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i’.?k
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LA-7482=PRProgress Report
C3● *REPRODUCTION
COPYIS-4 REPORT SECTION
(6.-C
Applied Nuclear Data
Research and Development
April 1–June 30, 1978
L’
L%%LOS ALAMOS SCIENTIFIC LABORATORY—
Post Office Box 1663 Los Alamos, New Mexico 87545
AnAffmmstiveAction/EqualOpportunityEmployer
Thefourmostrecentreportsinthisseries,unclassified,areLA4i971-PR,LA-7066-PR,LA-7200-PR,andL&7301-PR.
ThisworkwasperformedundertheauspicesoftheElectricPowerResearchInstituteandtheUSDepartmentofEnergy’sDivisionofMilitaryApplica-tions,ReactorResearchandTechnologyDivision,DivisionofBasicEnergySciences,andOfficeofFusionEnergy.
Thts report w.. prepu.d as . . .. C.UIII of work sponsoredbv the United Stale. G.vernmeIM. Nmher the Umted St.wsnor the Un&led St.les Detmrtrnmt of Ener.v. nor .ny of Ihew●mployees. nor . . . of thctr .mtr.cl. rs. s. bc. nlr..tms. orIJw1, ●nvloyee,. makes .“Y w.,,.”IY. ●xmrest o, ,rrwl,td. o,●-m.. .“Y 1.”1 h.btlats or r.mon”b, hw (OZ the .CCU”CV.complctencm. y usrfulmss of any !nfonn ation. .IUMr.tus.Droduct. or IMOC.U dmcloxd. or r. Dzewnla lh.t m usc wouldnot mfrmse Pnv.t.!v owned rishu.
b
i
.
UNITED STATES
DEPARTMENT OF ENERGY
CONTRACT W-740 S-ENG. Sm
LA-7482-PRProgress Report
8pecial DistributionIssued: September 1978
Applied Nuclear Data
Research and Development
April 1–June 30, 1978
Compiledby
C. 1. BaxmanP. G. Young
CONTENTS
I. THEORY AND EVALUATION OF NUCIJIAR CROSS SECTIONS............ 1
A.
B.
c.
D.
E.
F.
G.
H.
I.
J.
R-Matrix Analysis of the Four-Nucleon System.......... 1
EDA Code Development.................................. 4.R-Matrix Analysis of the T-N Scattering............... 4
Calculation of the39K(n,2n)
38K Cross Sections
from Threshold to 100 MeV................0..● ......... 5
Calculation of Proton Production from n +88,89Y
Reactions............................................. 6
Evaluation of the Tungsten Isotopes................... 7233
n+ U Evaluation................................... 8
n + 242Pu Evaluation.................................. 8
Addition of the Fission Channel to the GNASH Code..... 18
Gas Production and Activation Cross Sections.......... 20
II. NUCLEAR CROSS-SECTION PROCESSING....● .....0...● ● ..........● 20
A. Integral Testing of Methods and Data.................. 20
B. Phase II Testing of Preliminary ENDF/B-V Data......... 20
c. Power Reactor Cross-Section Processing Methods........ 21
D. The MATXS/TRANSX Cross-Section System................. 21
E. Thermal Reactor Cross Sections........................ 24
111. FISSION PRODUCTS AND ACTINIDES: YIELDS, YIELD THEORY,DECAY DATA, DEPLETION, AND BUILD-UP........................ 24
A. Fission-Yield Theory.................................. 24
B. ENDF/B-V Yields.....● ............● .................... 26
c. Decay Heat Standard................................... 26
D. Spectral Comparisons.................................. 27
E. Status of Fission-Product Data for AbsorptionCalculations.......................................... 27
F. Library for Processed ENDF/B AggregateFission-Product Spectra............................... 27
REFERENCES..............................● ......................● 42
iv
.. .
APPLIED NUCLEAR DATA RESEARCH AND DEVELOPMENTQUARTERLY PROGRESS REPORTApril 1 - June 30, 1978
Compiled by
C. I. Baxman and P. G. Young
ABSTRACT
This progress report describes the activities of theLos Alamos Nuclear Data Group for the period April 1 throughJune 30, 1978. The topical content is summarized in thecontents.
