1

National Cheng Kung University, Tainan, Taiwan

First Experimental Observation of the

Doubly-Excited 21g State of Na2

Chin-Chun Tsai, Hui-Wen Wu, and Thou-Jen WhangNational Cheng Kung University, Tainan, 70148 Taiwan

chin@ultracold.phys.ncku.edu.tw

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

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National Cheng Kung University, Tainan, Taiwan

Outline

Motivation

The Rydberg State and Doubly Excited State of Na2

Experimental ObservationsResults and Discussions

(A) Pumping to the Intermediate Levels

(B) Doubly Excited State 21g of Na2

(C) Vibrational Quantum Number Assignment

Conclusion

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National Cheng Kung University, Tainan, Taiwan

4 6 8 10 12 140

5000

10000

15000

20000

25000

30000

35000

40000

R(Å)

E(c

m-1)

X1g+ 3s+3s

3s+3p

3s+3d

3s+4p3p+3p

3s+4d

B1u

11g

21g

31g

41g31g

21g

Motivation/ Some Potential curves of Na2 and asymptotic limits

Solving the Schrodinger’s equation at fixed REigenvalues EvJ and Eigenfunctions vJ

Experimental observed transitions Assignment EvJ ,EvJ

Rs1, l1 s2, l2

2S+1g/u

Rydberg StatesDoubly Excited States

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National Cheng Kung University, Tainan, Taiwan

Term valuesMolecular constants

(Yij)

Dunham program

RKR program RKR

potential information

Origin

Potential curve

Franck-Condon factors

Polynomial expression for potential curve

Splin program

EIGEN programEigen values and

eigen functions for all vibration

states

FCF program

Flow Chart of Data Analysis

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National Cheng Kung University, Tainan, Taiwan

The Rydberg States and Doubly Excited States of Na2

Rydberg State of Na2

Doubly Excited State of Na2

New electronic states observedprovide various physical phenomenafor understanding the atomic nature However, More than 95% statesobserved belong to Rydberg states.

The doubly excited states need moreexperimental data for analysis.

Na2+

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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

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National Cheng Kung University, Tainan, Taiwan

M

 

BS

M

Block diagram of experimental set-up

Verdi-10Laser

Ti-sapphire laser

Ar+ Laser

PMT+filter

Computer

Interface box Lock-inamplifier

Heat pipe ovenPrism

BSL A A

Chopper controller

PMT

 

Monochromator

Computer

Fiber

Wavemeter

Fiber

M M

M

LL

 

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Ground State(X1g

+)

Intermediate State(B1u)

                  

  Excited State (21g 、 31g)

Scan Range of the term value: 31750 ～ 36800 cm-1

Ar+ laser

Ti-sapphire laser

National Cheng Kung University, Tainan, Taiwan

Experimental ObservationsCollision EnergyTransferred

Fluorescence to filtered-PMT or Monochromator

a3u+

Excited Triplet States(23g or 33g)

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National Cheng Kung University, Tainan, Taiwan

B1Πu X1Σg+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’) 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

Levels in B1u state populated by one of Ar+ laser lines

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525 528 531 534

0.1449X(11,30)

0.1016X(14,42/44)

0.0789X(12,30)

0.1554X(15,42/44)

0.1082X(16,42/44)

0.0282X(13,30)

0.007X(14,30)

0.1348X(17,27/29)

0.1468X(16,27/29)

0.0534X(15,27/29)

B1u → X1g+

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

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Ground State(X1g

+)

Intermediate State(B1u)

                  

  Excited State (21g 、 31g)

Scan Range of the term value: 31750 ～ 36800 cm-1

Ar+ laser

Ti-sapphire laser

National Cheng Kung University, Tainan, Taiwan

Experimental ObservationsCollision EnergyTransferred

Fluorescence to filtered-PMT or Monochromator

a3u+

Excited Triplet States(23g or 33g)

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National Cheng Kung University, Tainan, Taiwan

The excitation spectrum of Na2 dimer at transition: 21g(v, J)←B1u(11,49)

Doubly Excited State 21g of Na2

21g(12,48):12253.6070

P line

21g(12,49):12264.4060

Q line

21g(12,50):12275.3235

R line

12253.5 12253.6 12253.7 12264.3 12264.4 12264.5 12275.2 12275.3 12275.4 cm-1

Inte

nsit

y

13

0

20

40

60

80

100

120

0 5 10 15 20 25 30

National Cheng Kung University, Tainan, Taiwan

Vibrational and Rotational Quantum Number Observed in theDoubly Excited State 21g of Na2

Vibrational quantum number v

Rot

atio

nal q

uant

um n

umbe

r J

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﹡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 -αe γe δe .. 2 -De -βe .. .. .. 3 He .. .. .. .. 4 Le .. .. .. .. .. .. .. .. .. ..

Dunham coefficients (Yij):

Fitting Observed Levels to Dunham Coefficients

National Cheng Kung University, Tainan, Taiwan

Harmonic Osc.

