Relativistic-kinematic approach to the hydrogen atom. A possible family of two-particle optically-inactive bound states

TL;DR

This paper develops a relativistic-kinematic model for the hydrogen atom, predicting new two-particle bound states with unique properties and discussing their potential radiative transitions.

Contribution

It introduces a novel bound-state equation based on invariant mass and predicts the existence of two-particle bound states with distinct intraatomic motion scales.

Findings

Numerical solutions for two-particle bound states are obtained.

Predicted two-particle states involve simultaneous electron and proton state changes.

Two-photon emission processes for these states are highly suppressed due to proton mass.

Abstract

The invariant mass of free particles is used to derive a bound-state equation for the hydrogen atom at rest. This equation has the well-known solutions for the single-particle states. Existence of two-particle bound states, for which the electron and proton have different scales of intraatomic motions, is predicted. Two two-particle states are obtained numerically and discussed in detail. Radiative processes involving the two-particle bound state, should result in simultaneous changing the electron and the proton states and occur through the simultaneous two-photon emission. These processes will be extremely improbable, in comparison with electronic two-photon transitions, since they will be additionally suppressed by the large proton mass.