Perturbation theory of relativistic corrections

1989 ◽  
Vol 11 (1) ◽  
pp. 15-28 ◽  
Author(s):  
W. Kutzelnigg
Keyword(s):  
Perturbation Theory ◽  
Relativistic Corrections

Perturbation Methods

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Fine Structure ◽  
Dirac Equation ◽  
Perturbation Methods ◽  
Relativistic Quantum ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Perturbation Expansions ◽  
Relativistic Corrections

Perturbation theory has been one of the most frequently used and most powerful tools of quantum mechanics. The very foundations of relativistic quantum theory—quantum electrodynamics—are perturbative in nature. Many-body perturbation theory has been used for electron correlation treatments since the early days of quantum chemistry, and in more recent times multireference perturbation theories have been developed to provide quantitative or semiquantitative information in very complex systems. In the beginnings of relativistic quantum mechanics, perturbation methods based on an expansion in powers of the fine structure constant, α = 1/c, were used extensively to obtain operators that would provide a connection with nonrelativistic quantum mechanics and permit some evaluation of relativistic corrections, in days well before the advent of the computer. This seems a reasonable approach, considering the small size of the fine structure constant—and for light elements it has been found to work remarkably well. Relativity is a small perturbation for a good portion of the periodic table. Perturbation expansions have their limitations, however, and as well as successes, there have been failures due to the highly singular or unbounded nature of the operators in the perturbation expansions. Therefore, in recent times other perturbation approaches have been developed to provide alternatives to the standard Breit–Pauli approach. This chapter is devoted to the development of perturbation expansions in powers of 1/c from the Dirac equation. In the previous chapter, the Pauli Hamiltonian was developed using the Foldy–Wouthuysen transformation. While this is an elegant method, it is probably simpler to make the derivation from the elimination of the small component with expansion of the denominator, and it is this approach that we use here. Another convenient approach is to make use of the modified Dirac equation in the limit of equality of the large and pseudo-large components. This approach enables us to draw on results from the modified Dirac approach in developing the two-electron terms of the Breit–Pauli Hamiltonian. We then demonstrate how the use of perturbation theory for relativistic corrections requires that multiple perturbation theory be employed for correlation effects and for properties.

scholarly journals High-precision calculation of relativistic corrections for hydrogen-like atoms with screened Coulomb potentials

2021 ◽  
Author(s):  
Hui Xie ◽  
Li Guang Jiao ◽  
Ai Liu ◽  
Y.K. Ho
Keyword(s):  
Perturbation Theory ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
First Order ◽  
Relativistic Corrections ◽  
Relativistic Mass ◽  
Mass Correction ◽  
Direct Perturbation ◽  
Good Agreement

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 relativistic-corrected 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.

Sign in / Sign up

Export Citation Format

Share Document