In its original form, Glauber scattering theory achieves a considerable simplification by neglecting several factors of modest consequence in atomic scattering but of importance in molecular scattering. These include, in particular, the spread of the shadow cast by a scatterer as a wave propagates downstream in the target. Although such effects do not matter in the original range of validity of the theory, the characteristic distances in molecules restrict the unmodified theory to an excessively small angular range. The present treatment introduces phase factors to take into account the distribution of scatterers in the incident direction and the propagation of the scattered waves in the target. This appreciably extends the formal range of applicability.
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