Abstract
A first order relativistic correction to the standard Schrödinger Hamiltonian is used to obtain a relativistic correction to the Thomas-Kuhn sum rule for oscillator strengths of hydrogenic systems. The sum rule takes the form ∑ c f ac=1−δ a .Where δ a is the relativistic correction to first order in m 0 c 2 given by δ a= 5 3m 0c 2 <a|P 2|a> 2m 0 .
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