# Bound states of relativistic nature

## TL;DR

This paper investigates relativistic bound states arising from strong interactions, showing that abnormal energy levels predicted by the Bethe-Salpeter equation can exist with massive exchange particles, potentially observable in nature.

## Contribution

It extends the analysis of abnormal bound states to realistic massive exchange particles, suggesting their possible physical relevance.

## Key findings

- Abnormal relativistic states persist with massive exchange particles.
- Strong coupling constants can generate these abnormal states.
- Such states may be observable in natural phenomena.

## Abstract

Bethe-Salpeter equation, for massless exchange and large fine structure constant $\alpha>\pi/4$, in addition to the Balmer series, provides another (abnormal) series of energy levels which are not given by the Schr\"odinger equation. So strong field can be created by a point-like charge $Z>107$. The nuclei with this charge, though available, they are far from to be point-like that weakens the field. Therefore, the abnormal states of this origin hardly exist. We analyze the more realistic case of exchange by a massive particle when the large value of coupling constant is typical for the strong interaction. It turns out that this interaction still generates a series of abnormal relativistic states. The properties of these solutions are studied. Their existence in nature seems possible.