Influence of anomalous magnetic moment

Introducing a cut-off of the Coulomb potential at short distances introduces some arbitrariness. A method of regularization that works with the unmodified Coulomb potential is to take into account the anomalous magnetic moment of the electron. The Dirac operator now reads (in dimensionless units) 

It is interesting to look at the curves ( n.ni y) presence of the anomalous magnetic moment. Since no exact solution is known for this case, the eigenvalues have to be obtained numerically. The results are shown in Fig. 8. This figure displays some eigenvalues of the operator with = 0.00058, as functions of the coupling constant 7. 

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