Parity violating effects in an exotic perturbation of the rigid rotator

TL;DR

This paper investigates how a specific exotic perturbation affects the parity and electric dipole moments of a rigid rotator, revealing parity violation and altered wave functions without changing energy levels.

Contribution

It demonstrates that the trigonometric Scarf potential perturbation leads to parity violation and non-zero electric dipole moments in the rigid rotator's states.

Findings

Energy excitation patterns remain unchanged.

Wave functions are modified towards spherical harmonics with parity mixing.

States exhibit non-vanishing electric dipole expectation values.

Abstract

The perturbation of the free rigid rotator by the trigonometric Scarf potential is shown to conserve its energy excitation patterns and change only the wave functions towards spherical harmonics rescaled by a function of an unspecified parity, or mixtures of such rescaled harmonics of equal magnetic quantum numbers and different angular momenta. In effect, no parity can be assigned to the states of the rotational bands emerging in this exotic way, and the electric dipole operator is allowed to acquire non-vanishing expectation values.