Transition Rate and the Photoelectric Effect in the Presence of a   Minimal Length
  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. 
Behrooz Khosropour
physics.gen-ph hep-th