AECL-4910
NEUTRON SCATTERING DATH FOR LIQUID NEON
by
W.J.L. BUYERS, V.F. SEARS,
P.A. LONNGI and D.A. LONNGI
Chalk River Nuclear Laboratories
Chalk River, Ontario
August 1974
NEUTRON SCATTERING DATA FOR LIQUID NEON
by
W.J.L. Buyers and V.F. Sears
Chalk River Nuclear Laboratories
Chalk River, Ontario
P.A. Lonngi and D.A. Lonngi
Instituto Naaional de Energia Nuclear
Mexico, D.F.
Chalk River Nuclear Laboratories
Chalk River, Ontario
August 1974
AECL-4910
DONNÉES SUR LA DIFFUSION DES NEUTRONS POUR LE NÉON LIQUIDE
par
W.J.L. Buyers et V.F. Sears
Chalk River Nuclear Laboratories
Chalk River, Ontario
P.A. Lonngi et D.A. Lonngi
Instituto Nacional de Energia Nuclear
Mexico, D.F.
RÉSUME
La diffusion cohérente et inélastinue des neutrons dans le néon
liquide a été mesurée au moyen d'un spectrometre à trois axes.
La
fonction de diffusion van Hove, S(Q,v), a et! déterminée pour le
domaine 0.8Â
< Q < 12.5&" . Ce rapport contient les résultats
obtenus pour S(Q,v) après corrections apportées aux données originales
pour le bruit de fond et la diffusion multiple.
Cette compilation
constitue une source appropriée de données de référence pour la
dynamique du naon liquide.
L'Energie Atomique du Canada, Limitée
Laboratoires Nucléaires de Chalk River
Chalk River, Ontario
Août 1974
AECL-4910
NEUTRON SCATTERING DATA FOR LIQUID NEON
by
W.J.L. Buyers and V.F. Sears
Chalk River Nuclear Laboratories
Chalk. River, Ontario
P.A. Lonngi and D.A. Lonngi
Institute Nacional de Energia Naclear
Mexico, D.F.
ABSTRACT
The coherent neutron inelastic scattering in liquid neon has been
measured with a triple axis spectrometer.
The van Hove scattering
0-1
f u n c t i o n , S(Q,v), **as determined for the range 0.8A
9-1
< Q < 12.5A
.
This r e p o r t i s a compilation of the r e s u l t s obtained for S(Q,\>) a f t e r
c o r r e c t i o n s have been applied to the o r i g i n a l data for background and
multiple scattering.
The compilation provides a convenient source of
r e f e r e n c e data for the dynamics of l i q u i d neon.
Chalk Rivei Nuclear Laboratories
Chalk River, Ontario
August 1974
AECL-4910
- 1 -
NEUTRON SCATTERING DATA FOR LIQUID NEON
by
W.J.L. Buyers and V.F. Sears
Chalk River Nu<lear Laboratories
Chalk River, Ontario
P.A. Lonngi and D.A. Lonngi
Instituto Nacional de Energia Nuclear
Mexico, D.F.
This report is a compilation of neutron inelastic scattering measurements that were made on liquid neon at 26.9 K.
The experimental apparatus
was the triple axis spectrometer at the C5 facility of the NRU reactor and
the spectrometer was operated so that the wave-vector transfer, Q, and the
scattered energy, E, were held constant.
The results are therefore in the
form of the intensity of scattered neutrons as a function of frequency
transfer, V, and were obtained in the range 0.8A~
< Q < 12.5A~ . The data
at low wave vectors, Q < 4&~ , provided information on the collective
behaviour, while the data at large wave vectors, Q > 4A\ provided information
on the oscillations in the width and frequency of the single-particle peak.
A full description of the physical interpretation and theoretical
analyses of the results will be found in reference 1.
For the present
purposes it is sufficient to note that the van Hove scattering function,
S(Q,v), which describes the dynamical motions of atoms, is rather direct
— 2—
obtained from the neutron scattering results.
To do this the results
must be corrected for background and for multiple scattering.
corrections have been applied as described in reference 1.
These
Particular
mention is made of the simple and accurate method developed for calcu2
lating multiple scattering by Sears . The method worked well for the
geometry of ttv= present experiment in which the neon was contained in a
cylinder 1.3 cm in diameter in which were placed a set of concentric
cadmium-plated discs spaced 2,5 mm along the axis of the cylinder, the
plane of the discs being parallel to the scattering plane.
The multiple
scattering was found to account for less than 3% of the scattering at
moderate to large Q and could thus be accurately subtracted.
The corrected results for S(Q,v) are presented in Tables 1 and 2
0-1
with wave-vector transfer, Q, in A
and frequency, V, in THz.
Mo
correction has been applied for instrumental resolution as it is generally
more reliable to fold the four-dimensional resolution function with theory
before comparing with experiment rather than to attempt the hazardous
procedure of deconvolving a complex resolution function from the data.
In Table 1, each of the 35 cases or constant-Q scans is identified by the
number, N, of distinct frequencies, v., in the scan, the frequency range,
the wave vector, Q, and the structure factor
S(Q) = A(Q,v)dv
(1)
No extrapolation of the data was used to form S(Q) since the measurements
extended well out into the wings of the peaks.
have teen normalized
The data in Tables 1 and 2
and thus S(Q)-KL at large Q.
- 3 -
The data were obtained from measurements made with the spectrometer set
for three different ranges of resolution « the ranges corresponded to cases
1 to 16, 17 to 29, and 30 to 35. This has the consequence that results for
the same wave vector measured under different resolution conditions are different, e.g. scans 15 and 17 for Q = 3.6A*"" and scans 29 and 30 for Q = 10A. .
A brief description is therefore given of a method for calculating, approximately but simply, the effect of resolution on the results. The tabulated
scattering function, S(Q,v), is related to the resolution-free scattering
law, S (Q,v), by the relation
S(Q,v) =yR(v,v')So(Q,v')dv' /yR(v,v')dv'
(2)
where the resolution function is
, (v-V)2 s
R(v,v') = exp \— \ .
1
2a(v) '
(3)
The full width at half maximum of the resolution function, W(v) = 2.35a(v),
was measured at v=0 as the width of the vanadium scattering.
An expression
for W(v) at all frequencies Is given in reference 1 and W(v) is plotted in
Fig. 1 for the three resolution ranges for the convenience of those who wish
to perform calculations based on the data of Table 2.
In Table 2 the scattering law is given for each of the 35 scans in
column 2 and in the third column is given the statistical error.
Note that
positive V corresponds to neutron energy loss.
The results presented will form a useful set of reference data for
those who require accurate infoimation of th3 dynamics of the atomic motion
in liquid neon.
The results have provided considerable insight into the
nature of the collective motion and the interference effects in the singleparticle regime but the reader should consult reference 1 for a full
description of the implications of these results.
References
1.
W.J.L. Buyers, V.F. Sears, P.A. Lonngi and D.A. Loringi, Physical
Review A (to be published)
2.
