States Of NaK Research Articles

Experimental and theoretical studies of the coupledA1Σ+andbΠ3states of NaK

We report an extensive series of transitions (including collisional transfer lines) from pure and mixed levels of the NaK ${A}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and $b\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{\ensuremath{\Pi}}$ states to the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state, observed at the Universit\'e Lyon 1 using Fourier-transform spectroscopy. We then combine these data with previously reported data on these states from emission from the ${B}^{1}\mathrm{\ensuremath{\Pi}}$ and ${C}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ states and from mutually perturbed levels of the $D{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ and $d\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{\ensuremath{\Pi}}$ states. We obtain 2758 distinct term values: the full data set includes 11 624 term values, with many multiple determinations from transitions over a range of vibrational and rotational levels. The data are analyzed by fitting to potentials of the ``Hannover'' form [C. Samuelis et al., Phys. Rev. A 63, 012710 (2000)] plus spin-orbit (SO) functions in a simple Morse form, yielding an rms residual of approximately 0.029 ${\mathrm{cm}}^{\ensuremath{-}1}$. The empirical SO functions agree well with their ab initio counterparts obtained from electronic structure calculations based on nonempirical effective core potentials. From level energies of the $A\ensuremath{-}b$ complex calculated from the fitted potentials and SO functions, we identify reasonable candidates for transitions between Feshbach resonance states and mixed singlet-triplet gateway levels of the ${A}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{-}b\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{\ensuremath{\Pi}}$ manifold, leading either to $v=0$ levels of the $X$ state or to mixed singlet-triplet levels at higher energies that can be used for perturbation-facilitated double-resonance experiments.

Molecular beam study of thea3Σ+state of NaK up to the dissociation limit

We provide spectroscopic data for the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state of the $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecule. The experiment is done in an ultrasonic beam apparatus, starting from the ground state $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and driving the population to the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state, using a $\ensuremath{\Lambda}$ scheme with fixed pump and scanning dump laser. The signals are observed as dips of the total fluorescence. The intermediate level is chosen to be strongly perturbed by the $B{\phantom{\rule{0.16em}{0ex}}}^{1}\ensuremath{\Pi}/c{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ states mixing to overcome the singlet-triplet transfer prohibition. We observed highly resolved hyperfine spectra of various rovibrational levels of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state from ${v}_{a}=2$ up to the highest vibrational levels for rotational quantum numbers ${N}_{a}=4,6,8$. By the typical experimental linewidth of 17 MHz, the vibrational dependence of the hyperfine splitting is clearly revealed for NaK. The absolute frequency measurements of the vibrational levels are used for improvement of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ potential curve and of the derived scattering length of all natural isotope combinations. Applying the $\ensuremath{\Lambda}$ scheme in the reverse direction can provide a pathway for efficient transfer of ultracold $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecules from the $\text{Na}(3s)+\text{K}(4s)$ asymptote to the lowest levels of the ground state. We show spectra that couple the absolute ground state ${v}_{X}=0,J=0$ with an appropriate intermediate state for direct realization of the reverse path. The refined theoretical model of the coupled excited states of the $\text{Na}(3s)+\text{K}(4p)$ asymptote allows predictions of efficient paths for $^{23}\mathrm{Na}^{40}\mathrm{K}$; one example is calculated.

Studies on heteronuclear diatomic molecular dissociation energies using algebraic energy method

The algebraic energy method (AEM) is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states: a3Σ+ state of NaK, X2Σ+ state of XeBr, X2Σ+ state of HgI, X1Σ+ state of LiH, A3∏(1) state of ICl, X1Σ+ state of CsH, A(3∏1) and B0+(3∏) states of ClF, 21∏ state of KRb, X1Σ+ state of CO, and c3Σ+ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature.

On the [formula omitted] state of NaK

The C 1 Σ + state of NaK has been observed up to v ′′=72 in a compilation of measurements from resolved laser induced fluorescence and polarisation labelling spectroscopy experiments. Resolved fluorescence experiments followed single colour optical–optical double resonance (sometimes with the source placed inside a dye laser cavity), or two-colour double resonance using two infrared dye lasers, which excited either the 6 1 Σ + or 3 1 Π electronic states. Fourier transform resolved fluorescence spectra show that low vibrational levels of the 3 1 Π state are efficiently depopulated by collisional electronic energy transfer to nearby vibrational levels of 6 1 Σ + . Equilibrium constants for the C 1 Σ + state of NaK are: T e =17786.75 cm −1 (with respect to the minimum of the electronic ground state), Y 10=69.6123 cm −1, Y 01=0.05919 cm −1.

