An analytical potential for the for the a 3  + state of KLi, (derived from observations of the upper vibrational levels only) Houssam Salami, Amanda Ross, Patrick Crozet Université Lyon 1 & CNRS. Robert J. Le Roy University of Waterloo Pawel Kowalczyk Warsaw University Wlodzimierz Jastrzebski Polish Academy of Sciences, Warsaw

K + Li S + P P + S S + S Motivation Reliable description of molecular levels close to atomic asymptotes Looking for Born-Oppenheimer breakdown, K 6 Li / K 7 Li Cold atom photoassociation occurs R > 20 Å Cold molecules ? X 1  + limit accessible via B  X or A  X fluorescence. But not a 3  +.

1)Obvious Experiment Pump A/b mixed levels How to reach the triplet manifold in KLi ? 2) Reliable Experiment 2 known (Warsaw) B/c mixed levels 3) Others? All PE curves are close at large R. A priori, via B-X, high v’ Ab initio PE curves, from M. Frécon, associated with S. Rousseau, et al Chem. Phys. 247, (1999) produced K 2 Gave B-X KLi, NaK

Molecules formed in the KLi heatpipe IR beam completely absorbed by K 2 vapour, doesn’t excite KLi KLi spectrum is quite congested ~ cm -1 LIF does not discriminate transitions as well as the 2 photon polarisation labelling technique laser Why did we have to resort to random searches ?

Method : detect ~ 6000 cm -1 below laser (optical filter), then record spectrum Gas phase sample Pierced mirror to reflect fluorescence ~ Doppler resolution Laser : SP 380D. FTS : Bomem DA3. Source : heatpipe oven FTS meter cw laser Laser tuned to chosen transition

To a 3  + To X 1  + First observation, laser = cm -1 R(16) 10-1, 39 K 6 Li Collisionally induced spectrum, no link with any known state!

Mixed B 1  /triplet levels found in 39 K 6 Li, v’ 20, 5 J  12 Combination differences match in B – X and B-a systems … ? To v = 41, X state

Spectra establish an energy scale. v max is 7 cm -1 below Li(2s) + K(4s) limit NOT enough information, Found ONLY for K 6 Li. Q(J) to X 1  +, O P, S R, Q (N’=J) lines to 4 levels of a 3  + The largest  G v in LIF matches the smallest  G v in CIF Largest  G v ~ 20 cm -1, Ab initio (Rousseau)  e 47.3 So vmin(obs)  0

Assigning vibrational quantum numbers No isotopic data available. No obvious match with ab initio predictions.  G v   v min 5 B v  v min 4 Franck-Condon Factors ? Requires V(R) for upper and lower state. B 1  – a 3  + ? Attempted RKR curves for possible v min Pointwise potential curve Analytical potential, MLJ from DPotFit program (results not suitable for this audience)

Modified Morse/Long-range potential form Dispersion coefficients have been calculated. C 6 =1.119 x 10 7 cm -1 Å 6 Derevianko, Babb, Dalgarno, Physical Review A 63, (2001) C 8 =2.63 x 10 8 cm -1 Å 8 Porsev, Derevianko J. Chem. Phys. 119 (2003) 844 Ground state dissociation energy is known D e (X, K 7 Li) is known = (5) cm -1 Martin et al J. Chem. Phys. 115 (2003) 4118 with imposed long-range form : * Model published : R. Le Roy, D. Henderson, Mol. Phys. 105, *

The other variables ? p > 2 imposed by C n constraints OPTIMIZE R e, NS, NL, p,  i for possible values of V min Larger p  larger number of  coefficients for given rms deviation

Data and Results J 149 data, now includes some isolated bands Fit to experimental uncertainty, 0.01 cm -1 RMS error is not an adequate diagnostic

Options for Vibrational Numbering : clusters of similar results. v min =4 absurd v min = 5 closest to Ab initio results : D e = 273 cm -1 R e = 4.97 Å v min = 6 few solutions Concentrate on v min = 5

Spectroscopic parameters from V(R) eliminate some options immediately Find average R e from acceptable solutions, fix, and re-fit data

Fitting parameters for V(R) of the a 3  + state, KLi 149 data, rms error cm -1 MLR takes p=3 N s = 1 N L = 6

Comparison with homonuclear alkalis 7 Li 2 23 Na 2 39 K 2 23 Na 39 K 39 K 7 Li ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– R e Potential fit4.173 a b c d 4.99±0.09 (Å) ab initio5.45 e f Arithmetic mean D e Potential fit a b g d 287. ± 4 (cm -1 ) ab initio197. e 273. f Harmonic mean  e Potential fit 65.4 a h d i 44.2 ± 1.5 (cm -1 )ab initio f Harmonic mean

Conclusion: Sensible solution with few observed levels D e = 287 cm -1 Binding Energy (cm -1 ) % R (Ångström) Possible to incorporate simultaneous fit to X and a. Leads to D e = 289 (2) cm -1, R e = A.

v,J observed in X state of K 6 Li, in rectangle, also with transitions to a 3  +