V.F. Sears, Advances in Physica (to be published)
- 5 -
Table 1
Identification of constant-Q scans for liquid neon
CASE
1
2
3
k
5
6
7
3
9
10
11
12
13
RANGE
26
35
3k
3k
3k
3k
3k
3k
Sk
3k
3<»
3k
•+0
Ik
"•0
15
16
17
18
19
20
21
40
22
23
Zk
25
26
27
28
29
30
31
32
33
3<t
35
33
28
28
28
28
28
28
26
28
28
28
28
16
36
16
16
18
16
18
16
- 1 . 00
- 1 . 00
- 1 . 00
- 1 . 00
-1. 00
- 1 . 00
- 1 . 00
- 1 . 00
- 1 . 00
- 1 . 00
-1. 00
- 1 . 00
™ • 30
• •90
• 90
—
* •
2G
- 2 . 10
- 2 . 10
- 2 . 10
- 2 . 10
- 2 . 10
- 2 . 10
- 2 . 10
- 2 . 10
- 2 . 10
- 2 . 10
- 2 . 13
- 2 . <*Q
- 2 , 10
-i. 5Q
-1. 53
" i i ,50
-1.,50
-1,,50
0. ao
TO
TO
TO
TD
TO
TO
TO
Tn
TO
TO
TD
TO
TO
TO
TO
TO
TO
TO
TO
TD
TO
TO
TO
TO
TO
TQ
TO
TD
TQ
TO
TO
TO
TO
TO
TO
1. 50
2. <*0
2. 30
2. 30
2. 30
2. 30
2. 30
2. 30
2. 30
2. 30
2. 30
2. 30
3.00
3.00
3.ao
3. 00
6. 00
6. 00
6. 00
6. 03
6. 00
6. 00
6. 00
6. 00
6. 00
6. 00
6. 00
8.10
8. t»Q
9. 75
9.,75
11.,25
9,,75
11.,25
11. 25
•30
1. 00
1. 20
1. *0
1.60
1.80
2. 00
2. 20
2. kQ
2* 60
2. 80
3, 00
3. 20
3.kQ
3. 60
3. 80
3. 60
k. 50
5. 00
5. 50
6. 00
6. 5G
7. 00
7. 50
8. 00
8. 50
9. 00
9.50
10. 00
10. 00
10. ,50
11.,00
11.,50
12., 00
12.,50
• 096
• 097
• 11^
• 17k
• 231
* 337
• 669
1. 530
2. 298
1. it78
• 935
• 712
* 6i+S
•667
• 7kb
• 759
C 802
1. 351
*979
•800
• 951
1. 016
• 969
• 922
f 872
• 9^5
• 903
4
X • 112
1. 077
•978
•991
1. G03
1. 023
•92<*
«968
- 6 -
Table 2
1
T 1 < Q < 12
The s c a t t e r i n g law, S(Q,v) for 0.8&T
in l i q u i d neon a t 26.9 K
CASE
1
NU (THZ)
- 1 .00
- .90
- .30
- .70
- .60
- • P0
- .40
- .30
- *20
- . 10
0 .00
.10
.20
.30
.40
.50
.60
.70
.80
.90
1 .00
1 • 10
1.20
1 .30
1.40
1.50
THE SCATTERING FJNCTION AT 4 =
3(
-.3015
.0042
-.0072
.3359
. 0 05 9
-.0005
.0151
.0199
.0542
.1395
.191+
.1557
.3935
.0503
.0333
.0271
. 0 26 3
.0215
.0243
.0149
.0220
.0192
.0123
.0035
.0037
• OtJ29
NU)
<+-)
( f -)
(+ - )
(* - )
( 4- - )
{+• - )
(+-)
( t- )
-)
(+-)
( +-)
( +-)
( +-)
( +-)
( +-)
( + -f
(f -)
( +-)
-)
u
(f -)
<• - )
(+-)
(< - )
( + ->
(+- )
(+-)
< « •
.0050
.0052
.0G48
.0052
.0052
.0049
.0054
.1056
.0070
.0104
. 0 124
.0111
.0032
.0062
.0057
.0052
.0052
.0050
.0051
.0043
.OObU
. 0049
.0047
. 0042
.0042
.0042
- 7 -
CASE
NU
THE SCATTERING FUNCTION AT
(THZ)
-1
-
.00
.90
.80
.70
.60
.50
• 1+0
.30
.20
.10
0.00
.10
.20
.30
.1+0
.50
,60
.70
.ao
c90
1 .00
1 .10
1.20
1 .30
1 .1+0
1 .50
1.60
1.70
1 .80
1 .90
2 .00
2.10
2.20
2.30
2 un
S ( Q, NU)
.0361+
.0Q9<+
.0080
.0111
.0133
.0115
. 016«+
. 0151+
.0517
.1035
.121+5
.1057
.0303
.0553
• 0<+59
.0459
.0359
,0357
.0253
.0232
, 0 233
.0175
.023<+
.0203
.0155
.0112
.3055
. 0 06'+
.0030
.0058
.0018
.11023
* 38 ? 8
.'3055
-.001+2
< + ->
(+-1
(f - )
( « • - )
( * • -
)
<•-)
( * - )
( •-!
( + -1
(*-!
( + -)
(+-1
(•-
(+(+(*•( +»
.0050
.0050
• OQi+9
.001+9
.0050
.001+9
.0050
.0051
.0061+
.0092
.0101
.0095
.0077
.0060
.0055
.0055
.0051
.0051
(+-
.001+8
{*•-
.001+7
(+(+-
.001+7
.001+1+
(*( + -)
(+ -)
( +(+ (+ (+ -
.001+7
( < • -
(t-
(•-)
(*-)
(+ -)
(+ - )
.001+1+
.001+3
.001+1
.,0039
.0039
.0037
.0038
.0037
.0037
.0037
.0036
.0031+
1.0U
- 8 -
THE 3 C A T T E R I N 3
CASE
NU (THZ)
-1.00
-.90
-.80
-.70
-960
-.50
- . <+0
-.30
-.20
- . 10
0.00
.10
.20
.30
.1+0
.50
.60
.70
.80
.90
1.00
1.10
1.20
1.30
l.i+O
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
FUNCTION
S Cl,Nl J)
• -)
.0125
+ -)
.0113
+ -)
.0055
. 0 Id 7 + - )
.0167 ( • - )
.0171 i +•-)
.0152
* - )
.Q.+22
• -)
+ .0320
.1130 ( + ~
. l^ii
+ .1105
. 0 3 m < +•.0701+ + .0591 ; + • - ;
+ .0375
. 0 ? t+ 0 < +•.0316 ( + - )
.02 93
. 0 2 1 3 1 *+• —
.0271+ +•-)
. 0 32 3 (*--)
.0222 [ + - )
« 02 k1* 1 • - )
.021+7 [ * • - )
.0136
* - )
+ .0110
.0113
. QJ33 ; +•.3055
.30 58
. 0355
. 3U 13
.00 55 ( • • -
.0052
. 0 Q'u 0
.001+7
. 0 0<+d
. 0 0t+9
. ooi+a
• OOt+7
• 0 05*+
.0071
• Q092
.0103
.0092
.0073
.0063
.0058
.0051
.0050
.00«*9
.OOt+8
.00<+<+
. 0 01+6
.001+9
.QQ'-tb
. 0 01+6
.001+6
.00<+3
.001+0
. 0 0 k> 0
• 0 038
.0037
.0038
.0037
• 0 036
.0037
AT
i
=
1.23
- 9-
CASE
NU
k
( THZ)
- 1 . 00
90
80
—
• 70
60
50
—
• i+0
30
20
10
0 . 00
• 10
20
• 30
• 1+0
• 50
• 60
• 70
• 80
a 90
1 . 00
1 . 10
1 . 20
1< 30
1 . i+0
1 . 50
1 . 60
1 . 70
1 . 80
1 . 90
2 . 00
2 ..10
2,.20
2..30
THE SCATTERING FUNCTION AT a =
s<;1 , NLJ)
. 0209
.0212
.0152
.0130
.0210
.0291
. 0 38 0
. 0 + 37
.0(119
.141+3
.1922
.1885
.1353
,09?<+
.0915
.0573
.0509
.0501
.0565
.0511
.Q35<+
.031+0
.01+09
.0372
.^311
.0221+
.0250
.0206
.0203
.0151+
.0095
.0078
.0083
.0135
[ + -]
[•-:
( +- )
[+[+-!