Experimental study of the [formula omitted] and [formula omitted] states of NaK by polarization labeling spectroscopy technique

The polarization labeling spectroscopy technique is used to study the 6 1 Π←X 1 Σ + and 7 1 Π←X 1 Σ + band systems of the NaK molecule located in the UV range. For both excited states accurate molecular constants are derived which describe the 6 1 Π state to 68% and the 7 1 Π state to 71% of their potential well depths. The parameters deduced from the experiment are compared with the recent theoretical calculations.

The origin of Λ-doubling effect for the B 1∏ and D 1∏ states of NaK

The origin of Λ-doubling effect (q factors) for the regularly perturbed NaK B 1∏ and D 1∏ states has been investigated by means of ab initio many-body multipartitioning perturbation theory calculation of the electronic L-uncoupling matrix elements between the examined ∏1 and five lowest ∑+1 states for both Na3923K and Na4123K isotopomers. The hypothesis of pure precession was found to be valid for the B 1∏–A 1∑+ and D 1∏–C 1∑+ pairs of the interacted states, while the unique perturber approximation works properly for the D 1∏ state and completely breaks down for the B 1∏ state. The theoretical rovibronic q-factor values estimated for both states by means of the approximate sum rule agree well with their experimental counterparts and demonstrate high sensitivity to vibrational and rotational quantum numbers.

An improved potential energy curve for the ground stateof NaK

This paper presents an accurate potential curve for the groundstate of the NaK molecule. A series of resolved laser-inducedfluorescence spectra of the A-X system allowed a spread ofrotational levels in the lowest 70 vibrational levels (99.9%of the total well depth) to be observed. A variational methodcombining the inverted perturbation approach of Vidal andScheingraber (Vidal C R andScheingraber H 1977 J. Mol. Spectrosc. 65 46) forshort internuclear distances with an analytical expression forinternuclear distances beyond 8.5 Å has been used to constructa potential energy curve which reproduces the measured groundstate energies with an rms error of 0.003 cm-1. The dissociation energy and coulombicparameters governing the Na(3s) + K(4s) interactionderived from this potential curve are compared with recentvalues.

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

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.

A study of the predissociation of NaK molecules in the 6 1Σ+ state by optical–optical double resonance spectroscopy

Predissociation of a high-lying Σ+1 state of NaK is studied using the optical–optical double resonance technique. A single-mode ring dye laser is set to a particular 2(A)1Σ+(v,J)←1(X)1Σ+(v′′,J′′) transition. Another single-mode laser (Ti–sapphire) is then used to excite the molecule from the 2(A)1Σ+(v,J) level, to rovibrational levels of a higher predissociating electronic state, which we identify as 6 1Σ+. The predissociation is monitored by the atomic potassium emission on the 3 2D3/2→4 2P1/2 transition at 1.17 μm, while bound state radiative processes are monitored by total violet fluorescence from the upper state to the various rovibrational levels of the ground 1(X)1Σ+ state. By scanning the Ti–sapphire laser, different rovibrational levels of the 6 1Σ+ state can be excited. The vibrational levels probed range from v=13 to 20 with rotational states ranging from 9 to 99. The bound state energy level positions are measured from the center frequencies of lines recorded with the Ti–sapphire laser excitation scans. The 6 1Σ+ state is then described by the following molecular constants which are calculated from the experimental values of the level energies: Te=25 560.373 cm−1, ωe=89.179 26 cm−1, ωexe=0.730 691 cm−1, Be=0.067 327 0 cm−1, αe=0.000 675 35 cm−1, De=−3.298 31×10−8 cm−1, βel=1.518 17×10−8 cm−1. The potential well depth is De=4416.0 cm−1, if we assume the most likely asymptotic limit of Na(3 2S1/2)+K(5 2P1/2). The equilibrium separation is Re=4.158 Å. We also report measured and calculated intensities (Franck–Condon factors) for the 6 1Σ+→1(X)1Σ+ violet band. The absolute predissociation rates of 6 1Σ+ levels are directly measured from the linewidths recorded on the Ti–sapphire laser excitation scans. We measure predissociation rates ranging up to 9.4×109 s−1. The dependence of the absolute predissociation rates on rovibrational quantum numbers is studied with an attempt to predict the shape of the repulsive potential curve causing the predissociation, its crossing point with the bound state, and the type of perturbative interaction leading to the predissociation. The state causing the predissociation is determined from correlation diagrams to be the continuum of either the 3 3Π, the 3 1Π, or the 5 3Σ+ state with Na(3S)+K(3D) dissociation limit. We measure the collisional broadening rate coefficients of some 6 1Σ+←2(A)1Σ+ lines due to both argon and potassium perturbers, and obtain the average values, kbrAr=(1.1±0.2)×10−8 cm3 s−1 and kbrK=(1.1±0.6)×10−8 cm3 s−1. Velocity-changing collisions and collisional excitation transfer between individual rotational levels of the 2(A)1Σ+ state are also investigated.

