Mathematical model of beam intensity dispersion at the detector plane in a molecular-beam apparatus

A mathematical model of intensity dispersion at the detector plane in a molecular-beam apparatus has been developed for the case of a ribbon-shaped beam effusing from a narrow rectangular slit. The model is developed in terms of position probability distribution functions and Maxwellian velocity distribution functions. The relation derived for the axial flux density is nv-bar(δx')(δx')/4π2L2 in units of number of particles per unit area per unit time. A plot of flux density versus off-axis position agrees with the reported distributions obtained experimentally