[+-]
(+-]
{ [*•-]
( « • - )
(
(
(
(
(
+ + - 1
+ + - t
•- 1
l+- I
(+-]
(•- )
(+-)
(f- 1
(+-1
{ + ->
(t- )
(+-I
(+-)
<+ - )
(+-)
(+ -)
(f- )
( +->
(t- )
(+- )
(f- )
<^- )
.001+7
.001+7
. 00i+<+
.OQi+6
. 0 01+6
.001+8
.0051
.0055
.0071
. 009<+
.0111
.010<+
.0083
.0069
.0066
.0058
.0056
.0055
.0051+
.0053
.OOt+8
. 004 7
.00^9
.00<+3
.001+6
.001+2
.001+2
.001+1
.OOt+1
.0039
.0036
.0035
.0035
.0037
- 10 -
THE SCATTERING FUNCTION A W
CASE
NU (THZ)
-1.00
-.90
-.80
-.70
-.60
-.50
-.to
-.30
-.20
-.10
Q.QQ
.10
.20
.30
.<*0
.50
.60
.70
.30
.90
1.00
1.10
1.20
1.30
i.'+O
1.50
1.60
1.7Q
1.80
1.90
2.00
2,10
2.20
2.30
S ( Q,NU)
.0190
.011*5
.01<*8
.0170
.0223
.0339
.0^30
.0573
.1173
.131*6
.247L
.2132
.1951
.1529
.1256
.1105
.031*9
. 0950
.0331
• 0575
.0550
.0555
<*-)
( + -]
(+< +- )
(t-1
( + ( + -)
(
<
•
-
)
( +- )
C+- J
(•-
(+( +{f(t~
( « • -
(+ -
(+(+ (+ (t-
.QH91
(f-
.041-*
.0350
.0?9i?
.0293
,(12'+5
.0119
.0139
. 0 26 2*
. 0121
.0100
.0052
(+(*(+ (+-)
! * • - >
( + (f( + {•( + ( * • -
. oo'+g
.0Q<*7
.00^6
.00«t6
. 0 0t*8
.0051
.0051*
.0060
.0077
.0101
.Q117
.0109
.0096
. 0062
.0073
.0069
. 0062
.0065
.0061
.0057
.0053
.0053
.0051
. 3 0<+9
.00^7
.OO*+3
.001*3
«QO*1
.0036
.Q03<3
. OQitl
.0035
. 0 03<+
.0032
=
l.od
- 11 -
CASE
6
NU
(THZ)
-1-00
-.<bC
-.60
-.70
-.60
-.50
-.1+0
-.30
-,20
-.10
0.00
.10
.20
.30
/ n
THE
T TER.IN3 FUNCTION AT
5 ( 1,MI J)
.0135
)
(
+
)
.1172
.0175 ( + - )
.0299 ( + - )
)
.0*73
.051+2 ( + - )
.0719 < • - )
ol2<+2 ( t - )
.1986 ( + - )
.3010 ( + - )
(
«
<
«
•
•
-
:
-
.1677
.1337
.1059 ( * - )
.1057 ( + - )
.0879 ( + - )
.0610 ( + - )
. 0 7 0 1 u- )
.0578 ( + - )
1.50
i.60
1,70
1.80
1.90
2 . 00
2.10
2.20
2.30
. 0051+
nnflfl
t UUOO
.50
1.1+0
t f- •
|
/
• I"7 -*• X
1.00
1.10
1.20
1.30
. QQi+<t
.001*3
• 001+&
.0055
.0060
.0072
.0091
.0116
• 3«+7i+ ( + - > .0129
.3715 ( * - ) .0 129
.3115 ( • - ) . 0 1 1 3
.21*23 ( * - )
.0097
• "+U
.60
.70
.60
.90
.00<+3
( + -)
(+ -)
(+- )
.0327 ( + - )
.0293 ( f - )
.0271+
)
,02«*i+ t*- )
.0190 ( + - )
.041+1
.0062
.0071+
.0067
.0067
.0063
.0055
.0058
• 005<+
.0050
.00i+t»
.001+3
.001+2
,oom
.003b
.0167
.0106
(+ -)
( + -• )
.0037
. 0 1 i*i*
.301+7
.009?
<*-
.0035
.0030
.0032
(4--
(+-
)
• )
)
.0031+
1.60
- 12 -
THE SCATTERING FJNCTION AT
CASE
NU (THZ)
-1.00
-.90
-.80
s i:i , M U )
-.70
-.60
-.50
,0151
.0205
.0323
,0<»<+2
.0*9<+
.0893
-.i+O
. 1 5 1 5 <; +
-.30
-.20
-.10
0.00
.2950
.<+562
.7302
.9719
.9153
.72<+7
.1+353
« 3 66 o
.2791
.2052
.1307
.1399
.1023
.0330
.10
.29
.30
,<+0
.50
.60
.70
.30
.90
1.00
1.10
1.20
1.30
l.i+O
1.50
1.60
1.70
1.80
1.90
2.0n
2.10
2.20
2.30
'
1; + - )
1[ + - )
\[ + • - )
1[ + • - )
1
: * • - )
-)
i
<: + - )
1: + - )
1[ + - )
<+ - )
1[ + - )
I( + - )
i( + • - )
I[ • - >
1[ < - - )
1[ + - )
i[ + - )
1[ + - )
l[ + - )
.0521+
i[ < • - )
.0527
.01+53
.0352
.0315
.1)231
.0190
.0235
.0191+
.0130
.0129
.0Q5<+
l[ + - )
1[ + - )
i( 4 - - )
i( + - )
'[ < • - )
iU-)
.0112
(••-}
(+-)
.OO'+'t
. 00^6
.001+9
. 0053
.0051+
.006*+
.0079
.0105
.0131
.0168
.0195
.0187
.0162
.0132
.0115
.0100
.0087
,0083
.0073
.0065
.0060
.0051+
.0051
.001+8
.QQ<+<+
.OOt+2
.301+1
.0037
.0039
.0037
.0031+
(+-)
(+-)
( + -)
s003i+
.0031
.0033
- 13 -
CASE
8
NU (THZ)
-1 .00
.90
.80
—
,70
.60
.50
"" t
"• 1
><*0
.30
.20
.10
0 .00
.10
.20
.30
—
.t*0
.50
.60
.70
.80
.90
1 .00
1 .10
1 .20
1 .30
1 .40
1 .50
1 .60
1 .70
1 .80
1 .90
2 . 00
2 .10
2.20
2 .30
THE SCATTERING F U N C T I O N
S([J T NU)
.023t* ( + - )
.0178
.0259
.0466
.0902
.121*3
.2521
.5507
1.1S46
2 .2913
3 .101*7
2 .8073
1 .7301
.9382
.&023
.3777
.2973
.1971*
< • -)
< + -)
( + -)
( f->
.005<*
.0065
.0073
( • ->
+ ->
.0098
f-)
.0143
1 * - ) .0202
[ + - ) .0263
1 + ->
( + ->
[*•-)
( + ->
( + -)
( + ->
(*-)
( + ->
.1587 (*-)
.lli9E> U-)
.0913 U-)
.0351* <•-)
.01*35
(«•-)
.0358
.0300
.0329
.0235
.0201
.0137
.0136
.0061
.0057
.0081
.0132
.00t7
.001*3
.001*3
( + -;
( +(+- }
(+- )
(+-
>
(+- )
)
>
<•- >
(+- )
(•- )
(t-
.Q33<*
.0 315
.0 245
.0181
.0 146
.0117
.0104
.0087
.0080
.0068
.0063
.0056
. 0051
.0046
.0043
.0044
.0040
.0039
.0036
.0038
.0032
.0031
.0032
.0034
A,T U =
2.2U
- 14 -
CASE
9
THZ)
- 1 . 00
90
•*.# 80
70
60
50
40
30
20
10
0 . 00
u 10
9 20
• 30
• 40
•"
•
~
•
—
•
•
50
60
70
80
