Simplified solutions of the Cox–Thompson inverse scattering method at fixed energy

Abstract

Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta are contributing to the scattering process. Based on new formulas various approximate methods are introduced which prove applicable also to the generic scattering events.

On nonsingular potentials of Cox–Thompson inversion scheme

“…Applications (see Refs. [6,8,9,10,11,12]) of the Cox-Thompson scheme for |S| > 1 suggest the existence of a connection similar to the Corollary of Section 2 that specifies one nonsingular potential out of the possible infinite singular solutions. However such a theorem has, as yet, not been proven.…”

Quantum mechanical inverse scattering problem at fixed energy: a constructive method

“…Taking both equation ( 18) and ( 17) for large r's, i.e. at r → ∞ we get the system of nonlinear equations [11,12,13] connecting {δ ℓ } ℓ∈S to T :…”

“…It was used to recover interaction potentials (see e.g. [11,12,13]) for various physical system. Furthermore it is also possible to generalize the method to recover potentials having Coulomb tail e.g.…”

Development of a Cox–Thompson inverse scattering method to charged particles

“…with the coefficients a L , b L defined via the asymptotic expansion functions A a L (x) ≡ A L (x → ∞) which admits a periodic expansion [15] as…”

“…In the recent decade another procedure, the Cox-Thompson (CT) inverse quantum scattering method [12], has been investigated [13][14][15]. This method has the advantage that it requires a finite set of phase shifts and possesses a non-zero first momentum of the potential generated.…”