THE RADIAL HAMILTONIANS FOR THE $A^{1}\Sigma^{+}$ and $X^{1}\Sigma^{+}$ STATES OF $LiH$ and $Li_{2}$

Abstract

Extensive collections of literature data involving the $A^{1}\Sigma^{+}$ and $X^{1}\Sigma^{+}$ states of $LiH$ and the $A^{1}\Sigma^{+}{u}$ and $X^{1}\Sigma^{+}{g}$ states of $Li_{2}$ have been employed in direct least-squares fits of the radially dependent Hamiltonians. Vibration-rotational and pure rotational transition energies for the ground $X^{1}\Sigma^{+}$ state of $^{6}LiH$, $^{7}LiH$, $^{6}LiD$ and $^{7}LiD$, along with the entire collection of $A^{1}\Sigma^{+} - X^{1}\Sigma^{+}$ emission and absorption data for the four isotopomers, are used in the fit for LiH; the data set for $Li_{2}$ consists of more than 6000 $A^{1}\Sigma^{+}{u} - X^{1}\Sigma^{+}{g}$ absorption lines. The Born-Oppenheimer potentials are represented by a modified Lennard-Jones function that provides for correct behaviour in the near dissociation, long-range region of the potential. The LiH data set extends over $\approx 65%$ and 80% of the well depths of the $A^{1}\Sigma^{+}$ and $X^{1}\Sigma^{+}$ states, respectively, while the $Li_{2}$ data covers $\approx 70%$ and 99.97% of the well depths (extending out to more than 14 \AA in the ground $X^{1}\Sigma^{+}_{g}$ state). The fits take full account of Born- Oppenheimer breakdown effects, and reproduce the measured line positions to within their estimated accuracies.