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PPPL-2408
UC20-F
PPPL-2408
SATELLITE SPECTRA OF HELIUMLIKE NICKEL
By
H. Hsuan et al.
FEBRUARY 1987
PLASMA PHYSICS
LABORATORY
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PPPL2408 SATELLITE SPECTRA OF HELIUMLIKE NICKEL DE87 008065
H. HSUan, M. Bitter, K. W. Hill, S. von Goeler,
B. Grek, D. Johnson, L, C. Johnson, and S. Sesnic Bm Plasma Phys'ics Laboratory, Princeton University, S 5 =- - 5 H J
P.O. Box 451 - ^ J || =- Princeton, Sew Jersey 08544
mum C.P. Bhalla and K.R. Karim ft fe I f l'-'? " I I I
Department of physics , Kansas S ta te un ive r s i t y , 5 ^ I I J I ^ .
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I. INTRODUCTION
Heliumlike and hydrogenlike spectra of high-Z ions are of interest for
the diagnostics of tokamak plasmas and solar flares, and they are also
important for the testing of atomic theories which must include relativistic
and quantum electrodynamical effects. So far, spectra of heliumlike and
hydrogenlike ions with Z.< 26, especially Ar, Ti, Cr, and F , have been
studied in detail from tokamak plasmas. With the new generation of
tokamaks, e.g., the Joint European Torus (JET) and the Tokamak Fusion Test
Reactor (TFTR), 1 4 which are designed to obtain fusion breakeven, it is
possible to maintain plasmas of large volumes (V > 40 m J) with electron
densities, n e, in the range from 10 to 10 m and electron temperatures T e
> S keV in steady-state conditions for several seconds. Under these
conditions, elements with Z > 26 can be observed in the heliumlike and
hydrogenlike charge states.
In this paper spectra of heliumlike nickel, NiXXVII, are presented as
well as a detailed comparison of the experimental data with results from
Hartree-Fock-Slater atomic model calculations, 1 3' 1 0 and the results obtained
by the Z-expansion method. 17 - 1 The experimental results are presented in
sec. II. The identification of the observed spectral features and comparison
of wavelengths and intensities with theoretical predictions are described in
Sec. III. The analysis results and diagnostic applications ara discussed in
Sec. IV.
II. EXPERIMENT
The measurements have been performed on TFTR with a new c r y s t a l
spectrometer which cons i s t s of three c r y s t a l s and p o s i t i o n - s e n s i t i v e de tec to r s
in the Johann conf igura t ion . The instrument has been designed to record
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3
spectra from three approximately vertical chords of the plasma minor section
in order to measure radial profiles of the ion temperature and plasma rotation
velocity from the Doppler broadening and Dqppler shift of X-ray lines from
metal impurity ions of Ti, Cr, Fe, and Ni. Traces (-0.1%) of these elements
are present in TFTR plasmas from the Inconel (~ 70% Ni, ~ 15% Cr, - 7% Fe,
" 2.5% Ti) bellow protective plates and the stainless steel vacuum vessel.
The resolution of the spectrometer is >/A* > 10,000. 128 spectra per crystal
are recorded during a TFTR discharge for time-resolved measurements of these
plasma parameters. The wavelength range obtained with a single spectrometer
setting covers the entire spectral range of the dielectronic satellite lines
of heliumlike ions. It is thus possible to determine the satellite to
resonance line intensity ratios accurately from a simultaneous measurement of
these lines. This is important for diagnostic applications of these intensity
ratios for measureraents of the electron temperature, the ionization
91 2 equilibrium, and ion transport.
The nickel spectra were obtained from a. central vertical chord (at a
major radius R = 249 cm? with a 2233 quartz crystal (2d = 2.028 A) of the size
of 1.5 in. x 6 in. x 0.030 in. The curvature radius was R = 1013 cm, and the
spectral resolution was VA> = 18,000. Figure 1 shows a measured spectrum of
NiXXVII. The data were obtained from the steady-state phase of a TFTR
discharge with a central electron temperature of 4 keV and a very low central
electron density, n(0) = 8 x 10 2 cm" . The radial profiles of the electron
temperature and electron density as measured by laser Thomson scattering are
shown in Fig. 2. Under these conditions the plasma electrons and plasma ions
are weakly coupled, such that the ion temperature is well below the electron
temperature. The spectral features are, therefore, well resolved and not
obscured by Doppler broadening. Moreover, the collisionally excited
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lithiumlike and berylliumlike satellites are expected to be prominent spectral
features, since substantial deviations from coronal equilibrium occur under
these experimental conditions.
