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Hund’s case (b)

N=R+!

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Hund’s case(a)

#=!+"

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-2S, P, D, F, G....

! = 0, 1, 2, 3, 4 ,,,,

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'(

¼:y_Uk

2S+1: ¼:y_Uk

cdÎ

10

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fõ('({{'(2¯ghij&áklYmp\`RR"=0e#-g{{nö(op+)Jq>r/(op-)JpsqJRR"9õU-&&`3Ý¿(op+)_%3Ý¿(op-)

f¡çõ('({{dt\&Õ(¯4Yä[\r/dM+±hRR|el> &q>¿JLK]pRc"#(even) = g (gerade) q>¿JLMR d"#(odd) = u (ungerade)

#g, $u¡

|el> +|rot>j±PM

|rot>=YJM(%,&)~c`uvr/Ymp\VJw+YSTdMhJ=0jVnöh

uvr/=z2ß/(|el>nö)i'(2¯ghár/x(cJ)op+/- +÷^

¡çõ('(&çSaeyX(4r/iÕ(&84r/gYmp\

|el> |rot>R&q>nöRiRsym. RR{(+) , g } {(-), u }

RRRRRRq>r/Ri@antisym. RRzXY

e-parity : (-1)J f-parity -(-1)J j{|dM"A_

11

34'(#AB$CDEFGH&æÙß/}~

12

Õ(ÏÒ¾Ð&æÙß/}~

(n’, v’, J’) iÏn”, v”, J”)

!

I = h" # $ N A $ n % $ $ n

A $ n % $ $ n = 2.026 &10'6" 3

$ n $ v $ J µe$ $ n $ $ v $ $ J

2

2 $ J +1

$ n $ v $ J µe$ $ n $ $ v $ $ J

2

= $ v $ n µe$ $ n $ $ v

2

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= $ v Re(r) $ $ v

2

$ J $ $ J 2

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= Re2(r " v , " " v ) " v " " v

2

= Re2(r " v , " " v )q " v , " " v

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!

A " n # " " n =$%3Re2q " v " " v

S " J " " J

2 " J +1

S " J " " J " J

& = 2 " J +1

q " v " " v " v " " v

& =1 Franck-Condon (

Hönl-London (

P(branch) J’-J”=-1

Q(branch) J’-J”=0

R(branch) J’-J”=+1

13

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hijklmnoVUVp

15

z;

17

5x10-3

4

3

2

1

0

Sig

na

l in

ten

sit

y[a

rb.

un

it]

660640620600Wavelength [nm]

Q

R

(0-0)P

(1-1)P

(2-2)P(3-3)P

1 5 1 5 1 5 1 5 1 5 1 1(0-0) (1-1) (2-2) (3-3) (4-4) (5-5) (6-6)

4 0 4 0 4 0 3 0

2 6

2 6

2 6

2 5

J''

(0-0) (1-1)

!H

(b)

1m-Czerny-Turner (2400 G/mm), PMT(Hamamatsu R928)

Wavelength resolution(FWHM) < 0.03 nm @50 µm slit

#AB$CDE@89¥:@;¦D$§E9

18

!

RX ,vd,v'"qvv'

X #dexp{

#Ev(0) + Ev(v)

kTe}

tukl×¹ØÙÚBÊ˱Á,ÌÍ®ÚBÛÜsÝÞ8(MAR)

ØÙÚB9:@ßhoFulcher-!²,àF-CAðÍüý¹¼ã

case: d -> a : G Staszwska 1999

case: X -> d: Meneses, 1995

ÃBkl¡¢@ÈÉkl2þÆÇÿ!¼ã

X1"+g

d3#-u

a3"+g

!

Aa,v"d,v '"qvv '

d# a

!

