ON THE CAUSE OF RKR f-INTEGRAL ERROR NEAR A DIATOMIC MOLECULE DISSOCIATION $LIMIT^{*}$

Abstract

The discrepancy between actual f-integrals (from classical turning point separations) and RKR f-integrals is investigated for two diatomic vibrational potentials V. The V’s are Born-Oppenheimer potentials for the ground states of $H_{2}^{+}$ and $H_{2}$. The RKR f-integral errors are very large near dissociation even for vibrational levels $E_{\nu}$ determined within the first-order WBK approximation; this occurs even though the RKR f-integral is itself a first-order WBK inversion. We attribute the error to the form used for $E_{\nu}$ as a function of quantum number $\nu$. When $(\nu_{D}-\nu)^{m}$, with m=4 for $H_{2}^{+}$ and m=3 for $H_{2}$, is included as a factor in the $E_{\nu}$ representation, error in the RKR f-integrals is reduced by two orders of magnitude at the highest levels.