Laser-Induced Fluorescence (LIF)

Laser-Induced Fluorescence (LIF) has a large range of applications in spectroscopy.

Typical applications are as

• LIF can be used as sensitive monitor for the absorption of laser photons when frequency unresolved fluorescence spectrum is detected.
• LIF is well suited to gain information on molecular states if the fluorescence spectrum exited by a laser on a selected absorption transition is dispersed by a monochromator.
• LIF can be used for spectroscopic study of collisional processes.
• Important aspect of LIF concerns its application to the determination of the internal-state distribution in molecular reaction products of chemical reactions. Under certain conditions the intensity $I_{fl}$ of LIF excited on the transition $\vert i> \rightarrow \vert k>$ is a direct measure of the population density $N_i$ in the level $\vert i>$.

Let us assume that a rovibronic state ($v_k', J_k'$) in an excited state of a diatomic molecule has been selectively populated by optical pumping. With a mean lifetime $\tau_r = 1/ \sum_m A_{km}$ the excited molecules undergo spontaneous transitions to lower states ($v_m'', J_m''$). At a population density $N_k$($v_k', J_k'$) the radiation power of a fluorescence line with frequency $\nu_{km} = (E_k-E_m)/h$ is given by

$$P_{km} \propto N_k A_{km} \nu_{km}.$$ (82)

As we discussed before, the spontaneous transition probability $A_{km}$ is proportional to the squire of the matrix element

$$A_{km} \propto \left\vert\int \psi^*_k \bf {\mu} \psi_m dr_n d r_e \right\vert^2,$$ (83)

where $\bf {\mu}$ is the transition moment and the integration extends over all nuclear and electronic coordinates. Within the Born-Oppenheimer approximation the total wave function can be presented as a product

$$\psi = \psi_{el} \psi_{vib} \psi_{rot}$$ (84)

of electronic, vibrational, and rotational factors.

In case of electronic transitions, if the electronic transition moment $\mu$ does not depend critically on the internuclear distance $R$, eq. (83) can be presented as a product

$$A_{km} \propto \left\vert M_{el}\right\vert^2\left\vert M_{vib}\right\vert^2\left\vert M_{rot}\right\vert^2 ,$$ (85)

where the first factor

$$M_{el} = \int {\psi'}^*_{el} \bf {\mu} \psi''_{el} d r_e$$ (86)

represents the electronic matrix element which depends on the overlap of the coupling of the two electronic states. The second integral

$$M_{vib} = \int {\psi'}^*_{vib} \psi''_{vib} d r_{vib} \mbox{ with } dr_{vib} = R^2 dR$$ (87)

is the Franck-Condon factor which depends on the overlap of the vibrational wave functions $\psi_{vib}$ in the upper and the lower states. The third integral

$$M_{rot} = \int {\psi'}^*_{rot} \psi''_{rot} d r_{rot}$$ (88)

is called Hönl-London factor and depends on the orientation of the molecule relative to the electric vector of the incident light polarization.

Only those transitions for which all three factors are nonzero appear as lines in the fluorescence spectrum. As we already know, the Hönl-London factor is always zero unless

$$\Delta J = 0, \pm 1.$$ (89)

This means that if a single upper energy level ($v_k', J_k'$) has been selectively excited, each vibrational band $v_k' \rightarrow v_m''$ consists of at most three lines: a $P$ line ($J'-J''=-1$), a $Q$ line ($J'-J''= 0$), and an $R$ line ($J'-J''= +1$).

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