On the inversion of atomic scattering data: A new algorithm based on functional sensitivity analysis

A new iterative inversion scheme of atomic scattering data within the framework of functional sensitivity analysis is presented. The inversion scheme is based on the first order Fredholm integral equation δσ(θ)=∫∞0K(θ,R)δV(R)R2 dR, K(θ,R)≡δσ(θ)/δV(R), or symbolically, δσ=KδV, which relates infinitesimal functional changes in the elastic differential cross section δσ(θ) and in the underlying interatomic potential δV(R). This equation can be written equivalently, via integration by parts, as δσ(θ)=∫∞0K[n](θ,R) {RnxδV(n)(R)}R2 dR, or δσ=K[n]{RnxδV(n)}, under the a priori assumption that {R(2+n)xK[n](θ,R)xδV(n-1) (R)}|∞R=0=0. Here K[n](θ,R)≡-R-(2+n) x∫R0K[n-1](θ,R') R'(1+n)dR', δV(n)(R) ≡(dn/dRn)δV(R), with n=0,1,2,..., and K[0](θ,R)≡K(θ,R)