• 90
1 . 00
1 . 10
1 . 20
1 . 30
1 . 40
1 . 50
1 . 60
1 . 70
1 . 80
1 . 90
2 . 00
2 . 10
2, . 2 0
2 ..30
*
•
THE SCATTERING FUNCTION AT
s <:
Nil)
.0203 ( +-)
1
.0184
.0271 ( .0531 ( +
.07^3 <
.1772 1 + )
. 3 3 4 8 < +•- 1
.3i)19 ( 1.7717 1 +3 .7737 ( +-)
>
5.0731 <
*+. 3 9 5 7
—
2 .6050 I + - )
1 . 2 5 5 3 1[ • - )
.7503
*• - )
[
+- I
.4912
- >
•
.3523
.2348 1 - )
.1750
- )
.1246
.1139 [ + - )
- )
.0709
- >
.0502
- )
+
.0397
. 0 3 5 6 1[ + - 1
.0299 [ + - )
.0256 ( + - )
.Q131 U - )
.0140 u - )
.0090 ( + - )
.0105 ( + - )
.0133 u - )
. J092 ( + )
. 0033 ( + )
.0048
.0047
.0050
. J0 5 8
.0065
.0086
.0113
. 0 163
.0 246
.0360
.0418
.0389
. 0 299
.0208
.0161
.0131
.0113
.0094
.0083
.0071
.0069
.0053
.0054
.0048
.0047
.0043
.0042
.0C3S
.0037
.0034
.3035
.0036
.0033
.0033
2.40
- 15
CASE
NU
10
(TriZ)
- 1 .00
.90
.80
.70
- .60
.50
- , i*o
- .30
.20
.10
0 .00
.10
.20
.30
• <*Q
.50
.60
.70
.80
.90
1 .00
1 .10
1 ,,20
1 .30
1 »i+0
1 .50
1.60
1.70
1 • 80
1 .911
2 .00
2 .10
2 .20
2 .30
THE
Sa&TTf.RlNG
FUNCTION
sc * » N l J)
.0283 1 + -)
, 0 2 9 9 1 X. * 1i
.001*9
.001*9
.01*30
.0053
.0060
.0069
.0061*
1 +- )
• 0 o92 +
,1062 1
-)
,ifoa i
.321*1 1 + - )
.6332 > - )
1,1336 1
.0110
.0150
. 0 198
(
.0263
.0297
[ * • - )
.0282
(+-;
.0237
[*•-',
.0190
.0158
;+ .0139
[*•-',
.0118
(*-!
.0102
t+-)
. 0090
(t- \
.0065
(+ .0071
(+- 1
.0066
( +- 1
.0059
( +- )
.0056
.0051
(+- )
.001*9
* • - )
1.91*31
2.1*337
2« 2<*62
1.6132
1.0^50
,7192
.51*23
. 33 2k
• 2300
.211'+
. 1 8 33
,1237
.1030
.071+9
.06<*6
. 0 + 36
.0^*30
.0325
.(1253
.017 1
.0172
. Q121*
.0149
.0038
.0129
« • - )
( * • » )
(+ ->
U- \
(•- >
(+ - )
(+- )
( + -)
(+ - )
(+~ )
.00£*<*
»OQ<*1
.0037
. 0 036
.003^
.0035
.0032
.0033
AT
4 =
2.60
- 16 -
CASE 11
THE SCATTERING FJNCTION AT
i N l 1)
NU (THZ)
-1 .00
- .90
- .80
—. 7 0
- • 60
- .50
- .40
- .30
- .20
- .10
0.00
.10
.20
.30
.to
.50
.60
.70
.80
.90
1.00
1 .10
1.20
.30
1.4 0
1.50
1 .60
1.70
1.80
1 .90
2 .00
2.10
2 .20
2 .30
A.
.0357
.0279
.0545
. 0 d3 6
.1057
.1626
.2334
.4197
.5123
.9299
1.0550
1.0185
.8741
.7J39
.5715
.4750
• 3<J5Q
.3095
.2536
{ +-1
( +-)
( + -)
(+- ]
(+-)
(+-)
(
(
( t-)
( • -)
( + -)
(+ (
(+ (+ (
(+ (+ (t *
•
-
)
. 1924 I + .1131
.0315
.Qt>33
.0329
.G153
.0316
.0253
.0217
.0203
• 0149
eJOdl
.0030
+ -1
<• ( + -)
(+ <+ -1
1+ -•
>- )
t - 1
( ^>
I *•- )
1 f- )
+-)
*
•
-
.0051
.0048
.005b
.0065
.0069
.0082
.0095
.0123
. o mg
.0169
.0212
.0202
. 0 179
.0157
.0142
. 0 13 0
.0118
.0107
.0100
.0087
. 0085
.0077
.0069
.0061
.0057
.0056
.0047
» 0 044
,0042
.0040
.0039
.0037
.0034
.0033
- 17 -
CASE
NU
12
(THZ)
-1.00
-.90
-.80
-.70
-.60
-.50
-.40
-•3T
-.20
-.10
0.00
.10
.20
.30
.40
.50
.60
.70
.60
.90
1.00
1.10
1.20
1.30
l«40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
THE SCATTERING FUNCTION
S O , NUJ
.0440 ( f - )
.0303 { f-)
.0434 ( *-)
.0o98 ( * - )
.1005 ( * - )
.1237 ( + -)
.1731 ( + -)
.2930 < + - )
.3590 (
.5326 ( + -)
.60 0 9 [ + - >
.5434 [^-)
.5452 (f-)
.^952 [ + - )
.4434 [+-)
.3909
.3411 f + - )
.3036 U-)
.2574 ( + -)
.2293 [ + -)
.1972 If-)
.1708 (f-)
.1455 ( + -)
.1170 ( + « )
.0-32 9 C+-)
.0875 (*•-)
.0 595 (f-)
« 0558 { + -)
.0346 (+-)
.0382 (f-)
.0256 ( + -)
.0235 { + - )
.0203 (f-)
.0155 If-)
*•-)
.0055
.0050
.0054
.0061
.0069
.0074
.0085
.0105
.0119
.0155
.0166
.0184
.0155
.0138
.0127
.0119
.0112
.0105
.0098
.0093
.0067
.0082
.0077
.0069
.0063
.0062
.0054
.0053
.0044
.0046
.00!*Q
.0039
.0037
.0036
AT d =
i.GO
- 18 -
CftSE
NU
13
(
—
—
—
THZ)
90
80
• 70
• 60
•
50
<*0
—
• 30
20
*" fl 10
0 . 00
• 10
• 20
• 30
""
ft
• <*Q
• 50
60
• 70
• 80
• 90
1 . 00
1 . 10
1 . 20
1 . 30
1 . '•0
1 . 50
1 . 60
1 . 70
1 . 80
1 . 90
2 . 00
2 . 1U
2 . 20
2 . 30
2 , <+0
2 ,. 5 0
2<. 6 0
2 . .70
2 .. 8 0
2 .. 9 0
3 ,.00
THE SCATTERING
FUNCTION
5 U L,NU)
.0337 (
« • - )
.01*3 6
(
.0533
.033**
.100"+
.1507
.2210
.2353
.1*172
.5103
(+ -)
( + -)
( + -)
(t-}
( + -)
( + -)
( + -)
( + -)
.1*939
.<*653
.<+66i
.t»090
(
(
<
<
< • - )
.3*57 <
.3083
.2S93
.2535
.2273
.1989
.1390
.l3l<+
. 1 351
.1152
.1337
.0311
+ -)
f-J
+ -)
+ -)
*•-)
I+
<+
(+
1
-)
-)
-)
«•-)
.DOS'*
.0056
.0060
.0066
.0070
.0083
.0098
.0118
.Oi<+1
.0i5«*
.01<*8
.0132
.0129
.0121
.0112
.0105
. 0 099
.0096
.0092
.0087
[•-
