Applying quantum supersymmetry and perturbation theory to the energy-dependent Hulthen potential

We deal with the energy-dependent Hulthen potential, by using the supersymmetric quantum mechanics and the first-order perturbation theory. We consider the Hulthen potential linearly dependent on the energy which is introduced in the coupling constant. We evaluate the energy eigenvalues and the corresponding reduced radial eigenfunctions. We compare the analytical results with the numerical solutions of the Schrodinger equation in the energy-dependent and the energy-independent cases. We then investigate the screening effect in order to determine the critical screening parameter values for each state. After that, we look into the absorption oscillator strengths for different transitions.