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National Cheng Kung University, Tainan, Taiwan

National Cheng Kung University, Tainan, Taiwan. First Experimental Observation of the Doubly-Excited 2 1 D g State of Na 2. $$ : National Science Council and National Space Program Office, Taiwan. Chin-Chun Tsai , Hui-Wen Wu, and Thou-Jen Whang

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National Cheng Kung University, Tainan, Taiwan

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  1. National Cheng Kung University, Tainan, Taiwan First Experimental Observation of the Doubly-Excited 21Dg State of Na2 $$ : National Science Council and National Space Program Office, Taiwan Chin-Chun Tsai, Hui-Wen Wu, and Thou-Jen Whang National Cheng Kung University, Tainan, 70148 Taiwan chin@ultracold.phys.ncku.edu.tw

  2. National Cheng Kung University, Tainan, Taiwan Outline • Motivation • The Rydberg State and Doubly Excited State of Na2 • Experimental Observations • Results and Discussions (A) Pumping to the Intermediate Levels (B) Doubly Excited State 21Dg of Na2 (C) Vibrational Quantum Number Assignment • Conclusion

  3. National Cheng Kung University, Tainan, Taiwan Rydberg States Doubly Excited States 2S+1Lg/u s1, l1 s2, l2 R Experimental observed transitions Assignment  DEvJ ,EvJ Motivation/ Some Potential curves of Na2 and asymptotic limits 3s+4d 31Dg 3p+3p 41Pg 3s+4p 31Pg 21Dg 3s+3d 21Pg 11Dg 3s+3p Solving the Schrodinger’s equation at fixed R EigenvaluesEvJ and Eigenfunctions YvJ B1Pu E(cm-1) X1Sg+ 3s+3s R(Å)

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

  5. National Cheng Kung University, Tainan, Taiwan The Rydberg States and Doubly Excited States of Na2 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. Na2+ Rydberg State of Na2 Doubly Excited State of Na2

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

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

  8. National Cheng Kung University, Tainan, Taiwan Excited Triplet States (23Pg or 33Pg) Ti-sapphire laser Fluorescence to filtered-PMT or Monochromator Ar+ laser a3Su+ Experimental Observations Collision Energy Transferred Excited State (21Dg、31Pg) Intermediate State (B1Pu) Ground State (X1Sg+) Scan Range of the term value: 31750～36800 cm-1

  9. National Cheng Kung University, Tainan, Taiwan Levels in B1Pu state populated by one of Ar+ laser lines Laser line(nm) Energy(cm-1) B(v’,J’) TB(v’,J’) X(v”,J”) TX(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 References：* P. Kusch and M. M. Hessel , J. Chem. Phys. 68, 2591 (1978). J J Camacho , Spectrochimica Acta Part A56, 769 (2000). Pumping to the Intermediate Levels Ar+ laser B1Πu X1Σg+ Ar+ laser lines：514.5*, 501.7, 496.5*, 488.0*, 476.5*, 472.7, 465.8, 457.9*, 454.5nm

  10. National Cheng Kung University, Tainan, Taiwan B(7,43) X(v”,42/44) B(4,30) X(v”,30) B(8,28) X(v”,27/29) Laser Induced Fluorescence by Ar+ Laser line at 496.5nm B1Pu → X1Sg+ 0.1554 X(15,42/44) 0.1082 X(16,42/44) 0.1016 X(14,42/44) 0.1449 X(11,30) 0.1348 X(17,27/29) 0.1468 X(16,27/29) 0.0789 X(12,30) 0.0282 X(13,30) 0.007 X(14,30) 0.0534 X(15,27/29) wavelength(nm)

  11. National Cheng Kung University, Tainan, Taiwan Excited Triplet States (23Pg or 33Pg) Ti-sapphire laser Fluorescence to filtered-PMT or Monochromator Ar+ laser a3Su+ Experimental Observations Collision Energy Transferred Excited State (21Dg、31Pg) Intermediate State (B1Pu) Ground State (X1Sg+) Scan Range of the term value: 31750～36800 cm-1

