Effective Long Range Potential for the Scattering of Electrons by Atoms and Molecules

摘要

An effective potential Vtilde;f0is defined such that the direct scattering amplitude is expressed by a Borntype integral. It is found that Vtilde;f0consists of three types of potentials characterized by theirqdependence, whereqis the distance between the incident electron and the scattering center. The long range potential,Vtilde;f0LR, is important at largeq. It is expressed as an inverse power series and expressions up to theqminus;6term are obtained. The first nonhyphen;Born term inVtilde;f0LRis just the dipole polarization potential. The next term is proportional toqminus;5and complex. The oscillatory potential,Vtilde;f0OS, is also expressed as an inverse power series but multiplied byeiaq. The leading term inVtilde;f0OSis proportional toqminus;4. Because of the presence the oscillatory factor,Vtilde;f0OSwill decrease faster thanVtilde;f0LRat largeq. At smallq, the short range potentialVtilde;f0SRbecomes important. It is characterized by an exponential dependence onq. The symmetry properties ofVtilde;f0LRandVtilde;f0OSare studied and compared with the selection rules recently obtained by Lassettre. For elastic scattering, a semiempirical effective potential is introduced which incorporates the leading terms inVtilde;00LRandVtilde;00OS. It is found that some recent experimental results of Bromberg can be qualitatively accounted for by this potential.