On the essential spectrum of the Jansen-Hess operator for two-electron ions

TL;DR

This paper investigates the spectral properties of the Jansen-Hess operator for two-electron ions, establishing conditions under which the singular continuous spectrum is absent and analyzing eigenvalue confinement for related operators.

Contribution

It extends spectral analysis to the Jansen-Hess operator using HVZ theorem and dilation analyticity, providing new bounds for potential strength and eigenvalue confinement.

Findings

Singular continuous spectrum is absent for Z<90 in the Jansen-Hess operator.

Eigenvalues are confined below 2m for Z<50 in the Brown-Ravenhall operator.

Bound on potential strength is slightly higher (Z<102) for the Brown-Ravenhall operator.

Abstract

Based on the HVZ theorem and dilation analyticity of the pseudorelativistic no-pair Jansen-Hess operator, it is shown that for subcritical potential strength (Z < 90) the singular continuous spectrum is absent. The bound is slightly higher (Z < 102) for the Brown-Ravenhall operator whose eigenvalues are, by the virial theorem, confined to <2m if Z<50.math/m