The Spinless Relativistic Yukawa Problem

TL;DR

This paper investigates the spectral properties of the spinless Salpeter equation with Yukawa interactions, providing insights into semirelativistic bound states and employing established methods to analyze the spectra.

Contribution

It offers a detailed analysis of the Yukawa problem within the spinless Salpeter framework, highlighting constraints on the spectra of semirelativistic bound states.

Findings

Constraints on the energy spectra of Yukawa-bound states

Application of known spectral analysis tools to the relativistic case

Insights into semirelativistic bound state behavior

Abstract

Noticing renewed or increasing interest in the possibility to describe semirelativistic bound states (of either spin-zero constituents or, upon confining oneself to spin-averaged features, constituents with nonzero spin) by means of the spinless Salpeter equation generalizing the Schr\"odinger equation towards incorporation of effects caused by relativistic kinematics, we revisit this problem for interactions between bound-state constituents of Yukawa shape, by recalling and applying several well-known tools enabling to constrain the resulting spectra.