2,

0 0

1[ ( 1) ]

2

ij

v J iji j

T Y v J J

Rigid Rotator

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v Bv Gv + Y00 Gv+1/2 Rmin Rmax

0 0.1188631 62.3244 124.0350 3.361005 3.667974

1 0.1182726 186.3594 123.2219 3.260481 3.793620

2 0.1176816 309.5813 122.4091 3.194599 3.884770

3 0.1170901 431.9905 121.5966 3.142956 3.961834

4 0.1164981 553.5871 120.7844 3.099631 4.030732

5 0.1159056 674.3715 119.9724 3.061922 4.094169

6 0.1153126 794.3439 119.1607 3.028325 4.153649

7 0.1147191 913.5046 118.3493 2.997905 4.210113

8 0.1141252 1031.8539 117.5382 2.970031 4.264191

9 0.1135307 1149.3920 116.7273 2.944254 4.316336

10 0.1129357 1266.1193 115.9167 2.920244 4.366879

11 0.1123403 1382.0361 115.1064 2.897745 4.416079

12 0.1117443 1497.1425 114.2964 2.876560 4.464135

13 0.1111478 1611.4390 113.4867 2.856529 4.511210

14 0.1105509 1724.9256 112.6772 2.837521 4.557437

15 0.1099534 1837.6029 111.8681 2.819428 4.602926

16 0.1093555 1949.4709 111.0591 2.802160 4.647770

17 0.1087570 2060.5301 110.2505 2.785641 4.692048

18 0.1081581 2170.7806 109.4422 2.769804 4.735830

19 0.1075587 2280.2228 108.6341 2.754592 4.779174

20 0.1069587 2388.8569 107.8263 2.739956 4.822133

21 0.1063583 2496.6832 107.0188 2.725851 4.864753

22 0.1057574 2603.7021 106.2116 2.712241 4.907076

23 0.1051559 2709.9136 105.4046 2.699090 4.949139

24 0.1045540 2815.3183 104.5980 2.686367 4.990976

25 0.1039516 2919.9163 103.7916 2.674046 5.032617

26 0.1033487 3023.7078 102.9855 2.662101 5.074090

27 0.1027453 3126.6933 102.1796 2.650511 5.115420

28 0.1021414 3228.8729 2.639255 5.156631

RKR Potential Curve of Na2 21g State

---Y00 ＝ 0.0018878

National Cheng Kung University, Tainan, Taiwan

V=15

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RKR Potential Curve of Na2 21g StateNational Cheng Kung University, Tainan, Taiwan

32000

33000

34000

35000

36000

37000

38000

2 3 4 5 6 7 8

Magnier(1993)

This work

E(c

m-1)

R(Å)

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v'(B) v(2sdg)

0 1 2 3 4 5 6 7 8 9 10 11

0 8332 1427 210 27 3 0 0 0 0 0 0 0

1 1602 5718 2100 480 83 12 1 0 0 0 0 0

2 65 2695 3980 2326 735 160 29 4 0 0 0 0

3 0 158 3453 2833 2298 944 247 53 9 1 0 0

4 0 0 253 3992 2083 2133 1098 334 82 17 3 0

5 0 0 0 334 4392 1601 1904 1202 415 114 26 5

6 0 0 1 2 391 4703 1305 1650 1264 483 148 37

7 0 0 0 2 8 414 4956 1141 1396 1297 535 182

8 0 0 0 0 4 21 400 5164 1076 1151 1312 571

9 0 0 0 0 0 6 46 349 5329 1094 921 1319

10 0 0 0 0 0 0 8 86 265 5438 1186 709

11 0 0 0 0 0 0 0 9 147 162 5465 1352

12 0 0 0 0 0 0 0 1 8 227 62 5377

13 0 0 0 0 0 0 0 0 3 4 323 3

14 0 0 0 0 0 0 0 0 0 7 0 420

15 0 0 0 0 0 0 0 0 0 0 11 1

16 0 0 0 0 0 0 0 0 0 0 0 16

17 0 0 0 0 0 0 0 0 0 0 0 1

18 0 0 0 0 0 0 0 0 0 0 0 0

The Franck-Condom Factors between B1u and 21g States(*104)

National Cheng Kung University, Tainan, Taiwan

Vibrational Quantum Number Assignment

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810 820 830 840 850

0

2500

5000

7500

10000

12500

15000

17500

20000

21g(1,83) →B1u(v’,J’)

0.2659(2,82/83/84)

0.5718(1,82/83/84)

0.1427(0,82/83/84)

3D3/2→3P1/2

3D5/2→3P3/2

3D3/2→3PP/2

Spectrum of Result Fluorescence form 21g(1,83) to B1u States

Wavelength(nm)

Inte

nsit

y (a

.u.)

National Cheng Kung University, Tainan, Taiwan

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Yij(cm-1) This work* Standard Error (1)

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)

Molecular Constants of the Na2 21g State

* Observed regions: 0 v 28, 11 J 99≦ ≦ ≦ ≦

National Cheng Kung University, Tainan, Taiwan

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National Cheng Kung University, Tainan, Taiwan

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

Molecular constants of 21g state from different groups.

(all high quality ab initio calculation)

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National Cheng Kung University, Tainan, Taiwan

Conclusion

The doubly-excited potential curve of Na2 21g 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 1g symmetryDe = 7552.028(20) cm-1

Vibrational Constant Y10 124.848 cm-1 e = (k/m)1/2

Rotational Constant Y01 0.11916 cm-1 Be = h/2I

)(RUF

0F

Re = 3.50845 Å

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National Cheng Kung University, Tainan, Taiwan

Thank you for your attention!