Approximation of Dirac operators with δ‐shell potentials in the norm resolvent sense, II: Quantitative results

This paper is devoted to the approximation of two‐ and three‐dimensional Dirac operators HV∼δΣ$H_{\widetilde{V} \delta _\Sigma }$ with combinations of electrostatic and Lorentz scalar δ$\delta$‐shell interactions in the norm resolvent sense. Relying on results from Behrndt, Holzmann, and Stelzer‐Landauer [Math. Nachr. 298 (2025), 2499–2546], an explicit smallness condition on the coupling parameters is derived so that HV∼δΣ$H_{\widetilde{V} \delta _\Sigma }$ is the limit of Dirac operators with scaled electrostatic and Lorentz scalar potentials. Via counterexamples it is shown that this condition is sharp. The approximation of HV∼δΣ$H_{\widetilde{V} \delta _\Sigma }$ for larger coupling constants is achieved by adding an additional scaled magnetic term.