Transition Rate and the Photoelectric Effect in the Presence of a Minimal Length

TL;DR

This paper investigates how a minimal length, derived from the generalized uncertainty principle, affects transition rates and the photoelectric effect, providing modified formulas and estimating an upper bound on the minimal length.

Contribution

It introduces a modified framework for the photoelectric effect incorporating a minimal length scale based on GUP, extending previous models with new theoretical insights.

Findings

Derived the transition rate considering a minimal length

Calculated the absorption cross section within GUP framework

Estimated an upper bound on the isotropic minimal length

Abstract

In this work, according to the generalized uncertainty principle (GUP) and time- dependent perturbation theory, the transition rate in the present of a minimal length based on the Kempf algebra is studied. Also, we find the absorption cross section in the framework of GUP. The modified photoelectric effect is investigated and we show that the differential cross section of photoelectric effect in the frame work of GUP is related to the isotropic minimal length scale. The upper bound on the isotropic minimal length is estimated.