Effective path length corrections in beam-beam scattering experiments
The effect of the change of scattering geometry with scattering angle in beam-beam experiments is investigated. Atomic (molecular) target distributions associated with static gas, orifice, tube, capillary array (with and without further collimation), and jet sources have been considered in model calculations for a number of commonly used electron scattering geometries. The relationship between scattering intensity, cross section, and the geometrical integral called 'effective path length' is derived. Volume correction factors (the reciprocal of effective path length) have been calculated for sample cases to illustrate the effect of various beam and scattering geometry characteristics. The validity of the model calculation has been experimentally verified. Most of the commonly used scattering geometries require significant correction of the scattering intensity distributions, but with proper planning scattering geometries can be designed such that the intensity and the cross section angular distribution are identical within 1%.