The Magnetic Scott Correction for Relativistic Matter at Criticality

We provide a proof of the first correction to the leading asymptotics of the minimal energy of pseudo-relativistic molecules in the presence of magnetic fields, the so-called "relativistic Scott correction", when $\max{Z_kα} \leq 2/π$, where $Z_k$ is the charge of the $k$-th nucleus and $α$ is the fine structure constant. Our theorem extends a previous result by Erdős, Fournais, and Solovej to the critical constant $2/π$ in the relativistic Hardy inequality $|p| - \frac{2}{π|x|} \geq 0$.

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