1. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 1 Investigation of the Investigation of the L-uncoupling and Λ-doubling in the Rydberg states of the sodium dimer $$ : National Science Council and National Space Program Office, Taiwan Ray-Yuan Chang, Thou-Jen Whang, Chuen-Ping Cheng, and Chin-Chun Tsai National Cheng Kung University, Tainan, 70148 Taiwan

2. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 2 L-uncoupling for the Rydberg states L R K Case (d) Case (a) J N  L Na+Na For singlet state

3. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 3 J 0 2 3 1 0 4 4 2 2 4 3 2 1 4 3 2 1 0 4 3 2 3 4 1 5 6 4 3 2 3 1 5 1 2 3 2 R K Case (d) Case (a) 11 11 11 L R K Case (d) Coupling case transition Case (a) J N  L

4. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 4 Ground state (X 1  g + ) Intermediate state (B 1  u ) Fluorescence a3u+a3u+ (2 3  g or 3 3  g ) ( 5 1  g 、 5 1  g ) ( 35350 ～ 40300 cm -1 ) Experimental energy range 35350 ～ 40300 cm -1 Ar + laser 9-lines Dye-Ring laser ( DCM ) 6022.0286 cm -1 (29328 ～ 34278 cm -1 ) ( 19440 ～ 22000 cm -1 ) ( U.V. 292 ～ 341 nm ) Probing energy range Detection

5. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 5 Ar + Laser Interface Box Computer Lock-in Amplifier BS Dye-ring Laser Verdi-10 Laser PMT+Filter Chopper Controller Heat Pipe Oven I 2 Cell PMT+Filter L LI I C M M OODR-Experimental setup ～ 0.03cm -1 Systematic accuracy ～ 0.03cm -1

6. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 6 Lower terms of Dunham Coefficients (Y ij ) j\i 0 1 2 3 4 …….. 0 y 00 ω e -ω e x e ω e y e ω e z e 1 B e -α e γ e δ e.. 2 -D e -β e...... 3 H e........ 4 L e.................... Dunham Coefficients Harmonic Oscillator Anharmonic part

7. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 7 Data Fitting Energy (cm -1 ) J （ J+1 ） -Λ 2

8. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 8 J+1 J=JJ=J J-1 J  +1 J  =J J  -1 J e e f f e f e f e e e PP P R RQ Q R Q Separation of e/f levels Case (a) 51g51g51g51g

9. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 9 Corrected Description Splitting Constant

10. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 10  f-e (cm -1 ) 5 1 Δ g ： e/f level difference

11. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 11 Splitting constants 5 1 Δ g ： Least Square Fitting  =0.04 cm -1

12. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 12 Residuals (cm -1 )  =0.026 cm -1 Eigenvalue (cm -1 ) 5 1 Δ g ： Regenerate the eigenvalue

13. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 13  f-e (cm -1 ) 5 1 Π g ： e/f level difference

14. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 14 Splitting constants 5 1 Π g ： Least Square Fitting

15. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 15 Residuals (cm -1 )  =0.028 cm -1 Eigenvalue (cm -1 ) 5 1 Π g ： Regenerate the eigenvalue

16. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 16 ＊ We’ve observed the L-uncoupling in the Na 2 by using the high resolution OODR spectroscopy. ＊ The energy splitting of both the 5 1 Δ g 、 5 1 Π g states have been figured out with σ < 0.03 cm -1 Conclustion ＊ The transient Hund’s case transition process can be mapped out by the investigation of the higher Rydberg series in (nd) 1 Δ g 、 (nd) 1 Π g states

17. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 17 (B 1  u ) First order splitting constant The Λ -doubling splitting increases as a quadratic function of rotational quantum number J and the dependence on the vibrational quantum number v is weak. The large Λ -doubling splitting constants indicate that the effects are from the perturbations between the adjacent electronic states as well as the uncoupling of orbital angular momentum L. 26 intermediate levels of the B state are populated by nine Argon laser lines. 230 rovibrational levels are assigned to the 5spg state.

18. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 18

19. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 19

20. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 20 References ： * P. Kusch and M. M. Hessel, J. Chem. Phys. 68, 2591 (1978). J J Camacho, Spectrochimica Acta Part A56, 769 (2000). B 1 Π u X 1 Σ g + Ar + laser Ar + laser lines ： 514.5*, 501.7, 496.5*, 488.0*, 476.5*, 472.7, 465.8, 457.9*, 454.5nm 。 Pumping to the Intermediate Levels Laser line(nm) Energy(cm -1 ) B(v’,J’) T B (v’,J’) X(v”,J”) T X (v”,J”) 496.5 20135.057 (4,30) 20976.0696 (4,30) 840.8850 (7,43) 21430.7481 (6,44) 1295.6275 (8,28) 21415.3652 (7,29) 1280.2374 Levels in B 1  u state populated by one of Ar + laser lines

21. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 21 Symmetries in the cold collisions Two atoms collide with channels doubled Atom1, Rb 5s 2 S 1/2 Atoms, Rb 5s 2 S 1/2 Ground state collisions Electron spin s 1 =1/2s 2 =1/2total S=s 1 +s 2 Angular momentum l 1 =0l 2 =0total L=l 1 +l 2 R (interatomic distance) S=0 or 1 and L=0

22. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 22 Symmetries – Electronic states Orbital angular momentum ： L  L Λ =0, 1, 2, …, L, called  Π  Δ … Electronic states. M L = L, L-1, …., -L, and Λ =|M L |

23. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 23 Electronic spin S=  s i For Λ  0, the internal magnetic field causes a precession of S about the field direction (internuclear axis). Components of the precession:  = S, S-1, S-2, …, -S  S Symmetries – Electronic spin

24. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 24 J 0 2 3 1 0 4 4 2 2 4 3 2 1 4 3 2 1 0 4 3 2 3 4 1 5 6 4 3 2 3 1 5 1 2 3 2 R K Case (d) Case (a) 11 11 11 L R K Case (d) Coupling case transition Case (a) J N  L

25. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 25  For example (S=1) : 2S+1   33 33 33 Multiplet structure   S   S   S Symmetries – Total angular momentum

26. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 26 Symmetries – Hund’s coupling cases Hund’s case(a) S  ： individual electron spin Total electron spin  L ： individual electron angular momentum Total orbital angular momentum J N Nuclei rotation 

27. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 27 Symmetries – Hund’s coupling cases  S  N J L  Hund’s case(a) 2S+1  

28. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 28  (x, y, z) Case(a) Symmetries – Electronic eigenfunctions Plane symmetry Non-degenerate states Λ=0 +: even symmetry as + - : odd symmetry as -  (x, y, z) Inversion symmetry +: even symmetry as gerade state, g - : odd symmetry as ungerade state, u  (-x, -y, -z)

29. Ultracold Atomic Physics Laboratory National Cheng Kung University, Tainan, Taiwan 2007 OSU Symposium 22, 2007 Ray-Yuan Chang June 22, 2007 29 The standard deviation excess the systematic accuracy!! ～ 0.03cm -1 Is there something wrong!? Dunham Coefficients?