A study of the momentum dependence of the phase shift for finite range and Coulomb potentials and its possible applications

Exact solution of inverse-square-root potential V(r)=−αr

“…The regular solution is a solution satisfying the boundary condition at r = 0. At r = 0, the boundary condition for both bound states and scattering states is [4] lim r→0 u l (r) r l+1 = 1, (3.1)…”

“…where N (α, β, γ, δ, z) is the Heun biconfluent function [3,6], the constant 4) and the coefficient d ν is given by the recurrence relation…”

“…It is worth to compare the scattering boundary condition (4.14) with the scattering boundary condition of the Coulomb potential, lim r→∞ exp ±i kr − α 2k ln r u l (kr) = 1 [4].…”

Perturbation Theory for Proton-Neutron Scattering: Perturbing the Energy

“…In quantum mechanics the latter case corresponds to the situation where some particles tunnel through barrier into the interaction region. To escape, the particles must penetrate the barrier once more leading to a large time delay [4]. Our work is relevant here as the time delay may be easily expressed in terms of the variation of the phase shift with energy.…”

“…In a more recent work, Milward and Wilkin started from the probability density equation corresponding to a local potential and studied the energy dependence of the s-wave scattering phase shifts upon perturbing the energy by a small amount [3]. An interesting work by Romo and Valluri studied the momentum dependence of the phase shift for local finite range and Coulomb potentials [4]. As pointed out by the authors such studies are important as the time delay in the emergence of scattered particles is related to a change in the phase shift with respect to the wave number [5].…”