# Motion of half-spin particles in the axially symmetric field of naked singularities of static q-metric

## TL;DR

This paper investigates the quantum motion of half-spin particles in the axially symmetric field of static naked singularities described by the q-metric, revealing conditions for bound states and potential barriers depending on mass distribution shape.

## Contribution

It introduces a generalized effective potential method for Dirac particles in non-separable variables within the q-metric, analyzing bound states and barriers for different quadrupole moments.

## Key findings

- Bound states exist for prolate distributions with small q.
- Oblate distributions create potential barriers near the poles.
- Certain angles and states allow particles to approach the poles for specific q values.

## Abstract

Quantum-mechanical motion of a half-spin particle was examined in the axially symmetric field of static naked singularities formed by mass distribution with quadrupole moment (q-metric). The analysis was performed by means of the method of effective potentials of the Dirac equation generalized for the case when radial and angular variables are not separated. As $-1<q<q_{lim}, |q_{lim}|<<1 $ the naked singularities do not except the existence of stationary bound states of Dirac particles for a prolate mass distribution in the q-metric along the axial axis. For the oblate mass distribution, the naked singularities of the q-metric are separated from the Dirac particle by infinitely large repulsive barriers with the subsequent potential well deepening while moving along the angle from the equator (or from $\theta=\theta_{min}, \theta=\pi-\theta_{min}$) towards poles. The exception are the poles and, as $0<q<q*$, some points $\theta_{i}$ for the states of the particle with j>=3/2.

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Source: https://tomesphere.com/paper/1706.05229