Abstract
A detailed calculation of the $O(m{\ensuremath{\alpha}}^{6})$ corrections to the energy levels of positronium for the orbital angular momentum number $lg0$ is presented. The formulas obtained are in agreement with the known results for the particular case of $l=1$. The complete analytical formulas to $O(m{\ensuremath{\alpha}}^{6})$ are given for an arbitrary $lg0$ state, as well as numerical values of the energy levels $3\phantom{\rule{0.2em}{0ex}}^{2S+1}D_{J}$.
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