Femtosecond laser spectroscopy on the vibrational wave packet dynamics of the A 1Σ+ state of NaK

The vibrational wave packet dynamics of a heteronuclear diatomic alkali molecule in an excited state, the A 1 Σ + state of gaseous NaK, has been measured for the first time. At λ pump = 790 nm, a wave packet oscillation period of 442 fs and dephasing within 10 ps has been observed. This dynamics has been analysed by calculation of Franck-Condon factors and difference potentials. It is from this seen that initially the pump pulse prepares a wave packet at the inner turning point of the A-state. The wave packet then evolves in time and is probed at the outer turning point by a transition to the E-state with subsequent fluorescence detection.

Perturbation model for the X1 Σ+ and a3 Σ+ states of NaK at intermediate internuclear distances beyond 6 Å

The energy of the X1Σ+ and a3Σ+ states of NaK was estimated from a perturbative model for intermediate- and long-range internuclear distances. Both the charge overlap effects calculated from a model previously published and the exchange contribution estimated from the asymptotic formula were taken into account. Fitted analytical expressions are proposed for electrostatic and induction energy terms as well as for various dispersion damping functions. From comparison with accurate experimental results, the present model is seen to be valid for values of R greater than 6 Å (1 Å = 10−10 m) for the X1Σ+ state and R greater than 8 Å for the a3Z+ state.

Effects of magnetic field on the perturbation between the B 1Π and c 3Σ+ states of NaK

Zeeman spectra of the strongly perturbed lines between the B 1Π and c 3Σ+ states of NaK were measured by the Doppler-free laser polarization spectroscopy. Magnetic field dependence of the Zeeman pattern was studied and the line shapes were found to change remarkably because of the mixing of the B 1Π and c 3Σ+ states. The patterns of Zeeman splitting were found to be different depending on whether the level was located on the high energy side or the low energy side of the interacting level. The observed Zeeman spectra were studied by taking account of the spin–orbit, hyperfine, and Zeeman interactions. The Zeeman spectroscopy is shown to be useful to analyze the perturbation between the excited states.

An inversion procedure for oscillatory continuum spectra: Method and application to NaK

An inversion procedure is developed for determining an attractive potential energy well from the structure of an oscillatory absorption or emission continuum originating in a single vibrational level of that well. It is successfully applied to synthetic data for the 1Π1u←X(1Σ+g) absorption continuum of Br2, and to experimental data for d(3Π1)→a(3Σ+) emission of NaK. The latter application succeeds in spite of the facts that (i) the repulsive wall of the final-state potential is also not known, and (ii) this final-state curve has an attractive well whose location causes the structured emission continuum to be truncated, making the vibrational assignment uncertain. This analysis yields potentials for the well of the d(3Π1) state and the repulsive wall of the a(3Σ+) state of NaK, together with the slope of the transition dipole function coupling these two states.

The A(2) 1Σ + state of NaK

The A(2) 1Σ + state of NaK

Σ and Π molecular states for NaK +, KRb + and NaRb + molecular ions

A non-local pseudopotential method including polarization effects is used to calculate the Σ and Π states of NaK +, NaRb + and KRb + molecular ions, up to the sixth excited state. Crossing and pseudocrossing parameters are given.

NaK chemiluminescence

The gas phase reaction between a mixture of K and Na and CBr 4 produces, under low-density conditions, emission from high-lying vibrational levels (υ′ > 9) of the B 1 Π state of NaK.

Theoretical study of the lowest potential curves of NaK

The lowest nine states of NaK have been calculated with large Cl using non-empirical pseudopotentials. A recently developed perturbation treatment of the core—valence polarization and correlation effects is applied. It greatly improves the calculated atomic energies of Na and K; and appears to be very important for energy curves of NaK, leading to an overall good agreement with the experimental results.

The a 3Σ+ state of NaK. High resolution spectroscopy using laser-induced fluorescence (LIF)

We use laser-induced fluorescence (LIF) combined with a high resolution grating spectrometer to study the D 1Π→a 3Σ+ transitions of the heteronuclear alkali dimer NaK. Intense perturbations of the D 1Π state permit high resolution measurements and facilitate study of the corresponding intensities. From these spectra, we evaluate the molecular constants of the a 3Σ+ state of NaK and estimate the parameters involved in the perturbations of the D 1Π state. Various features of the perturbing levels are discussed. We compare the results of our analysis with the results of spin-exchange scattering experiments on the NaK system and with theoretical calculations. In addition, very accurate dissociation energies, De(NaK, 1Σ+) =5268.1±0.8 cm−1 and De(NaK, a 3Σ+) =203.1±0.5 cm−1, are obtained.