Hydrogen's Lamb shift

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Radiative transitions, external fields and collisions

Deriving the Spectrum, Ch Atoms in electric fields

Problem

Hydrogen's Lamb shift, the 2S1/22S_{1/2}-2P1/22P_{1/2} splitting ΔL\Delta_L, is quoted as 0.035285 cm−10.035285\,\mathrm{cm^{-1}}. Using 1 cm−1=29.9792 GHz1\,\mathrm{cm^{-1}} = 29.9792\,\mathrm{GHz} and the crossover condition 3 ea0E=ΔL/2\sqrt3\,ea_0\mathcal E = \Delta_L/2 (equating the Stark coupling within the j=12j=\tfrac12 pair to half the Lamb shift energy), find the field E\mathcal E in V cm−1\mathrm{V\,cm^{-1}} at which hydrogen's n=2n=2 Stark shift changes from quadratic to linear.

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