1. 1 National Cheng Kung University, Tainan, Taiwan First Experimental Observation of the Doubly-Excited 2 1  g State of Na 2 Chin-Chun Tsai, Hui-Wen Wu, and Thou-Jen Whang National Cheng Kung University, Tainan, 70148 Taiwan chin@ultracold.phys.ncku.edu.tw $$ : National Science Council and National Space Program Office, Taiwan

2. 2 National Cheng Kung University, Tainan, Taiwan Outline Motivation The Rydberg State and Doubly Excited State of Na 2 Experimental Observations Results and Discussions (A) Pumping to the Intermediate Levels (B) Doubly Excited State 2 1  g of Na 2 (C) Vibrational Quantum Number Assignment Conclusion

3. 3 National Cheng Kung University, Tainan, Taiwan R(Å) E(cm -1 ) X1g+X1g+ 3s+3s 3s+3p 3s+3d 3s+4p 3p+3p 3s+4d B1uB1u 11g11g 21g21g 31g31g 41g41g 31g31g 21g21g Motivation/ Some Potential curves of Na 2 and asymptotic limits Solving the Schrodinger’s equation at fixed R  Eigenvalues E vJ and Eigenfunctions  vJ Experimental observed transitions  Assignment   E vJ,E vJ R s 1, l 1 s 2, l 2 2S+1  g/u Rydberg States Doubly Excited States

4. 4 National Cheng Kung University, Tainan, Taiwan Term values Molecular constants (Yij) Dunham program RKR program RKR potential information Origin Potential curve Franck-Condon factors Polynomial expression for potential curve Splin program EIGEN program Eigen values and eigen functions for all vibration states FCF program Flow Chart of Data Analysis

5. 5 National Cheng Kung University, Tainan, Taiwan The Rydberg States and Doubly Excited States of Na 2 Rydberg State of Na 2 Doubly Excited State of Na 2 New electronic states observed provide various physical phenomena for understanding the atomic nature However, More than 95% states observed belong to Rydberg states. The doubly excited states need more experimental data for analysis. Na 2 +

6. 6 National Cheng Kung University, Tainan, Taiwan Table from: Li Li, Y. M. Liu, and A.M. Lyyra, J. Chin. Chem. Soc. 48, 291 (2001). Doubly Excited vs. Rydberg States

7. 7 National Cheng Kung University, Tainan, Taiwan M BS M Block diagram of experimental set-up Verdi-10 Laser Ti-sapphire laser Ar + Laser PMT+filter Computer Interface box Lock-in amplifier Heat pipe oven Prism BS L A A Chopper controller PMT Monochromator Computer Fiber Wavemeter Fiber M M M L L

8. 8 Ground State (X 1  g + ) Intermediate State (B 1  u ) Excited State (2 1  g 、 3 1  g ) Scan Range of the term value: 31750 ～ 36800 cm -1 Ar + laser Ti-sapphire laser National Cheng Kung University, Tainan, Taiwan Experimental Observations Collision Energy Transferred Fluorescence to filtered-PMT or Monochromator a3u+a3u+ Excited Triplet States (2 3  g or 3 3  g )

9. 9 National Cheng Kung University, Tainan, Taiwan 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 References ： * P. Kusch and M. M. Hessel, J. Chem. Phys. 68, 2591 (1978). J J Camacho, Spectrochimica Acta Part A56, 769 (2000). 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

10. 10 0.1449 X(11,30) 0.1016 X(14,42/44) 0.0789 X(12,30) 0.1554 X(15,42/44) 0.1082 X(16,42/44) 0.0282 X(13,30) 0.007 X(14,30) 0.1348 X(17,27/29) 0.1468 X(16,27/29) 0.0534 X(15,27/29) B 1  u → X 1  g + wavelength(nm) Laser Induced Fluorescence by Ar + Laser line at 496.5nm B(7,43) X(v”,42/44) B(4,30) X(v”,30) B(8,28) X(v”,27/29) National Cheng Kung University, Tainan, Taiwan

11. 11 Ground State (X 1  g + ) Intermediate State (B 1  u ) Excited State (2 1  g 、 3 1  g ) Scan Range of the term value: 31750 ～ 36800 cm -1 Ar + laser Ti-sapphire laser National Cheng Kung University, Tainan, Taiwan Experimental Observations Collision Energy Transferred Fluorescence to filtered-PMT or Monochromator a3u+a3u+ Excited Triplet States (2 3  g or 3 3  g )

