High‐precision calculation of relativistic corrections for hydrogen‐like atoms with screened Coulomb potentials

Abstract

The first-order relativistic corrections to the non-relativistic energies of hydrogen-like atom embedded in plasma screening environments are calculated in the framework of direct perturbation theory by using the generalized pseudospectral method. The standard Debye-Hückel potential, exponential cosine screened Coulomb potential, and Hulthén potential are employed to model different screening conditions and their effects on the eigenenergies of hydrogen-like atoms are investigated. The relativistic corrections which include the relativistic mass correction, Darwin term, and the spin-orbit coupling term for both the ground and excited states are reported as functions of screening parameters. Comparison with previous theoretical predictions shows that both the relativistic mass correction and spin-orbit coupling obtained in this work are in good agreement with previous estimations, while significant discrepancy and even opposite trend is found for the Darwin term. The overall relativisticcorrected system energies predicted in this work, however, are in good agreement with the fully relativistic calculations available in the literature. We finally present the scaling law of the first-order relativistic corrections and discuss the validity of the direct perturbation theory with respect to both the nuclear charge and the screening parameter.

Critical screening parameters and critical behaviors of one-electron systems with screened Coulomb potentials

“…It is known that the eigenenergies of the system-bound states would be lifted up monotonically while continuously increasing the screening parameter (see reference [16] and references therein). They would approach zero as λ approaches the corresponding critical screening parameters λ c and then finally merge into the continuum.…”

“…Several models have been developed to describe the screening effect of the environment on the Coulomb interaction, e.g., the Hulthén potential (HP) [8] in the form λ e −λr /(1 − e −λr ), the Debye-Hückel, Yukawa, or static screened Coulomb potential (SCP) [9] in the form e −λr /r, and the exponential cosine screened Coulomb potential (ECSCP) [10] in the form of e −λr cos(λr)/r. These potentials have attracted considerable interest in a wide variety of physics, such as plasma physics, astrophysics, atomic and molecular physics, nuclear physics, solid-state physics, etc, where the screening parameter λ is further related to specific parameters that characterize the system [11][12][13][14][15][16].…”

Multipole polarizabilities of spherically confined hydrogen atom and positronium in screened Coulomb potential

“…It is worth noting that the definition of such a critical screening parameter for spherically confined atoms is of no practical significance or is even misleading, because the electron would always be bound by the impenetrable sphere box with any large positive eigenenergies. For a complete view of the variation of different bound states of H atom only in screened Coulomb potential (as functions of screening parameter) and those of H atom only in spherical confinement (as functions of confinement radius), readers are referred to figure 1 in Xie et al [45] and figure 3 in Jiao et al [46], respectively.…”

“…(Continues) of screening parameter) and those of H atom only in spherical confinement (as functions of confinement radius), readers are referred to figure1in Xie et al[45] and figure3in Jiao et al[46], respectively.…”

Analyzing the effects of magnetic and Aharonov‐Bohm (AB) flux fields on the energy spectra and thermal properties of N2, NO, CO and H2 diatomic molecules

“…Also, it is well-known that the potential energy functions with more parameters have a tendency to fit experimental data better than those with fewer parameters [23]. Many researchers in recent times have researched the analytical solutions of SE with these potentials [24][25][26][27][28][29][30][31][32][33].…”