Analytical determination of the screening window for resonances in the Hulthén potential

Abstract We analytically derive the screening window for resonances in the Hulthén potential, defined as the range of screening parameters over which the potential supports resonance states without accompanying bound states, for arbitrary positive orbital angular momentum. Using the complex scaling method within the Slater-type orbital basis set, we present closed-form expressions for the matrix elements and accurately calculate all bound and resonance states for the angular momentum l = 1, 2, ..., 8 and the screening parameter λ ⩾ 0.01 . By tracking bound-state energy levels up the ionization threshold, we reveal their evolution into resonance levels with non-zero widths. We note the importance of the analytically determined critical value of λ for which the effective potential becomes totally repulsive and no bound or resonance states can exist. Our results provide a comprehensive characterization of the eigenspectrum of the Hulthén Hamiltonian, including the complex-energy nature of resonances.