Solution of the Energy Level of Hydrogen-Like Atom for the Debye Shielding Potential**The project supported by Natural Science Foundation of Chongqing Education Committee (Grant No. 20011075) and the Basic Research of Application of Chongqing Science and Technology Committee (Grant No. 199966)

Abstract

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-like atoms under the condition of Debye shielding potential are achieved by means of the Rayleigh–Schrödinger perturbation theory; meanwhile, the corresponding recurrence relations are obtained from the use of the solution of power series. Based on the above solutions and with the use of energy consistent method the equivalent value of second-order reversion under the condition of Debye shielding potential is produced as well and the result is compared with the data obtained by the numerical method. Besides, the critical bond-state and corresponding cut-off conditions are discussed.