Critical screening parameters of one-electron systems with screened Coulomb potentials: high Rydberg limit
Li Guang Jiao, Lei Xu, Ruo Yu Zheng, Aihua Liu, Yong Zhi Zhang, H. E. Montgomery, Y. K. Ho
Abstract
Abstract We develop an efficient numerical method to directly calculate the critical screening parameters for one-electron systems with Hulthén and Debye–Hückel screened Coulomb potentials (SCPs). Compared to indirect methods, which locate the critical screening parameters via searching the potential parameters with near-zero energy, the method developed in this work directly calculates the critical screening parameters as eigenvalues of a generalized eigenvalue problem. This feature allows us to simultaneously determine the critical parameters for bound states from low-lying excitation to high-lying Rydberg limit with high accuracy. The method is applied to SCPs to investigate the asymptotic behavior of critical screening parameters as the principal quantum number n approaches infinity. It has been shown that the critical screening parameters in Hulthén and Debye–Hückel potentials follow the 2 n −2 and 4 n −2 / π asymptotic laws, respectively, and that the orbital angular momentum affects the higher-order coefficients linearly.