Relativistic Effects in Atomic Structure Calculations: An Introduction
Let us first consider qualitatively how relativistic effects influence atomic structure calculations. Using atomic units (i.e. e = ħ = mo =1), the mean velocity of a 1s electron in a Coulomb field of charge Z is exactly equal to Z. In the same system of units the velocity of light is roughly 137; thus, for a rare earth atom the mean velocity of the 1s electron is already almost half the velocity of light, and its mass is about 1.15 that of the rest mass. We may get a feeling of the main changes induced by this variation in the mass by simply considering the Schrödinger equation for the apparent mass instead of the rest mass. As the energy is directly proportional to the mass (E = -Z2m/2n2) we conclude that the binding energy should increase while at the same time the charge density should contract towards the origin (the scaling factor is r/m). If we now consider electrons of higher quantum number n, we will conclude from the preceding argument that they will be essentially unaffected since their velocity is rather small compared to the light velocity. But as their wavefunctions have to be orthogonal to the inner electron ones, they experience an indirect relativistic effect which also results in a contraction of the charge density.
KeywordsLamb Shift Relative Contraction Coulomb Field Relativistic Counterpart Open Shell System
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