Coulomb corrections in non-relativistic scattering

Effective range function below threshold

“…momentum and the complex function g ℓ (k) can be interpreted as a generalized barrier penetration factor. This function has been studied in several papers [6,7,8,9,10,11], and, g ℓ (k) = i k 2ℓ+1 /[(2ℓ + 1)!!] 2 for Z = 0, whereas for Z = 0 its explicit form is…”

“…It should be recalled here that g ℓ (k) is not free from ambiguities and can be determined only up to a polynomial in k 2 (cf. [7,8]) but the latter is normally set equal to zero. This has been also our choice in the present work.…”

Extrapolation of scattering data to the negative-energy region. II. Applicability of effective range functions within an exactly solvable model

“…[12] that the analytic properties of f l on the physical sheet of E are analogous to the ones of the partial-wave scattering amplitude for the shortrange potential and it can be analytically continued into the negative energy region. The amplitudef l can be expressed in terms of the Coulomb-modified ERF K l (E) [12,14] bỹ…”

“…∆ l (E) is the ∆ function introduced in [9]. It was shown in [12] that function K l (E) defined by (10) is analytic near E = 0 and can be expanded into Taylor series in E. In the absence of the Coulomb inter-…”

“…Therefore, one has to introduce the renormalized Coulomb-nuclear partial-wave amplitudef l [12][13][14] …”