R2(X " d) = Re

2#qvv'X "d

# SJJ 'X" d

Ãklòó®vw".#,î$%ª&'()*ã

Ã

19

#B9¥$¨F¼(G Staszwska 1999)

Fulcher-!@vw".#,Re(r)

'"kg#«xy?¬$;?@

Franck-Condon¡¢`:j

TYZ' *(F-C®8)U¯°`|±@

²%³´ *@@)^@±@@@:?$AF9?"²RÏ=³>E©¥³$Ð

21

The comparison of qv’v” / R2 for d3$u – a

3"g

.268/.43261%

.555/.64386%

.154/.117137%

.015/.006250%

v'=3

.003/.00743%

.204/.32363%

.671/.74390%

.115/.08144%

v'=2

.137/.21364%

.79/.8494%

.064/.04160%

v'=1

.069/.10566%

.93/.93100%

v'=0

v"=4v"=3v"=2v"=1 v"=0 ad

2¦§¨'Schrödinger§©ª'^"+µ¶·¸@

Franck-Condon®8+ Spindler(1971)'¹wHº»o?@

./vw£@01»¼®23@45î678mnÜ*9

Ó./ÍÚ@5":

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23

#AB$CDEFG!-&·¸

24

:¹º»¼()@F--Y~M½¾

;j: %&'(?6'ABÚBCDî·@'ã

Arc discharge: 70-100V, 30-45AB = 0.02Tne ~ 2x10

12 cm-3, Te ~ 0.05-15 eVTi ~ 0.5 eV (@target chamber)

5uAB: on--> -CDEÉ off --> F-CDmn

MAP-II

25

¿:ÀÁ:}: Õ@2%Î(ÂÃ&¥¦¯8M

Discharge Condition:

230-270 V, 70 mA, 20-3000 Pa(300 Pa in this work)

ne~109 cm-3, Te = 2-5 eV

26

!

Ia " " v " " J d " v " J

=hc

#a " " v " " J d " v " J

Aa " " v " " J d " v " J

Aa " " v " " J d " v " J

v",J "

$% ne RXvJ

dv 'J 'Cv (2J +1)gas

Jexp &

FX (J,v)

kTrotX

&GX (v) &GX (0)

kTvibX

'

( )

*

+ ,

- . /

0 1 2 v,J

$

#AB$CDEF!Ï:?$!"#AF9?#²ÄÐ@Å©E@§CD@A.#²

ÄÏ=ÆBÐ@ÇD9ÈAEDÇD¥§

!

RX ,vJ

d ,v'J 'N

vJ

X{ }J

"v

" = Nv'J 'd Ad ,v'J 'a,v"J "J '

"•d GQX :

•d ÊQa¦

!

Id ,v 'J '

a,v"J"= h" # A

dv 'J '

av"J"N

vJ

d

Assuming X(vJ) is characterized by Boltzmann Tvib,Trot

!

Nv'JX

= Cv (2J +1)gasJexp "

FX (J,v)

kTrotX

"GX (v) "GX (0)

kTvibX

#

$ %

&

' (

measurement Reliable database required Fitting Parameter

X1#+g

d3$-u

a3#+g

Coronal

equilibrium

spin-changed

Fulcher)(

!

RXvJdv'J '

= qXvdv'

< Qv '"vGryzinski

ve > a0J1J '#

gas

g'as

a$K$ 'K '

K '

% =K '

% Q r' (2K '+1)K '

$'

r

$ & $'

K

&$

'

( )

*

+ ,

r

%2

=1

Multi-polar Q’r=1-4 :{0.76, 0.122, 0.1, 0.014}.

r = 1 ---> dipolar = Hönl-London factor

Excitation rate (adiabatic)

!

SJ 'J "

Q=

2J '+1

2,

SJ 'J "

P+ S

J 'J "

R=J'

2+J '+1

2=

2J'+1

2

Radiative transition ratio

Hönl-London factor

P,RHHLÅ伦Anomaly

27

!

