NaK Λ doubling and permanent electric dipoles in low-lying1Πstates: Experiment and theory

Abstract

The paper presents \ensuremath{\Lambda} splittings and q factors in the NaK $D{}^{1}\ensuremath{\Pi}$ state, directly measured from the electric radio-frequency-optical double resonance (RF-ODR) in laser-induced fluorescence (LIF) for a number of vibrational states $v=1--22$ with definite rotational levels J between 7 and 46. Permanent electric dipole moment values (d) have been obtained by measuring in LIF spectra the relative intensities of ``forbidden'' lines caused by dc Stark effect induced $e/f$ mixing in the ${}^{1}\ensuremath{\Pi}$ state, with their subsequent processing, which allowed us to obtain the $q/d$ ratio. A possible influence of the hyperfine structure on the RF-ODR signal and relative intensities has been calculated, showing that this influence can be neglected. The $q(v)$ values exhibited a decrease from $q(1)=1.529\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to $q(22)=1.171\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ which has been explained by an increase of the difference potential between $D{}^{1}\ensuremath{\Pi}$ and $C{}^{1}{\ensuremath{\Sigma}}^{+}$ states with internuclear distance (R); the respective L-uncoupling matrix element was evaluated as 1.87. It was shown, both by semiempirical treatment and population analysis of ab initio molecular wave functions, that considerable $\ensuremath{\pi}d$ and $\ensuremath{\sigma}d$ configuration admixtures are present in the $D{}^{1}\ensuremath{\Pi}$ and the $C{}^{1}{\ensuremath{\Sigma}}^{+}$ states. For the $B{}^{1}\ensuremath{\Pi}$ state, it was demonstrated that \ensuremath{\Lambda} doubling is caused by two competing perturbers $(A{}^{1}{\ensuremath{\Sigma}}^{+}$ and $C{}^{1}{\ensuremath{\Sigma}}^{+}),$ yielding q factors of $\ensuremath{\sim}\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ in agreement with high-resolution spectroscopy data given in the literature; single-configuration approximation is valid for interacting $B{}^{1}\ensuremath{\Pi}(\ensuremath{\sigma}{3s}_{\mathrm{Na}},\ensuremath{\pi}{4p}_{\mathrm{K}})\ensuremath{\sim}A{}^{1}{\ensuremath{\Sigma}}^{+}(\ensuremath{\sigma}{3s}_{\mathrm{Na}},\ensuremath{\sigma}{4p}_{\mathrm{K}})$ states. The measured $d(v)$ values, which varied from 6.6 to 4.6 D, have been used to obtain the empirical $D{}^{1}\ensuremath{\Pi}$ state $d(R)$ function for $R=6--12\mathrm{a}.\mathrm{u}.$ by means of an improved instability-free inversion procedure exploiting a special functional form. Two independent series of ab initio all-electron calculations of $d(R)$ and $d(v)$ have been performed for the $D{}^{1}\ensuremath{\Pi}$ and $B{}^{1}\ensuremath{\Pi}$ states of NaK. First, d values were computed as expectation values of the electric dipole operator with conventional multireference configuration-interaction wave functions. Second, the finite-field (FF) technique, combined with a multipartitioning perturbation theory (MPPT) treatment of electronic eigenstates, was applied for the calculation of $d(R)$ functions. The FF-MPPT calculations showed excellent agreement with experimental $D{}^{1}\ensuremath{\Pi}d(v)$ values obtained in the present work, as well as the proximity to experimental $B{}^{1}\ensuremath{\Pi}d(v)$ values given in the literature, thus showing that, as distinct from the ground state, it is important to account correctly for effective interactions of valence electrons arising from core-valence correlations, which could not be done properly with previously used pseudopotential techniques. The experimental d and q values dropping out from a smooth $v$ dependence have been considered as perturbed by $D{}^{1}\ensuremath{\Pi}\ensuremath{\sim}d{}^{3}\ensuremath{\Pi}$ interaction and exploited to evaluate respective ${d}_{t}$ and ${c}_{t}$ values for the perturbing $d{}^{3}\ensuremath{\Pi}$ state.