Theory of the inverse hook method for measuring oscillator strengths

The theory of a new method to measure oscillator strengths is presented. The method exploits the ac Stark interaction of a laser pulse detuned from a transition between an initially populated state a and a second state b of an atom. We assume the density matrix ρ of state a initially has only diagonal elements given by 〈m‖ρ‖m〉=C+${\mathrm{Dm}}^2$ where C and D≠0 are constants and m is the Zeeman sublevel quantum number. The laser pulse is linearly polarized along an axis different from the quantization axis and therefore rearranges the atoms among the various Zeeman sublevels. Changes of the relative Zeeman sublevel populations induced by the laser pulse can be readily detected by monitoring changes in the angular distribution or polarization of fluorescent light emitted when the atoms radiatively decay to some final state f. This paper considers the general problem where states a, b, and f have arbitrary angular momentum. We derive the functional dependence of the polarized fluorescent light fluence on the laser pulse fluence (pulse energy per unit area).