12. 12 National Cheng Kung University, Tainan, Taiwan The excitation spectrum of Na 2 dimer at transition: 2 1  g (v, J)←B 1  u (11,49) Doubly Excited State 2 1  g of Na 2 2 1  g (12,48):12253.6070 P line 2 1  g (12,49):12264.4060 Q line 2 1  g (12,50):12275.3235 R line 12253.5 12253.6 12253.7 12264.312264.412264.5 12275.212275.3 12275.4 cm -1 Intensity

13. 13 National Cheng Kung University, Tainan, Taiwan Vibrational and Rotational Quantum Number Observed in the Doubly Excited State 2 1  g of Na 2 Vibrational quantum number v Rotational quantum number J

14. 14 ﹡ Some physical meanings of lower term of Dunham Coefficients (Y ij ) j\i 0 1 2 3 4 …….. 0 T e 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 (Y ij ): Fitting Observed Levels to Dunham Coefficients National Cheng Kung University, Tainan, Taiwan Harmonic Osc. Rigid Rotator

15. 15 RKR Potential Curve of Na 2 2 1  g State --- Y 00 ＝ 0.0018878 National Cheng Kung University, Tainan, Taiwan V=15

16. 16 RKR Potential Curve of Na 2 2 1  g State National Cheng Kung University, Tainan, Taiwan E(cm -1 ) R(Å)

17. 17 The Franck-Condom Factors between B 1  u and 2 1  g States(*10 4 ) National Cheng Kung University, Tainan, Taiwan Vibrational Quantum Number Assignment

18. 18 2 1  g (1,83) →B 1  u (v’,J’) 0.2659 (2,82/83/84) 0.5718 (1,82/83/84) 0.1427 (0,82/83/84) 3D 3/2 →3P 1/2 3D 5/2 →3P 3/2 3D 3/2 →3P P/2 Spectrum of Result Fluorescence form 2 1  g (1,83) to B 1  u States Wavelength(nm) Intensity (a.u.) National Cheng Kung University, Tainan, Taiwan

19. 19 Y ij (cm -1 ) This work* Standard Error (1  ) T e 32416.75932 0.1477709620D-01 Y 10 124.8483681 0.3585601190D-02 Y 20 － 0.4067499402 0.2661393475D-03 Y 30 0.4644524015D-04 0.5910669692D-05 Y 01 0.1191581157D+00 0.3375726563D-05 Y 11 － 0.5900023078D-03 0.5649162551D-06 Y 21 － 0.2482960616D-06 0.2655962788D-07 Y 02 － 0.4132661566D-06 0.2515878157D-09 R e (Å) 3.50845102 0.48592D-04 D e 7552.028(20) Molecular Constants of the Na 2 2 1  g State * Observed regions: 0 ≦ v ≦ 28, 11 ≦ J ≦ 99 National Cheng Kung University, Tainan, Taiwan

20. 20 National Cheng Kung University, Tainan, Taiwan This work Jeung Henriet Henriet Magnier Magnier(1993) (1987) (1987) (1990) (Method A) (Method B) T e (cm -1 ) 32416.76(1) 32700 32800 32520 32360 32174 Y 10 (cm -1 ) 123.848(4) 115 124.4 127.8 R e (Å) 3.50845(5) 3.5984 3.5137 3.5455 3.5032 3.4873 D e (cm -1 ) 7552.028(20) 7255 7155 7435 7466 7500 Molecular constants of 2 1  g state from different groups. (all high quality ab initio calculation)

21. 21 National Cheng Kung University, Tainan, Taiwan Conclusion The doubly-excited potential curve of Na 2 2 1  g state has been accurately determined by OODR spectroscopy to provide stringently tested for high quality theoretical calculations. Interaction forces The strength of Na(3p) and Na(3p) interactions under 1  g symmetry D e = 7552.028(20) cm -1 Vibrational Constant Y 10 124.848 cm -1  e = (k/m) 1/2 Rotational Constant Y 01 0.11916 cm -1 B e = h/2  I R e = 3.50845 Å

22. 22 National Cheng Kung University, Tainan, Taiwan Thank you for your attention!