III. LINE IDENTIFICATION
The nine prominent features of the spectrum shown in Fig,1 have been
identified as the resonance line, the intercombination lines, and the
forbidden line of heliumlike nickel, NixxVII, and the associated strong
lithiumlike and berylliumlike satellites of the resonance line. The
transitions of these spectral features are listed in Table 1, The key letters
correspond to Gabriel's notation. Also listed in Table 1 are the
theoretical wavelengths and line strengths, F 2(sf), for the strong
dielectmnic satellites as obtained by Vainshtein and Safronova r 1 8 and from
our present calculations which are described below. The channel numbers, H,
in column 4 of Table 1 correspond to the center positions of the observed
spectral features. They were obtained from a least-mean-squares fit of Voigt
functions, and they were than used for determination of the experimental
wavelengths using the following relation:
x = 2d sin (a + ael o) v
o '
where fi8 (degree) = 3.719 x 10" 3(N - NQ) corresponds to the d ispers ion of the
inst rument . NQ i s the center channel number of peak 1 . Since the
spectrometer i s not absolute ly c a l i b r a t e d , the experimental wavelengths are
given in reference to the theoret ical , wavelength values for the resonance l ine
w by assigning x b e o r ' = 2d s i r 6Q to the center channel N 0 of peak 1. We
note from Table 1 tha t both s e t s of t h e o r e t i c a l wavelengths a re in good
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agreement with the experimental values. For a more detailed comparison
between theory and experiment synthetic spectra were constructed from the
theoretical transition arrays in Table 1 as well as from the transition arrays
for the n = 3,4 lithiumlike satellites, which are given in Table 2 and in
Ref. 19. To facilitate a direct comparison with the experimental data,
channel numbers were .converted into wavelengths by using Eq. (1), and Voigt
functions were then calculated from the theoretical transitions for this
wavelength array. The synthetic spectra are shown in Figs. 3 and 4 together
with the experimental data. The calculated contributions from the different
spectral components, i. e., the heliumlike lines, the dielectronic lithiumlike
satellites, and the collisionally excited lithiumlike and berylliumlike
satellites, to the total synthetic spectrum are shown separately by the shaded
areas in subftgures (b), (c), and (d). The line intensities of the synthetic
spectrum were normalized to the intensity of the resonance line w. The
intensities of the heliumlike lines x, y, and z were obtained from the
following expression:
I c (T 1 x,y,z _ x,y,zl e> , ,
~ c (T ) ( 2 } w w l eJ
Values for the exc i t a t i on r a t e c o e f f i c i e n t s , c _ , were ca lcu la ted using
the methods described in Refs. 7 and 9 . Here, we included only the
con t r ibu t ions from d i r e c t e x c i t a t i o n , r a d i a t i v e cascade t r a n s i t i o n s , and
c o l l i s i o n a l resonances, but we neglected the con t r ibu t ion to the l ine z from
the i n n e r - s h e l l i on iza t ion . The r e l a t i v e i n t e n s i t i e s for the d i e l e c t r o n i c
s a t e l l i t e s were ca lcula ted from the following express ion:
I d i e 1 , 2 -E s i
f(2Ti ft ) i3/2 , . . , s -. , , . ~r~ = ic^i fens1 V a f ) e x pkr-J ( 3 )
w w e e e e
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6
w i t h
g= A to the f ina l s t a t e | f>. In the present c a l c u l a t i o n s , the Hartree-Fock-Slater atomic model (HFS)
was employed to obtain the s i n g l e - p a r t i c l e wave func t ions . These wave
functions were then used to ca lcu la t e the r a d i a l Auger and e l e c t r i c d ipole
matrix elements. Configuration s t a t e functions belonging to the same complex
were allowed to mix. The diagonal elements of the energy matrix were
corrected for r e l a t i v i s t i c e f f e c t s . The ef fec ts due to s p i n - o r b i t i n t e r a c t i o n
were included. The energy matrices were diagonalized to obta in cor re la ted
atomic s t a t e functions and energies ; these were used in ca l cu l a t i ng t r a n s i t i o n
r a t e s . For the w, x, y, j . q, $, and z l i nes the wavelengths were ca lcu la ted using the mult i -conf igurat ion Dirac-Fock model including r a d i a t i v e cor rec t ions
of quantum electrodynamics. The dif ference between the Dirac-Fock wavelength
and the Hartree-Fock-Slater wavelength for the j - l i n e was 0.0025 A. This was added to the wavelengths of a l l o ther d i e l e c t r o n i c s a t e l l i t e l i n e s . The
syn the t ic spectrum shown in Fig. 3 was constructed from the HFS r e s u l t s . In
Ref. 17, the Z-expansion method i s used to ca l cu l a t e the atomic q u a n t i t i e s
which were used in the synthet ic spectrum shown in Fig. 4 .