(+
1+
.008**
.0079
.0073
.0068
.0065
[+-)
.0059
. Qo6<+ [ • .0055
.055!* l + - > . 0 0 5 3
.0^-30 E + - ]
. 0 0<*9
.0330 [•.0G<*<*
• 03£f9 ( f . 0 0<*3
. 0 2 0 8 {*•-)
.0038
.0222 ( f .0033
.0170 ( + - ) . 0 0 3 6
. 0 1 1 5 (*•- 1
.0033
.0115 [ ^ — )
.0033
.0070 ( + - > . 0 0 3 1
.0091 ( * - )
.0032
. JQ30
.001*3
-)
-)
[+ -)
i + -)
(+(+ -
>
.0031
.0029
AT 4 =
3.2Q
- 19 -
CASE
Ik
THE SCATTERING
FUNCTION
NU ( T H Z )
-.90
-.80
-.70
-.60
-.50
-.1*0
-.30
-.20
-.10
0.00
.10
.20
.30
.1*0
.50
.60
.70
.80
u90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
l.SO
1.90
2.00
2.10
2.20
2.30
2.1*0
2.50
2.60
2,70
2.80
2.90
3.00
. 0 4 9 6 (*• - ]
• 04-78
.0559 ( + -1
.0795
*1139
.1536 (+-]
.2059 ( + - ]
.2371 ( + -)
,3916 ( + - i
. •+&6S ( + - ]
.1*951* U - l
. 4 541 < + - ]
. 43 5 4 ( t - )
.3852 ( t - 1
. 3 5 1 1 (*•- >
.3040 ( t - >
.2340 ( + - >
.2508 ( + - >
.2404 ( • - 1
. 2 238 ( + - )
.2101 ( + - )
. 1 3 1 3 (*•- )
.1521 ( + - »
.1351 ( • - )
.1238 ( + - )
.1043 ( + - )
.0354 ( + - )
.Q77^ u- )
.0705 { • - )
.0536 ( • - )
.0515 ( + - )
. 042^ ( • - )
.0372 ( + - )
.0237 ( + - J
.0202 ( + - )
. 0 1 9 3 («•- )
.0171 ( +- )
. 0 1 3 3 (+ - )
.0107 {*•- )
.0091 (•- )
( < • - )
.0055
.0054
.0056
.0063
.0071
.0060
.0091
.0108
.0132
. 0 148
.0146
.0132
.0125
.0117
.0112
• 0 104
.0101
.0095
.0093
.0091
.0088
.Q0S3
.0077
.0072
.0069
. 0 6 5
.0059
.0057
.0055
.0051
.0049
. 0 044
.0043
.0037
.0036
.0035
.0034
.0031
.0030
.0029
AT 1 =
3.<*Q
- 20 -
CASE 15
THE SCATTERING FUNCTION AT
j)
MU (THZ)
90
• *80
70
60
50
40
~" a 30
20
10
0. 00
• 10
?0
•30
• 40
• 50
• 60
•
70
80
90
l. 00
l. 10
l. 20
l. 30
l,.40
l..50
l..60
i..70
l .80
l .90
2 . 30
2 .10
2 .20
2 .30
2 .40
2 .50
2 .60
«
i
2 .70
2 .30
2 .90
3 . 00
.Q-+98 ( *-}
.0515
.0555
.0374
.1192
.1693
.2421
.3353
.4402
[«•-]
(
(
*-)
(
(
<
(+•-)
.5563 i + -
.5439
)
.5522 4- .4932 [ + - I
.4424 < + - 1
.3351 [ +•- 1
.3*21 t + -)
.2936
1
.2752 + - I
. 2653
)
.2179
)
.2090
)
.1320 (+ - )
.1555 [ + - >
.1446 f+ - )
.1349
)
.1242 ( + -)
.1059 (*- )
.0304 ( + - )
.0739
)
.0630 (•- )
.0511 (+ .0*97
)
.0413
.0324 ( + .0325 (+.0240 (••.0132 ( + -)
.0147
)
.0141 (+• - 1
. JQ53 (•(*•-
(*•-
(*•-
( < • -
.0054
. 0054
.0057
.0063
,0070
.0082
.0097
.0111
.0139
.0157
. 0 151
.0146
.0133
.0126
.0118
.0111
.010**
.0100
.0098
.0090
.0088
.0083
.0078
.0076
.0072
.0070
.0065
.0058
.0058
.0053
.0052
.00+6
. 0044
.0041
.0041
.0037
.0035
.0032
.0032
.0027
3.60
- 21 -
CASE
16
THt
SCATTERING F U N C T I O N
3 ( 3l i N U )
NU (THZ)
-.20
-.10
0.00
.10
.20
.30
.1+0
.50
.60
.70
.80
.90
1 . 00
1.10
1.20
1.30
l.'40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2 . 40
2.50
2.60
2.70
2.80
2.90
3.00
,3409
»5>+82
.7252
.7288
.6321
.5759
*5159
tk4kl
.3736
.3233
.3135
.2772
.2571
.2445
-1935
.1769
.1577
.1296
.1210
.0997
.0335
.0753
.0o82
.0650
.0503
.0478
.0417
.0289
.0221
.0249
.0229
.0133
.0172
(+->
( *-»
( + -)
(+ -)
(
«
( f-)
i + -)
-)
(+
(+
<
-)
*-)
( +- )
i~ I
(*- )
1 • -)
( . 1
.
1
.0126
.0151
.0173
.0170
• 0 15<+
. 0H+4.0135
.0125
.0116
.0109
.0107
.0100
.0097
.0095
.0086
.0082
. Q07d
1 + -;
([ +-)
[*•-]
1[ +-]
> -
.0071
.0069
.0063
.0059
.0057
. 0 05*+
.0053
. 0 0^8
[ + -)
• 00^7
(*•(+(+(+ -
. 0 0<+<+
.0039
.0036
.0037
.0036
.003^
• 0 034
AT
i
=
3.80
- 22 -
CASE 17
MU CTHZ)
-2.10
-1.80
-1.50
-1.20
-.90
-,60
-.30
0.00
.30
.60
.90
1.20
1.50
1.80
2.10
2.<*0
2.70
3.00
3.30
3.60
3.90
<t.2O
<t.5Q
<t.8O
5.10
5.<tO
5.70
6.00
THE S3ATTERIN3 FUNCTION AT A =
S U i NilJ)
-.0053
-.0001
.0056
.0^03
.1110
.1973
.3337
.3966
.37t*7
.3174.
.2686
.1326
.its'*
(« - J
( +-)
(t C+
<• » • ( +(+( +-)
(• -)
( + -)
( +-)
1+-)
( +-)
( +- )
.111*7
.0775
. 0 5 3 3 ( • _ V*
.0195 ( + - )
.014'* ( + - }
.001*2 ( + - )
.Ql<*9 ( + - >
-.0002 ( +- )
. 0 3 8'+ ( t - !
-.0071 { t- 1
-.0053 (+- >
.90?<* ( + - 1
-.0097 ( t- 1
( +- )
.Q0&0
-.0026 (+ )
.0095
.0097
.0100
• OiH*
.0139
.016<*
.0198
.0216
.0212
.0200
.0187
.0165
. 0 148
.0142
.0130
.0122
.0110
.0109
.0104
.0109
.0102
.0107
.0101
.0102
.0107
.0102
.0109
. 0 106
3.bO
- 23 -
CfcSE 16
NU ( THZ)
- 2 . 10
- 1 . 80
50
- i . 20
- . 90
60
-It
— •30
0 . 00
30
60
* 90
1 . 20
1 . 50
1 . 30
2 . 10
2 . 40
2 . 70
3 . 00
3 . 30
3 . 60
3 . 90
4 . 20
4.
