Solution of the fully-mixed-state problem: Direct deperturbation analysis of theAΣ+1–bΠ3complex in a NaCs dimer

Abstract

Laser-induced fluorescence (LIF) spectra $(4)\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and collisionally enhanced $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ LIF spectra measured by Fourier transform spectrometer with the resolution of $0.03--0.05\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ provided about 1160 term values of the $e$-symmetry rovibronic levels of the fully mixed $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ states of a NaCs molecule. Direct deperturbation treatment of the experimental data field, covering rotational quantum numbers $J∊[5,151]$ of the $A\text{\ensuremath{-}}b$ complex in the energy region $E∊[10577,13668]\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, was accomplished in the framework of the inverted channel-coupling approach by means of the $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian constructed on Hund's coupling case $(a)$ basis functions. The nonequidistant spin-orbit splitting of the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{\ensuremath{\Omega}=0,1,2}$ substates and the indirect coupling $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{\ensuremath{\Omega}=1}$ matrix element were introduced in the Hamiltonian phenomenologically to account for the regular perturbations by remote states manifold. The expanded Morse oscillator model was used to approximate both potential energy curves of the mutually perturbed states and spin-orbit coupling matrix elements as an analytical function of internuclear distance. Overall 31 fitting parameters have been required to reproduce 98% of experimental term values with a standard deviation of $0.006\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is consistent with the uncertainty of the experiment. The term values deperturbation analysis was confirmed by a calculation of relative intensity distributions in the $A--b\ensuremath{\rightarrow}X$ LIF progressions. The predicted probabilities for both weakly and strongly perturbed levels agree with their experimental counterparts within the accuracy of measurements. The evaluated nonadiabatic $A\text{\ensuremath{-}}b$ wave functions were applied for a prediction of radiative lifetimes of the $A\text{\ensuremath{-}}b$ complex as well as transition probabilities of the $a\ensuremath{\rightarrow}A--b\ensuremath{\rightarrow}X$ cycle proposed in Stwalley, Eur. Phys. J. D 31, 221 (2004), for efficient transformation of ultracold molecules to their absolute ground level ${v}_{X}=0$; ${J}_{X}=0$.