Quantum-defect theory for $-1/r^4$ type of interactions

TL;DR

This paper develops a quantum-defect theory for long-range $-1/r^4$ interactions, providing a systematic framework for understanding charge-neutral quantum systems and their scattering resonances.

Contribution

It introduces an advanced quantum-defect theory for $-1/r^4$ potentials, extending previous models and including detailed resonance and universal property descriptions.

Findings

Unified framework for charge-neutral systems

Description of scattering resonances for $-1/r^n$ potentials

Enhanced understanding of resonance spectra

Abstract

We present a quantum-defect theory (QDT) for the $-1/r^4$ type of long-range potential, as a foundation for a systematic understanding of charge-neutral quantum systems such as ion-atom, ion-molecule, electron-atom, and positron-atom interactions. The theory incorporates both conceptual and mathematical advances since earlier formulations of the theory. It also includes more detailed discussions of the concept of resonance spectrum and its representations, universal properties in charge-neutral quantum systems, and the QDT description of scattering resonances that is applicable to any $-1/r^n$ potential with $n>2$.