STUDY OF EXCITED VIBRATIONAL LEVELS OF THE $Na_{2} A^{1}\Sigma^{+}_{u}$ STATE USING MODULATED GAIN

Highly excited vibrational levels of the $Na_{2} A^{1}\\Sigma^{+}_{u}$ state are observed from $v=62$ to $v=131$. The highest level of excitation corresponds to a binding energy of 0.65\\% of the potential well depth, a classical outer turning point $R_{+}\\sim 19.1{AA}$ in contrast with $R_{+}(v=0)\\sim 3.8{\\AA}$, and a vibrational frequency of $\\omega \\sim 4.6 cm^{-1}$ in contrast with $\\omega_{e} \\sim 117 cm^{-1}$ These excited levels have poor Franck-Condon factors with thermally populated levels of the ground $X^{1}\\Sigma^{+}_{g}$ electronic state. Therefore, modulated gain spectroscopy (MGS) is based upon a triple resonance excitation scheme where $Na_{2}$ is used as a gain medium in an optically-pumped-laser (OPL) to transfer thermal population, state-selectively, to high v of the ground state. Transitions from these high v levels of the X-state to high v levels of the A-state have good vibrational overlaps and are excited with a third laser. These absorption resonances are monitored by detecting increases in the saturated gain of the OPL. The three cw lasers are each independently frequency stabilized, resulting in a frequency accuracy of $\\pm 0.005 cm^{-1}$. A ``long range'' analysis of the vibrational and rotational levels determines the Van der Waals coefficients $C_{3}, C_{6}$, and $C_{8}$. These reflect the atomic properties of $Na (3^{2}S_{1/2})$ and $Na(3^{2}P_{3/2})$ states into which the A-state dissociates, such as the transition dipole moments, dipole polarizabilities, and quadrupole polarizabilities. From the $C_{n}$-values, we have determined the most accurate value to date of the oscillator strength for the $Na ({^{2}}S\\rightarrow {^{2}}P)$ D lines as well as the dipole polarizability of the $Na({^{2}}P)$ state.