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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
$$ : 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
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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)
17
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