Abstract
Herbst and Simon [Phys. Rev. Lett. 41, 67 (1978)] have proven that the complex-scaling method (CSM) is applicable to the Stark effect in atoms. However, their proof is limited to complex scaling with an argument /3. Their method makes no statement as to the validity of CSM beyond this region. This article reports on a detailed numerical study of the use of CSM for the Stark effect in hydrogen. The results suggest a limitation on the range of energies of Stark resonances that can be calculated by CSM. We find that CSM does not produce resonances with energies $\mathrm{Im}E~\sqrt{3}\mathrm{Re}E,$ which corresponds precisely to the range of validity of the Herbst-Simon theory.
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