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

Abstract

A problem of analytical continuation of scattering data to the negative-energy region to obtain information about bound states is discussed within an exactly solvable potential model. This work is continuation of the previous one by the same authors [L. D. Blokhintsev et al., Phys. Rev. C 95, 044618 (2017)]. The goal of this paper is to determine the most effective way of analytic continuation for different systems. The d+α and α+ 12 C systems are considered and, for comparison, an effective-range function approach and a recently suggested ∆-method [O. L. Ramírez Suárez and J.-M. Sparenberg, Phys. Rev. C 96, 034601 (2017)] are applied. We conclude that the ∆-method is more effective for heavier systems with large values of the Coulomb parameter, whereas for light systems with small values of the Coulomb parameter the effective-range function method might be preferable.

Connection formulas between Coulomb wave functions

“…27,28 The in-depth survey of these functions has led to recent advances in the theory of effectiverange function for charged particles. [29][30][31][32] The main purpose of this paper is to determine the relations between the regular and the irregular Coulomb functions, respectively denoted as F η (ρ) and G η (ρ), in an easy-toread fashion. These relations are generically referred to as the "connection formulas" in the NIST Handbook.…”