"eH2

(Te) : e +H

2(v)# H

2

-( )*

#H +H$

"eH$(Te ) : e +H

$ # e + e + H

"H+H$(Ti) : H

++H

$#H + H

*

Ï.Ð#AB$CDEG!-Y~Myk&Éë[µ, ÊË]

!

0 =d H

"[ ]dt

= ne

H2(v)[ ]#eH2

0$v$9

% " H"[ ](ne#eH" + H+[ ]#H+H") "H

"[ ]&

transport

!

H2(v)[ ] = N0 exp "G(v) "G(0)

kTvib

#

$ %

&

' (

Tvib : Fulcher-band spectroscopy

Te¦/double probene¦/double probe[H-] ¦Laser photodetachmentdeg. dissociation¦H-H2 intensity ratio

=ne

dissociative attachment (DA)

e-impact electron detachment00

mutual neutralization ( = NI-MAR)

vibrational distribution of H2

depletionproduction

We first discuss w/o transport.

QcIPIZJQ_bKZbLQMGONOPRMOLPQcQQIWHSSQRSQGHRKIePTZQQSOUQdaXP\QMOMOSHRMOL

28

Ï5ÐC©ÈÈFD=D¥§@Ì@¦C©§©¥

!

H2" Loss" events

H# " photon=$ H

2" Loss( )

% H#( )=

ne[H2](S + D+ CX + DA )

ne[H2](X1&3diss + FX

1&3

dir)B H#( )

!

H2" Loss" events

Fulcher " photon=# H

2" Loss( )

$ H2(d% a)( )

=ne[H2](S + D+ CX + DA )

ne[H2]Xd&X (Te )

!

" H2(d# a)( )" H$( )

=Xd%X (Te )

X1#3

diss(T

e)B(H$ )

H!YTÛÌqM(¼ýzº8&'(&©ª

§ÍY½[\^M((H{'((H2= )(H:H!), )(H2:H!), )(H2:Fulcher-!)

ÎRkÏ&ÐF

ÃkÑÒ : Õ¡Ywp\RkÏJKTe¯ðMÈF=0

F=[H]/[H2]

!

" H#( )" H$( )

=(X

1%4

diss + FX1%4

dir)B H#( )

(X1%3

diss + FX1%3

dir)B H$( )

F!-Ókj%²Ë¿Ì^]M+Ôk¿ÕÖM

29

Ï?ÐGDÄG5໼!"#$&%²ke()@F--gFµH

!

" H#( )" H2(d$ a)( )

=ne[H]X1$6

eff(ne,Te )B(H# )

ne[H2]Xd%X (Te )F/(2+F)%²k

F=[H]/[H2]Kado et. al., Journal of Nuclear Materials 337-339 (2005)116.

·Ø2He!"#$3.1 mTorrYH2»¼¯exene

31

ÏOÐæÙk{ß/k&âè'e¢¨'Sg[µ]

6

5

4

3

2

1

0

Te [

eV

]

-4 -2 0 2 4Position [cm]

3

2

1

0

ne [1

0-1

1 cm

-3 ]

Te

en

(3.8mTorr)

4000

3000

2000

1000

0

Tv

ib [

K]

-4 -2 0 2 4Position [cm]

800

600

400

200

0

Tro

t [K]

Tvib

Trot

(3.8mTorr)

Ð5678'ÑÒÇ [ÓÔ¼ 1 km/s]/[ÕÖ 10 cm] = 100's

Ð1234×7Ø'6Ù©'ÈÚÇ 1/[H2,ne] ~ 10 ms

ÛÜÅÆ(X)'1234+ºÝ'+Þß

àáÅÆ'âã+40 ns ©¼

0/_'Y'äå,?@

à12347Á;æCçèG7Á,éǺÝ,>WTe;ºÝ,ehUhêehKëìP/íTe'¿9H&'@

Tvib@ÓÕVWÜo§$¾Úìp@mnÜîXY×8ã

4000

3000

2000

1000

0

Tv

ib [

K]

-4 -2 0 2 4Position [cm]

800

600

400

200

0

Tro

t [K]

Tvib

Trot

!"#$%&'%(#)*+,-./

32

col

colpre

4'

30'

exp

fit

KA

KDA

N

Nf

v

v

X

+

++==!