The i n t e n s i t y of the c o l l i s i o n a l l y exci ted Lithiumlike (beryl l iumlike) s a t e l l i t e s was obtained from the following expression:
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7
, C O l l . / , ! h _ C s T e "Hi*
( ( 4 )
Jw Cw ^Te J ViXXVII
where i\,t* (= "HixyvT o r "ilixxv' a n < ^ "NiXXVtl a r e t n e < ^ e n s i t : ' - e s l i th iura l ike
or (beryl l iumlike) and heliumlike n i c k e l . c s f T e ' * s t h e r a t e coe f f i c i en t for
e l ec t ron impact exc i t a t i on of the l i th iuml ike (or beryl l iumlike) ion from the
ground s t a t e .
The syn the t ic spectra were ca lcu la ted for the experimental ly observed
e l ec t ron and ion temperatures of T = 4 kev and Tj = 2 keV, r e s p e c t i v e l y .
Values of "uixxvi/'HUXXVII = '75 a n d "NiXXV-^NiXXVII = 0-1 &* the r e l a t i v e
abundance of hel iumlike , l i t h iuml ike , and bery l i iuml ike nickel were chosen to
obta in a bes t f i t with the observed spectrum.
IV. DISCUSSION
The detailed comparisons shown in Pigs. 3 and 4 indicate that the
predictions from both theories are in very good agreement with the
experiment. The predictions differ only slightly with respect to the
wavelength for the satellite r (feature 6), where the value of Vainshtein and
Safronova is in somewhat better agreement with the experiment than the value
obtained from the present calculations. The predicted intensities for feature
3 are in both cases slightly higher than the observed value.
The observed MiXXVII spectra confirm the trend of the charge-dependent
wavelength shifts reported in Ref, 24, in particular, we observe that the
satellite q overlaps with the y line. Similarly, the satellite 3 is very
close to the line 2. On the other hand, the dielectronic satellite k and the
collisionally excited satellite r are well separated. These charge-dependent
wavelength shifts imply that the line q is no longer appropriate for the
diagnostic of the relative abundance of the lithiumlike and heliumlike charge
states. The satellite r can be used instead.
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a
The values far the abundance of NiXXV and NiXXVI relative to that of
NiXXVII, which were obtained from the analysis in Sec. Ill, are substantially
larger than the predictions for the fractional abundance of these charge
states in coronal equilibrium (see Fig. 5). Modeling calculations, such as
those described in P.ef. 9, make it possible to deduce values for the radial
ion transport coefficients from these observed deviations. The resonance
lines w of NiXXVII as well as FeXXV have been successfully used for Doppler
measurements. Doppler ion temperatures TJ > 20 keV have recently been
measured in TFTR experiments with intense neutral beam heating from these
2 6 27 impurity lines. '
ACKNOWLEDGMENTS
The technical assistance of J. Gorman, J. Lehner, P. Howard, and the TFTR
operating crew is highly appreciated. We also gratefully acknowledge the
continuing support of Dr. K.M. Young, Dr. H.P. Furth, Dr. R. Goldston,
Dr. D. Grove, Dr. D. M. Meade, and Dr. P. H. Rutherford.