4.
5.
5.
5.
6.
50
80
10
40
70
00
THE S3&TURIN& FUNCTION AT
5 (
i,NU)
.0181
.0258
.01*57
.1130
.2123
.3454
.5440
.6549
.6508
.5659
.3633
.2733
.2290
.1528
.0949
.0523
.0230
.0203
.0317
.0195
.0100
.0118
.0144
• GO ?3
. 0015
.3007
-.0035
. 0 03 4
< + -)
( « • - !
(••-J
( + -i
(•-:
<«•-)
( + -]
c +(fr-1
( + • -
u->
( + -)
(•-)
(+ -)
(+ - )
<
«
•
-
(+ ( * • -
(+(+(+ (+ - )
(^-)
(«•-)
(•-)
(+-)
( - ( • - )
{ + -)
. 0086
.0090
.0099
.0129
.0164
.0201
. 0 245
.0268
.0268
.0254
.0214
.0192
.0175
.0147
.0129
.0118
.0102
.0101
.0106
.0100
.0097
.0097
.0098
.0092
.0092
.0092
.0090
.0093
4.50
- 24 -
CASE 19
NU (THZ)
-2.10
-1.80
-1.50
-1.20
-•90
-.60
-.30
0.00
.30
.60
.90
1.20
1.50
1.80
2.10
2.1*0
2.70
3.00
3.30
3.60
3.90
'+.20
2.50
<+.8Q
5.10
5.1+0
5.70
6.00
THE SCATTERING FUNCTION AT
3 ( Q , NU)
.0025
.0180
.0275
,Q7<*0
.1276
.2190
.3027
. k05k
. ki 39
. <*250
.3375
.2708
.2161
• mi7
( +
(+ -
]
( • -1
-]
(• -
(t
(+
-
{+ (+
>
(+ - >
(f
(+ (+ (t (+ (+ -
1
1
)
.1235
.0706
I
. 0 3 1 3 (f -:
.0265 (+- >
.0309 (+- )
.0127 (+ - >
.0092 (f - )
- . 0 0 5 1 * ( 4- - )
-.0002 (+- )
- . 0 0 3 7 ( t- - >
-.0106 (+- )
- )
-.0079
- . 0 0 5 2 (+ - )
- . 0 0 5 2 (+ )
(
•••
. 0078
.0086
.0090
. 0 1H+
.0135
.0165
.0188
.0212
.C216
.0218
.0198
.0181
.0165
. 0 1<*3
.0 135
.0115
.0100
.0098
.0099
.0091
.0089
.0082
.0086
.0085
.0082
.0086
.0088
.0089
5.00
- 25 -
CASE
20
(THZ)
-2 .10
- 1 .80
- 1 .50
- 1 .20
- .90
- .60
- .30
0.00
.30
.60
.90
1 .20
1 .50
1 .80
2 .10
2 .1*0
2 .70
3 .00
3 .30
3 .60
3 .90
.20
.50
<+. 8 0
5 .10
5 • <*0
5 .70
6 .00
THE SCATTERING
5(
-.0053
.0093
.0239
. 0 1*0 2
.091*7
.1310
.1928
.237t
.2502
.3029
.2935
.2736
.2323
. 17i*<+
.1397
. 11<*7
.0528
. 033i»
.0239
.0300
.0136
.0057
. DQ56
.0315
-.0O3C
-.0028
- . J 0 79
-.001*5
a, N U )
u->
(+-)
(• ->
(••-)
(• - )
( + -)
(*•-)
(+-)
( +-)
(+-)
(+-)
( +-)
{ + -)
(+-)
(• - )
( + ™)
( • ->
{+ - )
( + ->
( 4-- )
+ -)
* • - )
[
*•-)
. + -)
f-)
;*•-)
[*•-)
>-)
FUNCTION
.007*+
.0081
.0089
.0097
.0115
.0133
.0151*
.0168
.0171*
.0188
.0187
.0181
.0170
.0151*
. 0 11*1
.0130
.0112
.0100
.0096
.0098
.0090
.0083
.0089
.0087
.0081*
.0088
.0087
.0089
AT a =
5.50
- 26 -
CASE 2 1
NU (THZ)
-2.10
-1.80
-1.50
-1.20
-.90
-.60
-.30
0.00
.30
.60
.90
1.20
1.50
1.80
2.10
2.40
2.70
3.00
3.30
3.60
3.90
4.20
4.50
4.80
5.10
5.40
5.70
6. 00
THESCATTERING
FUNCTION
51 U,N U)
-.0044
.0Q42
.0206
.0429
.1059
.1519
.234*
.3235
.330d
.3236
.3230
.2933
.2*30
.1911
.1659
.1399
.0872
.0750
.0368
. 0 239
.0326
.0110
.0110
.0041
-.0071
-.0236
-.0045
-.0061
( + -)
(+-)
{+- )
(•- )
. 0074
.0079
. 0087
.0098
.0125
.0145
.0167
.0192
.0195
.G192
.0192
.0183
.0166
<+(*(+-
.0153
.0146
.0137
( +-)
(•- )
(+- )
(+- )
<+- )
(+- )
( +-}
(+-
)
U-
f
)
c+(*-
u(+(+-
)
(t-
)
(+-
)
(f-
)
(+- )
(+- )
(+-)
( +- )
.0121
.0115
.0109
.009b
.0099
.0090
.0091
.0089
.0084
.0077
.0069
.0089
AT 4 = o . O O
- 27 -
CASE 22
THE S3ATTERIN3 FUNCTION AT
MU (THZ)
-2.10
-1.80
-1.50
-1.20
-.90
-.60
-.30
0.00
.30
.60
.90
1.20
1.50
1.80
2.10
2.t+0
2.70
3 . 00
3.30
3.60
3.90
<*.2Q
**.50
<t.30
5.10
5*<*Q
5.70
6.00
l,l»U)
• Oil it2
.0059
. JJ3 5
.0360
.11159
.1539
• 25 !*3
.3710
.3379
.3075
.3117
.3211
.2527
.2076
.1335
.1356
.1105
.0757
.0578
.Ot*73
.0+21
.0300
.0179
-.005**
-.0019
-.0002
-.3053
-.0010
(• -)
(
i
1. *
( , »
<
(*-)
1• -)
( t-)
( + -)
[*•-)
[ *•-)
(+ - )
[ + -)
[ * • - )
( * • - )
(+-)
(+ - )
(t-)
(•-)
O-)
{t-)
(I--)
(<•-)
( * • - )
. 0079
.0079
.0081
. 0095
.0122
.01**3
.Qlb7
.0197
.0191
.0187
.0189
.0190
.017**
.0159
.0153
.0136
.0128
.0115
.0109
.010**
.0102
.0093
.0092
.0082
.0066
.0089
.0087
.0091
b.5Q
- 28 -
CASE 23
MU ( T H Z )
-2.10
-1.80
-1.50
-1.20
-.90
-.60
-.30
0. 00
.30
.60
.90
1.20
1.50
1.80
2.10
?,,kQ
2.70
3.00
3.30
3.60
3.90
<t,20
<t.5O
<+.80
5.10
5.40
5,70
6 , GO
THE SCATTERING FUNCTION AT
liNU)
-.010*+ < • - )
. 0 137 ( • - )
.0065 ( • -]
.0506 ( + - ]
.1135 ( +- )
.1568 [•- •
.I960 < • .2250 < • -]
.2507 1 * .2911 ( • .231*5 ( + - )
.2711 [ +- ]
.3168 [ +- )
. 2 5 1 1 < + - 11
+- 1
.1*36
.1732 1
1
.0998 1 + - 1
.0972 1 • .0661 <
. 0 6 5 3 1[ + - )
.0308 [ + - >
. 0 2 5 6 ; t- )
.0170 (+- >
.0213 (*- >
- . 0 0 5 3 u- I
-.011^ (f- >
- . 0 0 1 0 l +- )
-.00«*5 ( +- )
.0070
. 0 08 *t
.0080
•0 1 0 2
.0135
.0178
.018<t
.0181
.0179
.Old'*
.0161
.0175
.0185
.0166
.0150
.01<t6
.0123
.0122
.0110
.0111
.009?
