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

Abstract

An effective potential Ṽ_f0 is defined such that the direct scattering amplitude is expressed by a Borntype integral. It is found that Ṽ_f0 consists of three types of potentials characterized by their q dependence, where q is the distance between the incident electron and the scattering center. The long range potential, ${Ṽ}_{\text{f0}}^{\mathrm{LR}}$ , is important at large q. It is expressed as an inverse power series and expressions up to the q⁻⁶ term are obtained. The first non‐Born term in ${Ṽ}_{\text{f0}}^{\mathrm{LR}}$ is just the dipole polarization potential. The next term is proportional to q⁻⁵ and complex. The oscillatory potential, ${Ṽ}_{\text{f0}}^{\mathrm{OS}}$ , is also expressed as an inverse power series but multiplied by e^iaq. The leading term in ${Ṽ}_{\text{f0}}^{\mathrm{OS}}$ is proportional to q⁻⁴. Because of the presence the oscillatory factor, ${Ṽ}_{\text{f0}}^{\mathrm{OS}}$ will decrease faster than ${Ṽ}_{\text{f0}}^{\mathrm{LR}}$ at large q. At small q, the short range potential ${Ṽ}_{\text{f0}}^{\mathrm{SR}}$ becomes important. It is characterized by an exponential dependence on q. The symmetry properties of ${Ṽ}_{\text{f0}}^{\mathrm{LR}}$ and ${Ṽ}_{\text{f0}}^{\mathrm{OS}}$ are 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 in ${Ṽ}_{00}^{\mathrm{LR}}$ and ${Ṽ}_{00}^{\mathrm{OS}}$ . It is found that some recent experimental results of Bromberg can be qualitatively accounted for by this potential.