Deriving the Spectrum, Ch Atoms in electric fields
Problem
(a) An excited 5p level of an alkali-like atom is dipole-coupled significantly to only two other levels: a 5s level lying 1.0eV below it, with ∣⟨5s∣z∣5p⟩∣2=9a02, and a 6s level lying 2.5eV above it, with ∣⟨6s∣z∣5p⟩∣2=3a02. Using second-order perturbation theory, predict whether the applied field pushes the 5p level up or down, and explain in one sentence why this need not be the same direction as for a ground state. (b) A different level in the same atom has J=2. Its static polarisability has a tensor part proportional to 3M2−J(J+1). Predict into how many distinct energy components the level splits in a static field, and state which ∣MJ∣ components sit furthest from the mean, and on which sides of it.