Abstract
We present a scheme for calculating atomic single-particle wave functions and spectra with taking into ac-count the nonspherical effect explicitly. The actual calculation is also performed for the neutral carbon atom within the Hartree-Fock-Slater approximation. As compared with the conventional atomic structure of the spherical approximation, the degenerate energy levels are split partially. The ground state values of the total orbital and spin angular momenta are estimated to be both about unity, which corresponds to the term P3PP in the LS-multiplet theory. This means that the nonspherical effect may play an essential role on the description of the magnetization caused by the orbital polarization.
Highlights
Let us start with revisiting the conventional atomic structures
We present a scheme for calculating the atomic structures beyond the spherical approximation and investigate to what extent the single-particle picture of atomic systems needs to be modified
Compared to the conventional atomic structures, we find that the atomic levels are partially split
Summary
Let us start with revisiting the conventional atomic structures. We consider the isolated neutral atom with the atomic number Z. Neglecting the relativistic effects, the Schrödinger Equation for the stationary state is given by H E (1) with H Z i 1 i i j ri 2 rj (2). Where ri and ri stand for the position of the ith electron and its magnitude, respectively, and where the atomic unit is used. Equation (1) can be numerically solved only in small atomic systems, but in larger atomic systems we have to utilize the theories to reduce Equation (1) into the effective single-particle Equation such as the Hartree [1], Hartre-Fock [2] and Kohn-Sham [3,4] Equations, etc. The single-particle Equation is generally written by (3) nlm r.
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