Critical screening parameters of one-electron systems with screened Coulomb potentials: high Rydberg limit

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Vol. 55; no. 19; pp. 195001 - 195012
• Main Authors: Jiao, Li Guang, Xu, Lei, Zheng, Ruo Yu, Liu, Aihua, Zhang, Yong Zhi, Montgomery, H E, Ho, Yew Kam
• Format: Journal Article
• Language: English
• Published: IOP Publishing 05.10.2022
• Subjects: critical screening parameters; Debye–Hückel potential; generalized pseudospectral method; Hulthén potential; Rydberg states
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/1361-6455/ac8add

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.