=

"=

#

#

pre

col

1

1

D

KA

f

+=

!

16.7

33

%56&'(è )*¾56+Z&'(è

, 16.7nsîï

Ð 19.0nsîï

! îïej

!8ÛÜ'12-(.¼kg/´

0

¿À0

Kcol`X),V?MAP-II'12&'(èHîï^`34

56

78w9:w;¿À

TvibX=3945[K]

TvibX=2044[K]Tvib

X=1693[K]

TvibX=4871[K]

æç¬&£I[äå`µ]

* D. Yamasaki, S. Kado et

al., J. Phys. Soc. Jpn. 75

044501 (2006).

34

P+Q

Ð5678'1234+WG?£W@ûAG`BCT×mZHû?¹"D'E£Hû¤WFGkgHIJHK>´T&'(è'ÓL1MHNo?OÚ;?@

Ð)þÿ'Fulcher-!P(QQ)+*9;RS,?T+;?@

à¹ww÷+UUVjh;W@@WXYZehÎÏ[;\SsVsh?i

ÐFulcher-!P(P,Q,RQ)'7å+]^'Ý_e)4'OÚ`\jsh?i

èé&êë

Ð78'34`¹CUFulcherPU'¯°

ÐaÓbcÚKdThóeö÷'fÒP',gWéÇhi'j´@

Ð-ékl÷mDC(Lyman, WernerP)U'¯°en

35

ìsíî

[-] S. Kado, Y. Iida, S. Kajita, D. Yamasaki, A. Okamoto, B. Xiao,

T. Shikama, T. Oishi and S. Tanaka,

“Diagnostics of Recombining Plasmas in Divertor Simulator MAP-II” (Review)

J. Plasma Fusion Res. 81, 810 (2005) .

[-] S. Kado, S. Kajita, D. Yamasaki, Y. Iida, B. Xiao, T. Shikama, T. Oishi, A. Okamoto and S. Tanaka

“Experimental study of negative ion profiles in H2-MAR plasmas in divertor simulator MAP-II”

J. Nucl. Mater. 337-339, 166-170 (2005).

[-] B. Xiao, S. Kado, S. Kajita and D. Yamasaki,

“Rovibrational distribution determination of H2 in low temperature plasmas by Fulcher-! band spectroscopy” Plasma Physics and Controlled Fusion 46, 653-668 (2004).

[-] !"#$% &'()*+,-./012324 56!7819:23;?5@ -./0A'()BCD80, 749-756E2004F

[-] !"#$GHIJKGLMNOGP"Q, &9:23FulcherRS4TUVWP,RX1YZ[@\]^%_(8), (15) -./0A'()BCD80, 783-791(2004).

[-] B. Xiao, S. Kado, S. Kajita, D. Yamasaki and S. Tanaka,

“Rovibrational distribution of H2 in low temperature plasma: the dependence on plasma parameters”

J. Nucl. Mater. 337-339, 1082-1086(2005) .

[-] S. Kado, D. Yamasaki, B. Xiao, Y. Iida, A. Okamoto, S. Kajita, T. Shikama and S. Tanaka,

“On the Anomalous Characteristics in the P and R Branches in a Hydrogen Fulcher Band”

J. Plasma Fusion Res. SERIES, 7, 54 (2006) .

[-] Daisuke Yamasaki, Shinichiro Kado, Bingjia Xiao, Yohei Iida, Shin Kajita and Satoru Tanaka,

“Experimental Evaluation of Predissociation Rate in v = 4 State Usable for Analysis of H2 Fulcher-”

J. Phys. Soc. Japan, 75, 044501 (2006).