根据Brown和Ravenhall的重原子能量：Scott修正
The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction
摘要：
我们考虑相对论多粒子运营商-根据布朗和Ravenhall -描述重原子的电子态。在大核电荷和光速的限制下，研究了它们的基态能量。我们表明，领先的准经典行为所给出的Escheras-Fermi理论提出了一个subleading修正，斯科特修正。我们的结果适用于包括临界耦合常数在内的最大范围的耦合常数。作为一种技术工具，对临界原子Brown-Ravenhall算子建立了Sobolev-Gagliardo-Nirenberg型不等式.此外，我们还证明了类氢Brown-Ravenhall算子的本征值在临界耦合常数以下的精确上下界。
英文摘要：
We consider relativistic many-particle operators which - according to Brown and Ravenhall - describe the electronic states of heavy atoms. Their ground state energy is investigated in the limit of large nuclear charge and velocity of light. We show that the leading quasi-classical behavior given by the Thomas-Fermi theory is raised by a subleading correction, the Scott correction. Our result is valid for the maximal range of coupling constants, including the critical one. As a technical tool, a Sobolev-Gagliardo-Nirenberg-type inequality is established for the critical atomic Brown-Ravenhall operator. Moreover, we prove sharp upper and lower bound on the eigenvalues of the hydrogenic Brown-Ravenhall operator up to and including the critical coupling constant.
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