Screening windows for resonances in the Deng–Fan potential: an analytical approach

Source abstract

Abstract We derive the analytical form of the screening window for resonances in the Deng–Fan potential. This window is defined as the interval of screening parameters for which the potential supports only resonance states, with no bound states, and is expressed as a function of an arbitrary positive angular momentum and the remaining potential parameters. The lower endpoint of the screening window corresponds to the critical value at which the potential ceases to support bound states. In turn, the upper endpoint specifies the value at which the potential becomes fully repulsive, thereby precluding the existence of both bound and resonance states. Our approach is entirely analytical and does not rely on any approximations. Numerical values of the screening window are also presented for selected sets of potential parameters. The results provide a rigorous criterion for identifying physical resonances.