# Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles

## TL;DR

This paper demonstrates that under certain conditions, relativistic spin-1/2 and spin-0 particles have identical energy spectra in vector and scalar potentials, independent of potential shapes, with implications across physics fields.

## Contribution

It reveals that spin and pseudospin symmetries lead to equivalent spectra of spin-1/2 and spin-0 particles, regardless of potential shapes, and discusses conditions for isospectrality and their physical implications.

## Key findings

- Spin and pseudospin symmetries produce equivalent spectra.
- Conditions for isospectrality imply vanishing spin-orbit and Darwin terms.
- Scalar and spin-1/2 particles share energy spectra and orbital angular momentum.

## Abstract

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. The conclusions do not depend on the particular shapes of the potentials and can be important in different fields of physics. When both scalar and vector potentials are spherical, these conditions for isospectrality imply that the spin-orbit and Darwin terms of either the upper component or the lower component of the Dirac spinor vanish, making it equivalent, as far as energy is concerned, to a spin-0 state. In this case, besides energy, a scalar particle will also have the same orbital angular momentum as the (conserved) orbital angular momentum of either the upper or lower component of the corresponding spin-1/2 particle. We point out a few possible applications of this result.