Consider two levels of a two-electron atom: level has configuration

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

Deriving the Spectrum, Ch Radiative transitions and lifetimes

Problem

Consider two levels of a two-electron atom: level AA has configuration 1s21s^2, term 1S0^1S_0 (the ground level), and level BB has configuration 1s 3s1s\,3s, term 1S0^1S_0. Someone argues:"The configurations are different (1s21s^2 against 1s 3s1s\,3s), so the electron distribution changes character and the parity of the level must change between AA and BB. The electric-dipole rule allows ΔJ=0,±1\Delta J = 0, \pm1, and here J=0J = 0 for both levels, which is covered by ΔJ=0\Delta J = 0. Both terms are singlets, so ΔS=0\Delta S = 0 is satisfied. All three checks pass, so the A→BA \to B line should be an allowed electric-dipole (E1E1) transition." ((a)) Find every error in this argument. ((b)) State whether the A↔BA \leftrightarrow B line can occur as an E1E1, M1M1 or E2E2 transition to lowest order, and justify each conclusion.

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