This work was supported by U.S. Department of Energy contract No.
DE-AC02-76-CH0-3073. Two of us (G.P.B. and K.R.K.) were supported by the
Division of Chemical Sciences, Office of Basic Energy Sciences, Office of
Energy Research, and the U.S. Department of Energy. Computations of
excitation rate coefficients were carried out on the NAS 980 - CIKCE computer
in Orsay, France,
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% 9
REFERENCES
1J. Dubau and S, Volonte, Rep. Prog. Phys. 43, 199 (1980).
2C. De Michelis and M. Mattioli, Nucl, Fusion _21_, 677 (1981).
3R. K. Janev, L. P. Presnyakov, and V.P. Shevelko, in Physics of Highly
Charged Ions, Vol. 13 of Springer Series in Electrophysics, edited by
G. Ecker (Springer, Berlin, 1985).
4 T F R Group and p. Bombarda, in proceedings of the 11th European Conference on
Controlled Fusion and Plasma Physics, Aachen, FRG,1983, edited by S.
Methfessel (European physical Society, Aachen, 1983), Vol. 7D, Part I,
p. 89. Br"
TFR Group, F. Bombarda, F. Bely-Dubau, P. Faucher, M Cornille, J. Dubau,
and M. Loulergue, Phys. Rev. A _3_2, 2374 (1985).
3E. Kallne, J. Kallne, A. Dalgarno, E. S. Marmar, J. E. Rice, and A. K.
Pradhan, Fhys. Ruv. Lett. ^ 2_, 2245 (1984).
F. Bely-Dubau, P. Faucher, L. Steenman-Clark, M. Bitter, S. von Goeler, K.
W. Hill, C. Camhy-Val, and J. Dubau, Phys, Rev. A _26^ , 3459 (1982).
P. Lee, A. J. Lieber, and S. S. Wojtowicz, Phys. Rev. A_3_1_, 3996 (1985).
M. Bitter, K. W. Hill, M. Zarnstorff, S. von Goeler, R. Hulse, L, C.
Johnson, N. R. Sauthoff, S. Sesnic, K. H. Young, M. Tavernier, F. Bely-
Dubau, P. Faucher,M. Cornille, and J, Dubau, Phys. Rev. A 32, 3011 (1985).
TFR Group, J. Dubau, and H. Loulergue, J. Phys. B J_5_, 1007 (1981).
H. L. Apicella, R. Bartiromo, F. Bombarda, and R. Giannella, Phys. Lett.
98A, 174 (1983).
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10
1 2 M . Bitter, K. W. Hill, N. R. Sauthoff, P. C. Efthimion, E. rteservey,
W. Roney,S. von Goeler, R. Horton, and W. stodiek, PhyT. Rev. Lett. 43, 129
(1979).
1 3R. J. Bickerton, Plasma Phys. Controlled Fusior. 2, O e 5 (1984). 1 4 K . H. Young et al., plasma phys. controlled Fusior, J^ cj. r; (I9i4). 1 5C.p. Bhalla and K.R. Karim, Phys. Rev. A _34_, 3525 (1986).
1 6 K . R . K-.rim and C.P. Bhalla, to ba published in chys. Rev. A.
L. A. vainshtein and U. I. Safronova, At. Daca Nucl. Data Tables Z\_, 49
(1978).
U. I, Safronova, A. M. Urnov, and L. A- Vainshtein, Proc. P. N. Lebedev.
Phys.Inst. [Acad., Sci. USSR 119, 13 (1980);}
L. A. Vainshtein and U. I. Safronova, At. "Jata Nuel. Data Tables _25_, 311
(1980).
2 0 H . J a h a n n , Z. Pixys. 6 9 , 189 ( 1 9 3 1 ) . 21
M. Bitter, K. W. Hill, S. Cohen, S. von Goeler, K. Hsuan, L.C. Johnson, R,
Raftopulos, M. Reale, N. Schechtman, S. Senic, F. Spinos, J. Timberlake, s.
