What is Transition dipole moment, oscillator strength?

The transition dipole moment between states $\Psi_i$ and $\Psi_f$ is $\boldsymbol\mu_{fi} = \langle\Psi_f|\hat{\boldsymbol\mu}|\Psi_i \rangle$, with $\hat{\boldsymbol\mu} = -e\sum_k\mathbf r_k$ (plus the nuclear charges, which cancel between orthogonal states). The oscillator strength $f$ is the dimensionless measure of the intensity of a band, about 1 for the strongest transitions.