Extrapolation of scattering data to the negative-energy region II

TL;DR

This paper investigates methods for analytically continuing scattering data into the negative-energy region to identify bound states, comparing effectiveness across different nuclear systems using an exactly solvable model.

Contribution

It evaluates and compares the effectiveness of the $ riangle$-method and effective-range function approach for different nuclear systems, providing guidance on their applicability.

Findings

The $ riangle$-method is more effective for heavier systems with large Coulomb parameters.

The effective-range function method is preferable for lighter systems with small Coulomb parameters.

The study offers practical recommendations for analytical continuation techniques in nuclear physics.

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 $d+\alpha$ and $\alpha +^{12}$C systems are considered and, for comparison, an effective-range function approach and a recently suggested $\Delta$-method [O. L. Ram\'{\i}rez Su\'arez and J.-M. Sparenberg, Phys. Rev. C 96, 034601 (2017)] are applied. We conclude that the $\Delta$-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.