Weicher, N. Young, and K. M. Young, Rev. Sci. Instruin. 57, 2145 (1986). 22
M. B i t t e r , S . von G o e l e r , N. Sau tho f f , K. W. H i l l , K. Brau, D. Eames, M.
Goldman, E. S i . lver and W, S t o d i e k , i n I n n e r - S h e l l and X-Ray P h y s i c s of Atoms
and S o l i d s , e d i t e d by a. J . F a b i a n , H. K l e i n p o p p e n , and 1 . M. Watson (Plenum
P r e s s , New York, 1981) , p . 8 6 1 . 2 3 A . H. G a b r i e l , Mon. No t . R, A s t r o n . S o c . 160, 99 ( 1 9 7 2 ) . 24 TFR Group, M. Cornille, J, Dubau, and M. Loulergue, Phys. Rev. A _3_2_, 3000 ( 1 9 8 5 ) .
25 * C. B r e t o n , C. De M i c h e l i s , M. F i n k e n t h a l , and M. M a t i o l i , Fon tenay~aux-Roses Laboratory Report No. EUR-CEA-FC-948, 1978 (unpublished).
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11
JH. Hsuan, M. Bitter, s. von Goeler, S. Sesnic, J. Timberlake, and S. Cohen,
Bull. Asa. Phys. Soc. _31_, 1611 {1986).
W. Bitter, K. W. Hill, S. Hiroe, H. Hsuan, S. von Goeler, S. Sesnic, and
M. Zarnstorff, Bull. Am. Phys. Soc. _31_, 1414 (1986).
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TABLE CAPTIONS
Tab le 1 . E x p e r i m e n t a l wave l eng ths and t h e o r e t i c a l p r e d i c t i o n s Cor t h e
r e s o n a n c e , i n t e r c o m b i n a t i o n , and f o r b i d d e n l i n e s of NiXXVII, and t h e /
a s s o c i a t e d s a t e l l i t e l i n e s due t o t r a n s i t i o n s 1s 21 - \s2t'2j." * Wavelengths a r e i n A and s a t e l l i t e l i n e s t r e n g t h s F _ ( s f ) a r e i n u n i t s of 1 0 1 3 s _ 1 .
Tab le 2 . Atomic d a t a c a l c u l a t e d wi th the HFS a tomic model fo r s a t e l l i t e l i n e
t r a n s i t i o n s : 1 s 2 n - 1 s 2 l ' n " wi th n = 3 , 4 of NiXXVI. The
wave l eng ths a r e i n A. The l i n e s t r e n g t h s F 2 ( s f ) a r e i n u n i t s of 1 0 " 1 3 s " . L ines wi th F , - v a l u e s l e s s than l O ^ s - 1 a r e n o t l i s t e d ^
-
Peak key Transit ton H *expt 'uieor. 4^^^ 'expt. 4h'or- F 2 b ) < 3 f >
1 u la 2 ' s 0 - la 2p 'p, 116.11 1.5879" 1.5879 1.5886" 1.5886
2 x is 2 'S 0 - 1a2p 3 P 2 193.18 1.5917 1.5918 1.5921 1.5925
1a 22a 2 S ) / 2 - Is2a2p 2 P 3 / 2 1.5926 0.0106 1.5935 2.110 U 2 2 p 2 P 1 / 2 - ls2p 2 2 P 3 / 2 1.5929 0.157 1s 22p 2 P J / 2 - ls2p 2 2 S , / 2 210;21 1.5931 1.5932 6.00 1.5938 1.5910 1.98 la 22a z S 1 / 2 - )32a2p 2 P ) / 2 1.5931 12.fl 1.5910 11.12
y la 2 ' s 0 - 1s2p 3P 1.5959 1.5968 1
? S ' o 218.01 1.5962 1.5969 q 13^23 d S 1 / 2 - Ia2s2p 4 P 3 / 2 1.5965 0.172 1.5972
a 1a 22p 2 P 3 / 2 - Ia2p 2 2 P 3 / 2 1.5973 17.5 1.5981 11.10 5 k .la 22p 2 P ) / 2 - ia2p 2 2 0 3 / 2 267.17 i.5978 1.5980 38.1 1.5985 1.5987 39.32
d 1a 22p 2 P , / 2 - la2p 2 2 P , / 2 1.5980 0.166
6 r ls 22a 2 S , / 2 - I32a2p 2 P , / 2 283.50 1.5991 1.5992 6.93 1.5998 1.600? 7.19
7 J 13 22p 2 P 3 / 2 " la2p 2 2 D 5 / 2 298.31 1.6003 1.6005 58.0 1.6010 1,6011 53.19
L la 22p 2 P , / 2 - |s2p 2 2 D , 1.6021 5.73 1.6033 1.81 8 2 1 7 330.17 I.COIl) 1.6036
2 13 ' S 0 - 1s2a iSy 1.6031 1.6035