  12. National Cheng Kung University, Tainan, Taiwan 21Dg(12,49):12264.4060 Q line 21Dg(12,50):12275.3235 R line 21Dg(12,48):12253.6070 P line Doubly Excited State 21Dg of Na2 Intensity 12275.2 12275.3 12264.3 12264.4 12264.5 12253.7 12253.6 12275.4 cm-1 12253.5 The excitation spectrum of Na2 dimer at transition: 21Dg(v, J)←B1Pu(11,49)

  13. National Cheng Kung University, Tainan, Taiwan Vibrational and Rotational Quantum Number Observed in the Doubly Excited State 21Dg of Na2 Rotational quantum number J Vibrational quantum number v

  14. National Cheng Kung University, Tainan, Taiwan Harmonic Osc. Rigid Rotator Fitting Observed Levels to Dunham Coefficients Dunham coefficients (Yij): ﹡Some physical meanings of lower term of Dunham Coefficients (Yij) j\i 0 1 2 3 4 …….. 0 Te ωe -ωexe ωeye ωeze 1 Be -αeγe δe .. 2 -De -βe .. .. .. 3 He .. .. .. .. 4 Le .. .. .. .. .. .. .. .. .. ..

  15. National Cheng Kung University, Tainan, Taiwan V=15 RKR Potential Curve of Na221DgState --- Y00＝0.0018878

  16. National Cheng Kung University, Tainan, Taiwan RKR Potential Curve of Na221DgState E(cm-1) R(Å)

  17. National Cheng Kung University, Tainan, Taiwan Vibrational Quantum Number Assignment The Franck-Condom Factors between B1Pu and 21Dg States(*104)

  18. National Cheng Kung University, Tainan, Taiwan Spectrum of Result Fluorescence form 21Dg(1,83) to B1Pu States 21Dg(1,83) →B1Pu(v’,J’) 3D5/2→3P3/2 3D3/2→3PP/2 Intensity (a.u.) 3D3/2→3P1/2 0.5718 (1,82/83/84) 0.2659 (2,82/83/84) 0.1427 (0,82/83/84) Wavelength(nm)

  19. National Cheng Kung University, Tainan, Taiwan Molecular Constants of the Na221Dg State Yij(cm-1) This work* Standard Error (1s) Te 32416.75932 0.1477709620D-01 Y10 124.8483681 0.3585601190D-02 Y20 －0.4067499402 0.2661393475D-03 Y30 0.4644524015D-04 0.5910669692D-05 Y01 0.1191581157D+00 0.3375726563D-05 Y11 －0.5900023078D-03 0.5649162551D-06 Y21 －0.2482960616D-06 0.2655962788D-07 Y02 －0.4132661566D-06 0.2515878157D-09 Re(Å) 3.50845102 0.48592D-04 De 7552.028(20) * Observed regions: 0≦v≦28, 11≦J≦99

  20. National Cheng Kung University, Tainan, Taiwan Molecular constants of 21Dg state from different groups. (all high quality ab initio calculation) This work Jeung Henriet Henriet Magnier Magnier(1993) (1987) (1987) (1990) (Method A) (Method B) Te (cm-1) 32416.76(1) 32700 32800 32520 32360 32174 Y10 (cm-1) 123.848(4) 115 124.4 127.8 Re (Å) 3.50845(5) 3.5984 3.5137 3.5455 3.5032 3.4873 De (cm-1) 7552.028(20) 7255 7155 7435 7466 7500

  21. National Cheng Kung University, Tainan, Taiwan Conclusion The doubly-excited potential curve of Na2 21Dg state has been accurately determined by OODR spectroscopy to provide stringently tested for high quality theoretical calculations. Re = 3.50845 Å Interaction forces The strength of Na(3p) and Na(3p) interactions under 1Dg symmetry De = 7552.028(20) cm-1 Vibrational Constant Y10 124.848 cm-1we = (k/m)1/2 Rotational Constant Y01 0.11916 cm-1 Be = h/2pI

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

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