.0096
.0092
.0095
.0082
.0081
.0089
.0089
7.00
- 29
CASE 24
NU ( THZ)
- 2 , 10
- 1 . 80
- 1 . 50
- 1 . 20
- , 90
- . 60
- , 30
0 . 00
30
60
* 90
1 . 20
1 . 50
1 . 80
2 . 10
2 . 40
2 . 70
3 . 00
3 . 30
3 . 60
3 . 90
4 . 20
4 . 50
4 . 80
5 . 10
5 . 40
5 , 70
6 . 00
THE S U T U R I N G FUNCTION &T
S< Gli NU)
-.0353
.0102
,0168
. 0 + 29
.0774
» Q3 70
.1375
.1917
.2305
.2459
.2373
.2578
.2531
.2351
.2144
t19l7
.1571
.1164
.0990
.0773
.0704
.0393
.0316
,017d
.0013
-.0335
-.3072
-.0132
(•->
(+-)
( +-)
(+-)
(•-]
(*•-)
<*-)
(f-J
(+-1
(•*•-]
(+-)
(•-)
(+( +{ + (f-
(+{+ -
(+(+->
(t-)
( +- )
(
*
•
-
)
( +-)
<
«
•
-
>
(+-)
.0071
. 0060
.0066
.0097
.0111
. 0 120
.0133
.0151
. 0 162
.0168
.0183
.0176
.0180
.0169
.0161
.0152
. 0 142
.0130
.0124
. 0 117
. o im
.0102
. 0100
.0095
.0088
.0087
.0087
.0085
*
7.50
-
CASE
25
THE S 3 A T T E R I N 3
J (THZ)
-2.10
-1.80
-1.50
•1.20
-.90
-.60
-.30
0.00
.30
.60
.90
1.20
1.50
l.ao
2.10
2.40
2.70
3.0 0
3.30
3.60
3*90
<».2O
4.50
4.80
5.10
5.40
5.70
6.00
30 -
FJNCTION
NU)
.0010
.0 025
-.0012
.0316
.0554
.0521
.1346
.1534
.1343
.2300
.2369
.2550
.2553
.2395
.2014
.1305
.1549
.1321
.1243
.0340
.0672
.0378
.0240
.0127
.0050
.0007
-.0010
.0050
<+( +(«•( +( +-
c+( +(+(+(*( +-
u-
<+(+( +<+ (+-
• -)
->
-)
<+ - )
{*-)
.0076
.0078
.0077
.0095
.0106
.0119
.0139
.0146
.0156
.0168
.0169
,0173
.0170
.0165
.0154
.0143
.0 144
.0134
.0134
.0125
.0116
.0106
.0101
.0097
. 0093
.0092
.0092
.0097
AT 4 =
3.00
- 31 -
CASE
26
NU (THZ)
- 2 .10
-1 .80
- 1 .50
-1 .20
- .90
- .60
- .30
0 .00
.30
.60
.90
1 .20
.50
i .80
2. 1 0
2 • <*0
2 .70
3 .00
3 .30
3.60
3 .90
i* . 2 0
It
.50
.30
5.10
5 .1+0
5.70
6 .00
•»
THt
SCATTERING F U N C T I O N
s (2 , N U )
-.0027
• 0036 ( • • .0035
. 0 3 9 5 U-)
.Q5l<t ( + - )
.0901 ( + - ]
.1331 ( + -)
.15B3
. 1 9 2 6 (+•-)
. 1 7 0 3 (+ - )
.2359 (+ - )
.21*51 ( 4 - - )
.2770 ( + - )
.2'4 Ob < + - )
.235^ ( *- )
.1871 (4--)
.1383
+ -)
.1520
. l-tO** ; t .1171 [ + .0990 [ +.0583 + . O'+3 0 [ + .0303 [ + .0331+ [ * • . 0 2 2 2 ; ••. 0 137 ; t - . 0 0 5 3 '. + ( « • - )
( * • - )
.0076
. 3331
.0081
. 0 097
.0101
.0117
.0133
.01^5
. 0 15^
.0153
.0167
.0163
.0159
.0158
.0157
. Oltfl
. 0 1****
.0135
.0129
.0122
.0115
.0106
. 0099
.0093
.0096
.0091
.0068
.0079
AT a =
S.5G
- 32 -
CASE 27
NU (THZ)
-2.10
-1.80
-1.50
-1.20
-.90
-.60
-.30
0.Q0
.30
• 60
.90
1.20
1.50
1.80
2.10
2.40
2.70
3. 00
3.30
3.60
3.90
if.20
4.50
4.80
5.10
5.40
5.70
6.00
THE SCATTERING FUNCTION AT 4 =
3 O,NU>
-.0019
-.0036
. >)Q5 8
.0377
.0333
.0712
.1012
.1201
.1203
.1448
.1913
.2i»57
.2512
.251*2
.2152
.2030
.2013
.1922
.1571
.111*7
.1132
.091*8
.0520
.0161
. 0 326
.0119
.0153
.0069
( +-)
(+-)
(••-)
<•->
(+-)
(*-)
( + -)
( + ->
(+-)
(+ -)
(+-)
(*->
(+ -1
( *-',
i +(•-)
(*-
(+(+(+-]
(+ -
(+(*(f«•-
( + -]
u-
(+-
.0076
.0075
.0079
.0C96
.0093
.0111
.0126
.0136
.0139
.0147
.0159
.0169
. 0 167
.0166
.0155
.0152
.0147
,01<t?
.0134
.0120
.0121
.0112
.0114
.0097
.0104
.0097
.0099
.0096
9, 00
- 33 -
CASE 26
NU ( THZ)
to
-2.
-2.
-1.
-1.
-1.
-.
••
10
80
•
50
20
90
60
30
0 . 00
30
60
90
1 . 20
1 . 50
1 . 80
2 . 10
2 . kO
2 . 70
3 , 00
3 . 30
3 . 60
3 . 90
ht 20
k a 50
80
5 ,. 1 0
5, kO
5 .70
6 .00
6 ,. 3 0
6 .60
6 .90
7 .20
- .
7 .50
7 .80
8 .10
THE S G A T T L R I N G FUNCTION AT
S<
.QJQ8
. 0 155
.0206
.0110
.0359
.Q<*53
.07<+5
.0363
.1016
.12T2
.1572
.2133
.2217
.2467
.2321
. 2*»76
.2606
.2356
.2002
.1959
.173^
.1562
.122^
.1190
.0310
.0828
. 0 + 56
. 0 + 65
.0250
.0319
. JQ35
.0070
.0J78
.0132
.0132
-.001*9
1)
(+ -)
(+-)
<•->
(<•-)
(+-)
<•->
(+ - )
(+ - )
(*-)
(fr-)
1+ -]
(*-)
(+-]
(+•-!
