
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