Causality constraints for charged particles

TL;DR

This paper derives causality-based bounds on scattering parameters in quantum systems with Coulomb and short-range interactions, impacting effective field theories and nuclear halo state analyses.

Contribution

It introduces an upper bound on the Coulomb-modified effective range and relates it to nuclear halo state properties, providing new theoretical constraints.

Findings

Derived an upper bound for Coulomb-modified effective range.

Established relations for asymptotic normalization coefficients of halo states.

Extracted ANCs for excited states in O-16 from scattering data.

Abstract

In quantum systems with short-range interactions, causality imposes nontrivial constraints on low-energy scattering parameters. We investigate these causality constraints for systems where a long-range Coulomb potential is present in addition to a short-range interaction. The main result is an upper bound for the Coulomb-modified effective range parameter. We discuss the implications of this bound to the effective field theory for nuclear halo systems. In particular, we consider several examples of proton--nucleus and nucleus--nucleus scattering. For the bound-state regime, we find relations for the asymptotic normalization coefficients (ANCs) of nuclear halo states. As an application of these relations, we extract the ANCs of the excited 2+ and 1- states in O-16 from alpha--C-12 scattering data.