9 8 l a 2 2 a 2 lSQ - | 3 2a 2 2p ' P , 310.32 1.6037 1.6011 1.6017
The experimental wavelengths are normalized to the t heo re t i ca l values fo r the I s 2 1 S i J - l32p ' p , t r a n s i t i o n . a l lcferenoe 17, 18 b Present HKS Calu lat lona
Table 1
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14
Final State I f >
Autoionizing State
|s>
1s 2p( 'pjsp 2 S s1/2 TS 2p{ 1P)4p 2 P P3/2 Is 2p< 1P>4p 2n D3/2 1s 2p( 1P)4p 2 D 5 / 2 Is 2p( 1P)3p 2 p3/2 Is 2p( 1P)3s 2 P P1/2 Is 2p( 'p)3p 23/2 Is 2p( P)3p 2
5/2 is 2p( P)4d F5/2 Is 2p( P)4d 2 D5/2 Is 2p( P)4d 2 P F7/2 1s 2p(-JP)3p
2D D5/2 1s 2p( P)3d 2u F5/2 1s 2p
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15
FIGURE CAPTIONS
FIG. 1 . Satellite spectrum of NiXXVII. The data were recorded fron an
ohmically heated TFTR discharge during its steady-state phase.
FIG. 2 Radial profiles of the electron temperature and the electron
density as measured by the TFTR Thomson scattering diagnostic.
FIG. 3. Comparison of the observed NiXXVII spectrum with a synthetic
spectrum constructed from the results obtained by the present HFS
atomic model calculations. The experimental data are shown in
(a). The contributions from the heliumlike lines, the dielectronic lithiuralike satellites, and the collisionally excited
lithiumlike . and beryllium-like satellites to the synthetic
spectrum are shown by the shaded areas in (b), (c), and td), respectively. The envelope shown in (b), (c), and (d) is the total synthetic spectrum,, i.e., the sum of the various components.
FIG. 4. Comparison of the observed NiXXVII spectrum with a synthetic
spectrum calculated from the theory of Vainshtein and
Safronova. 1 ' The experimental data are shown in (a). The contributions from the helium-like lines, the dielectronic
lithiumlike satellites, and the collisionally excited lithiumlike
and berylliumlike satellites to the synthetic spectrum are shown
by the shaded areas in (b), (c), and (d), respectively, also shown in (b), (c), and (d) is the total synthetic spectrum, i.e., the sum of the various components.
FIG. 5. Fractional abundance of the ionization states of nickel for nc.
coronal equilibrium.
-
#86X1469
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f 1 1 1
1 :s. i
/ "* - i i i r | i -r**^* i" I r~i|iiiIiiii|iii'|iiir
100 150 200 250 300 350 400 CHANNEL NUMBER
Fig. I
K-
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17
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LO o
(c- lU3ci0lx)AllSN3a N0cJ10313 21
^ CM O
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(a) 2 3 1 5 6 7 89
I I A | i | JJ i i ii 1 1 i 1 1 = ^ i -
50 100 150 200 250 300 350 400 CHANNEL NUMBER
(b)
% vx\
0-
iiiiIiH'Ti i T"'i i Y* i P ir-]i i i f P i T ir 1.585 1.595 o 1.605
WAVELENGTH(A) (O
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605
I 595 WAVELENGTH (A)
Fig, 3
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19
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EXTERNAL DISTRIBUTION IN ADDITION TO OC-20
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