1. Coupled channel analysis of the D 1P~ d 3P complex in NaK : potential energy curves and spin-orbit functions
Anastasia Drozdova1,2 Amanda Ross1, Andrey Stolyarov2, Wlodzimierz Jastrzębski3, Paweł Kowalczyk4
1 LASIM Université Lyon 1
2 Department of Chemistry, Moscow State University
3 Institute of Physics, Polish Academy of Sciences, Warsaw
4 Institute for Experimental Physics, University of Warsaw
E cm-1
24000
22000
20000
Na*(3p) + K(4s) R
Na(3s) + K(4p)

2. Polarisation labelling spectrum shows obvious vibrational patterns
Polarisation labelling spectrum shows obvious vibrational patterns. In most cases, J assignments are known from the pump transition. Rotational spacings are a problem.
De (D 1P) = cm-1
Converging to Na 2P3/2 + K(4s)
limit …
cm-1
Dominant D-X series of P(38),Q(38), R(38) triplets, with many ‘extra lines’. Pump transition was B-X Q(38) 7-2 ( cm-1)

3. 1400 term energies for the D1Π~d3П complex of NaK
Term energies are located to ± cm-1
All series are very irregular.
Robust fit gave a reasonable V(R) for the D 1P state, but only 74% of the data set is within 2 SD of measurements

4. Adiabatic approximation4

5. Starting point for analysis of the D1Π~d3П states of NaK
E (cm-1)
Overlap on inner wall produces large FCF overlap between d,D vibrational levels.
Spin-orbit mixing tangles the spectrum.
D 1P (experimental)
d 3P (ab initio)
R (Å)

6. Coupled channel calculation
ΦCC is a total nonadiabatic rovibronic wave function , V is the potential energy matrix ECC is the total nonadiabatic energy of the jth level of the complex aр are fitting parameters (Morse-Lennard Jones potentials, Morse SO functions) 6

7. Potential energy matrix.
Spin orbit matrix elements
Diagonal ASO
off-diagonal SO
where x = J(J+1), and B(R) =
Proceed with ‘normally’ weighted least squares fit to 30 parameters Expanded Morse Oscillator for SO functions Morse/Lennard Jones function for PE curves, with ab initio limiting behaviour ULR(R) = D – C6/R6 - C8/R8

8. Analytical representation of matrix elements
Potential energy curves
Morse/Lenard-Jones (MLJ) model
Spin-orbit functions
Expanded Morse oscillator (EMO) model
Potential energy curves
Morse/Lenard-Jones (MLJ) model
Potential energy curves
Morse/Lenard-Jones (MLJ) model
Potential energy curves
Morse/Lenard-Jones (MLJ) model
Potential energy curves
Morse/Lenard-Jones (MLJ) model

9. Results: spin-orbit functions and revised PE curves
D 1P V(R) not very much altered from 1 channel calculation …
E cm-1 8 6 4
SONa(3p) 5.73 cm-1
R (Angström) 9

10. Definite improvement with the four-channel model
Obs-Calc
(cm-1)
Na 3p 2P1/2
limit 10

11. This model is nonsense at the asymptote : D 1P and d 3P share a common limit!

12. Asymptotic energies for W = 1 states
K(4s) + Na(3p)  data from Marinescu & Sadeghpour Phys. Rev. A, (1999) C6 (S) = a.u. (repulsive), C6 (1,3P) = a.u. (attractive) ;
Energy matrix courtesy M. Aubert-Frécon (following J.Mol. Spectrosc (1998))

13. Next model for the asymptote ?
1 states only

14. Comments
A reasonable model for the two lowest 1 states is within reach.
The model still neglects effects of the continuum (lower SO limit)
ACKNOWLEDGEMENTS
- A. Drozdova, A. Stolyarov at MSU (Co-authors and principal contributors)
- M. Aubert-Frécon, LASIM

15. Results: potential energy curves
R, A
Enonad - Ead
3.300
0.798
5.000
-0.074
3.400
0.907
5.200
-0.367
3.500
-0.120
5.400
-0.482
3.600
-0.888
5.600
-0.491
3.700
-0.983
5.800
-0.475
3.800
-0.572
6.000
-0.458
3.900
-0.052
6.200
-0.431
4.000
0.229
6.400
-0.389
4.020
0.241
6.600
-0.338
4.040
0.238
6.800
-0.298
4.080
0.191
7.000
-0.290
4.100
0.150
7.200
-0.333
4.120
0.100
7.400
-0.438
4.140
0.043
7.600
-0.607
4.160
-0.017
7.800
-0.836
4.180
-0.079
8.000
-1.119
4.200
-0.139
8.200
-1.442 15

16. 2-colour polarisation labelling : J selective excitation
Experiment performed at IF-PAN, Warsaw
Excimer laser
Dye laser
Pump laser (Ar+) FD
computer MC
Ar HCL
PMT FP PD
boxcar 2
boxcar 3
boxcar 1
NaK source P1 P2
l/4 plate
(removable) A
PUMP beam goes through crossed polarisers placed either side of the heatpipe, then to a monochromator and PMT. The PROBE beam is scanned. PMT signals rise when probe resonance involves one of the ‘pumped’ levels.

17. Another spectrum (one of the better ones)
v’ =
NaK D-X P,R doublets, J"=24 by P(24) 3-3 label, nm Ar+. Extra lines are indicated by asterisks
o indicates Na2 B-X signals, J’=43 o o
v’ = 27 30 o o o 35 40

18. Fit to a potential energy curve, eliminating all line/extra-line , using ‘robust’ weighting 1/[(si2 +( /3) 2] to compensate an inadequate model.
V(R) is a 'Morse/Lennard-Jones' analytical expression given by Hajigeorgiou & Le Roy. J. Chem. Phys. 112, (2000)
P=2, NS=2, NL = 8
Parameters to be determined are Re and f
C6 case c limit is known from ab initio work  106 cm-1 Å6, Chem. Phys. 116, (1987)

19. Comments on the fit to a potential curve
74 % of the data set is reproduced to within 2 SD
~ 60 severe outliers (|Eobs – Ecalc | > 0.25 cm-1).
Te (cm-1) (2)
De (cm-1) fixed
Re (Å ) (24)
C6 (cm-1 Å6)  fixed
qL (1/ cm-1) 1.21(50)  10-3
This can be a starting point for a coupled state calculation.

20. Left over from late ’80s : small selection of T(v,J) energies, inadequate description of the D 1P molecular state, mixed with d 3P.
E cm-1 4
AR thesis, Lyon Breford & Engelke, Bielfeld : T’ values from Ar+ dispersed LIF
P. Kowalczyk : some 3P1 levels J. Mol. Spectrosc. 136, (1989) 1-11
Ferber group, Riga : L doubling low v Phys. Rev. A 58, (1998)
Zaitsevski group, Moscow, deperturbed earlier data Mol. Phys. 96, (1999) 3
Na(3p) + K(4s)
D,d 3
Na(3s) + K(4p) B c
1S+ 1P
3S+ 3P b A