Deriving the Spectrum, Ch Electronic spectra of diatomic molecules
Problem
A homonuclear diatomic molecule is built from two identical nuclei, each a boson with nuclear spin I=1. Its ground electronic state is X1Σg+, and a candidate excited state is A1Σu−.
((a)) Using the electric-dipole selection rules for a diatomic electronic transition, together with the fact that the electric dipole operator is odd under spatial inversion, decide whether the transition A1Σu−→X1Σg+ is electric-dipole allowed. Justify each rule you apply.
((b)) For the ground state X1Σg+, the pure rotational Raman spectrum shows an intensity alternation between even and odd initial rotational quantum number J′′. Using the requirement that the total wavefunction (electronic times vibrational times rotational times nuclear spin) be symmetric under exchange of the two identical bosonic nuclei, find the ratio of the statistical weight of an even-J′′ rotational level to that of an odd-J′′ level, and state which set of Raman lines (those starting from even J′′ or from odd J′′) is the stronger.