(•-]
(+-]
( + -]
(*- I
( +- >
(*•-]
U- 1
( + -
)
( * • -
>
.0079
.0087
.0090
.0085
.0097
.0101
.0113
.0121
.0129
.omo
,. 0oma
166
.0165
.0169
.0166
.0169
.0173
.0166
.0156
.0155
.0150
. 0 1**^
.013<t
)
( + -)
( •- )
(#•- )
l + -)
( + -)
( :~- )
)
)
(+ -)
(*- )
( + -)
.0133
.0121
.0122
.0109
.0110
.0102
.0107
. 0 099
.0100
.0102
.0107
.0109
(t- )
. 0 10<4
(+ -
(•(•-
(
*
•
•
"
=
9
-
CASE 2 9
NU (THZ)
-2.10
-1.80
-1»5Q
-1.20
-.90
-.60
-.30
0,00
.30
.60
.90
1.20
1.50
1.S0
2.10
2.<fQ
2.70
3.00
3.30
3.60
3.90
H-2Q
<*.5Q
'* - 8 0
5.10
5.1+0
5.70
6.00
6.30
6.60
6.90
7,20
7.50
7.80
a.io
8 . ^0
34 -
THE S C A T T E R I N G
FUNCTION
5(Gl i N l J)
.0035 ( + -)
.0110 ( + - )
.003*+ i *->
+-)
.0287
.0353 1 + - )
+ -)
. Qsatf > - )
.0953
+ «)
. 1 1 1 1 ([ + - 1
. 007b
.0060
.OOFtt
.QC66
.1371*
.1793
.2311
.2031
.2359
.2171
.23 65
.2192
.2379
.1970
.13&5
.157«*
.1521
• 12«t7
.1136
.0755
.0700
. 0533
.Q1A1
t•-!
[ < • - 1
[*•1
>
>
)
>
( +- >
( +- )
(*•- )
( *-)
(•- )
( * =)
(+- )
( +- )
)
e 031*0
)
.0279 ( + - )
.0287 ( • - )
.0133 ( • - )
.0132 ( • - )
.0030 ( • - )
.00 9*+ ( * - )
-.0018 ( • - )
- • 30 l*f ( + - )
[ « • -
( * • -
( < • -
.0091
.0096
..0103
.0123
.0132
.0151
.0163
.0155
.0161
.0155
.0161
.0156
.0153
. 0 15 0
.Qlkb
.0139
.0137
.0129
.0128
.0113
.0112
.0111
.0102
.0102
.0106
.Q10<+
.0104
.0102
.0108
.0106
.0107
AT 4 = 1 0 . 0 0
- 35 -
CASE 3 0
NU
(THZ)
-1.50
-.75
0.00
.75
1.50
2.25
3.00
3,75
<+.5O
5.25
6.00
6.75
7.50
8.25
9.00
9.75
THE S C A T T E R I N G F U N C T I O N
S (a,NU)
U-)
.0712
.0315
.1383
.1377
.2001
.1327
.101*9
it-)
( + -)
U->
(•-)
(+-)
{•-)
(4--)
.1135
.0333 ( + - )
. Oa^l ( * • - >
.0233
.0313 ( + - )
.0075
.0132
( « • - )
-.011*2
.0081
.0097
.0102
.0117
.0129
.0132
.0130
,0123
.0126
.0116
.0109
.010b
.011G
.0107
,0110
.0105
AT a =
10.00
- 36 -
CASE 31
NU (THZ)
-1.50
-.75
0.00
.75
1.50
2.25
3.00
3.75
<+.5O
5.25
6.00
6.75
7.50
8.25
9.00
9.75
THE SCATTERING FUNCTION
3(Q,NU)
.031*2
.05<t8
.0953
.1321
.1588
.2052
.157<+
.1M9
.1055
.0914
• 0*6b
.0208
.0193
.021<t
-.0328
.0075
< +-)
1 *•-)
( + -)
« + -)
1 *-)
[t-)
[+-)
1[*•-)
1
1+-)
*•-)
+ -)
[•->
(+ -)
[+ -)
<[ + - )
[ + -)
.0063
. 0 091+
.0105
.0117
.012*+
.0131
.0127
.0122
.0125
.0121
.0110
.0107
.0111
.0115
.0111
.0113
AT i = 10.50
- 37 -
CASE 32
NU (THZ)
-1.50
-.75
0.00
.75
1.50
2.25
3.00
3.75
4.50
5.25
6.00
6.75
7.50
8.25
9.00
9.75
10.50
11.25
THE S2ATTE.RIN& FUNCTION AT >i =• 1 1 . 0 0
SQ»HU)
.0075
(+-)
.0542 (••->
.0592
.1039
.1526
.1965
.1315
.1+77
.1214
.0399
.0b73
,0573
.0322
.0179
,307'*
.0092
-.0019
<•-)
(+-)
{+-)
(+->
(+-)
(+->
(+- )
(+->
U->
(+ - )
(+-)
(+-)
(+- )
(+-)
( +-)
« 0 3 kk
(••- )
.0074
.0098
.0104
.0117
.0 126
.0134
.0132
.0128
.0124
.0117
.0113
.0112
O 0107
.0105
.0105
.0113
.0118
.0128
- 38 -
CASE 33
THE SCATTERING FUNCTION AT J = 1 1 . 5 0
1)
NU (THZ)
-1-50
-.75
0.00
.75
1.50
2.25
3.00
3.75
<t.50
5.25
6.00
6.75
7.50
8.25
9.00
9.75
.0087
(+-)
tQ*kb
.0719
(••-]
(•-)
.l'oO
.1396
.1762
,171a
.1510
.135^
.1061
. 0 i 3 i
<+-)
(+-)
<*•-)
(+-1
(+-]
(+(+(+-)
. 05 0*•
{+ -]
.0339
.0211
(+~
<•-
>
. 0 0 3 1 <«•- )
.0013
(+- >
.0061
,0098
.0111
.0127
.0128
.0131*
.0133
.0131
.0126
.0120
.0117
.0113
.0109
.0109
.01(18
.0111
- 39 -
CASE
3k
(THZ)
- 1 .50
- .75
0 .00
.75
1 .50
2 .25
3 eOO
3 .75
k .50
5 .25
6 .00
6 .75
7 .50
8 .25
9 .00
9 .75
10 . 5 0
11 .25
THE SCATTERING F J N C T I U N
S C i»Nlj)
+ -)
+ -)
.0090
.0095
f-)
.0423
.0099
. 0 7 8 2 1[ + .0109
. 1 3 2 1 1L + - ] . 0 1 2 1
.1417 [ * .012*+
.1578
.0129
+ .1532
.0133
.1505 [ + - ] .0131
• 1130 [ * .0126
.0337 i + - 1 .0121
.0521
1 .0116
.0356
> .0117
.0251 ( +- 1 .0118
.01<*0 ( + - > . 0 1 1 7
.0057 ( + - 1
.0119
.0001 ( + - )
.0122
-.0095 ( +- )
.0125
.015<+
.0296
(
(
(
«
•
-
AT
i
=
12.00
- 40 -
CASE
35
NU (THZ)
0.00
,75
1.50
3.25
3.00
3.75
<t.5O
5.25
6.00
6.75
7.50
8.25
9.00
9.75
10.50
11.25
THE SCATTERING
FUNCTION
S Q,NU>
.0515
.0766
.0935
+-)
[+-)
.11*1%
[*•-)
+-)
.1531
.1532
.1502
.1392
.0950
.0772
.0<+B3
.0<»33
[*•-)
u->
[+-)
[ +- )
[ +- ]
C+ - ]
!+-
.Q33C+
.0193
.0087
.0065
(+-]
(+-]
.0101
.0109
.0115
.0126
.0130
.0131
.0132
.0 131
.0122
.0120
.0116
.0120
.0119
.0118
.0120
.0127
AT 4 = 1 2 . 5 0
- 41 -
Q>IOA H
X
4<Q< IOA"1
IE
IQ
O
\Z)
o
Q<4A"
C/)
LJJ
I
-2
0
2
4
6
FREQUENCY TRANSFER v
Fig. 1.
8
10
12
(THz)
The full width at half height of the resolution function
for the three resolution ranges.
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