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, Taiwan $$ : National Science Council and National Space Program Office, Taiwan

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 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 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 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 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 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 Ground State (X 1  g + ) Intermediate State (B 1  u ) Excited State (2 1  g 、 3 1  g ) Scan Range of the term value: ～ 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 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”) (4,30) (4,30) (7,43) (6,44) (8,28) (7,29) Levels in B 1  u state populated by one of Ar + laser lines

X(11,30) X(14,42/44) X(12,30) X(15,42/44) X(16,42/44) X(13,30) X(14,30) X(17,27/29) X(16,27/29) 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 Ground State (X 1  g + ) Intermediate State (B 1  u ) Excited State (2 1  g 、 3 1  g ) Scan Range of the term value: ～ 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 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  g (12,48): P line 2 1  g (12,49): Q line 2 1  g (12,50): R line cm -1 Intensity

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 ﹡ Some physical meanings of lower term of Dunham Coefficients (Y ij ) j\i …….. 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 H e L e Dunham coefficients (Y ij ): Fitting Observed Levels to Dunham Coefficients National Cheng Kung University, Tainan, Taiwan Harmonic Osc. Rigid Rotator

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

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

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

 g (1,83) →B 1  u (v’,J’) (2,82/83/84) (1,82/83/84) (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 Y ij (cm -1 ) This work* Standard Error (1  ) T e D-01 Y D-02 Y 20 － D-03 Y D D-05 Y D D-05 Y 11 － D D-06 Y 21 － D D-07 Y 02 － D D-09 R e (Å) D-04 D e (20) Molecular Constants of the Na  g State * Observed regions: 0 ≦ v ≦ 28, 11 ≦ J ≦ 99 National Cheng Kung University, Tainan, Taiwan

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 ) (1) Y 10 (cm -1 ) (4) R e (Å) (5) D e (cm -1 ) (20) Molecular constants of 2 1  g state from different groups. (all high quality ab initio calculation)

21 National Cheng Kung University, Tainan, Taiwan Conclusion The doubly-excited potential curve of Na  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 = (20) cm -1 Vibrational Constant Y cm -1  e = (k/m) 1/2 Rotational Constant Y cm -1 B e = h/2  I R e = Å

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