I. THEORY AND EVALUATION OF NUCLEAR CROSS SECTIONS
A. R-Matrix Analysis of the Four-Nucleon System (G. M. Hale and D. C. Dodder)
The four-nucleon system is of interest for applied reasons because it con-
tains neutron-source and therumnuclear reactions, but it is also of considerable
intrinsic scientific interest, particularly as a testing ground for presumed
charge-independence properties of nuclear forces. Our comprehensive R-matrix
analysis of this system provides an excellent macroscopic model for these charge-
independence properties, while accounting for a large body of experimental
measurements for the four-nucleon reactions. The isospin-1 parameters are first
determined from analyzing p + 3He scattering data, then incorporated essentially
fixed in a larger analysis of data from the six independent reactions possible
among p + t, n + 3He, and d + D (i.e., the 4He system). “
One aspect,of this approach is illustrated in Fig. 1 by the analyzing-3
power differences for p + He and p + T scattering at proton energies near 5 MeV.
The differences between measurements of the p and 3He analyzing powers for p + He3
scattering (left of figure) determines the parameters of the singlet-triplet
spin transitions in the T = 1 (isospin-1) levels. The dominant such transition
at these energies occurs for Jp = l-. Because the singlet Jp = 1- state is ex-
cluded in T = O levels due to symmetrization considerations, the 1- singlet-
1
3HE(P,P)3HE T(P,P)T
.
. r,“ A(p) 5.51 MeV /
Wisconsin 68,. I
,. /
. / I
.9 /
.* /
,, !
., 1 .
.a,.lu 9 .CuOmn m Uss Uc4i
* —
A(3He) 4.89 MeV \Rice 70
“
,.
,.
/
.. t
,.. ,-” ● . * n .
wtm5wsm
Fig.
a - T
A(P) 4.80 MeV., — Erlangen 76
i
..
*
4
q,,
..#. r \
i... \.-. . a . . a
.A(T) 4.96 MeVLASL 76 I \
-.0Ii ~
.,0.. 9 . la * . d IL
Measured and calculated analyzing powers for the ~He(p,p)~He(left) and T(P,P)T (right) reactions at proton energies near5 MeV .
triplet transitions in 4He are completely determined by the T = 1 parameters,
which are fixed in our model by analyzing p + 3He data. The resulting differ-ences predicted for the p and T analyzing powers for p -1-T elastic scattering are
seen
cant
2
in the right side of the figure to agree well with the measurements.
The major progress of this analysis in the past quarter has been a signifi-
improvement in the fit to data for the d + D reactions at deuteron energies
D(d, p)T D(d,n)3He
*.
.
iT1l
’20
fT1
’20
CIWC*m -%s mu
.-z.7c0 s IuSs .Ici,
Fig, 2.Differential cross section and analyzing power T20 = $ Azz
for the reaction D(d,p)T at Ed = 4 MeV (left), Differential
cross section and analyzing power A~z for the reaction
D(d,n)3He at Ed = 4 MeV,
up to 5 MeV. Some of these data are shown in Fig. 2 for the D(d,p) and D(d,nj
reactions. The fits illustrate a point that has been characteristic of the charge-
independent analysis from the beginning: the calculation does not reproduce meas-
ured differences in the cross sections for the two branches of the D + d reac-
kions nearly as well as it does for the analyzing powers.
— —
3
B, EDA Code Development lK, W~tte (C-3), D, C. Dodder, and G. M. Hale]
The EDA program and its auxiliary codes have now been converted for use on
LTSS (time-sharing)system using the FTN compiler. The programs have been de-
bugged and checked for a wide range of operating circumstances. Because of the
large number of options and features of EDA, it is not possible to test it under
all possible configurations. However, it is now reliable under almost all pos-
sfble arrangements. The program under the batch configuration of LTSS is now
running about 10% slower than under the CROS system.
The conversion to LTSS-FTN has meant three important improvements. First,
the code is now available as an interactive tool, including graphics display.
While it is much slower under the conditions usually present in this mode, it is
now suitable for short calculations. Second, the change to a dynamic storage
allocation incorporated at the same time as the conversion has allowed problems of
larger size in certain respects to be run. And third, it should be possible in
the future to make a portable version of the program, suitable for use at other
installations where the FTN compiler is available. This was not previously feas-
ible because the structure of its code, particularly its storage arrangements,
were very closely matched both to the CROS operating system and to the exact
hardware configuration at LASL.
c. R-Matrix Analysis of T-N Scattering (D. C. Dodder)
An R-matrix analysis of the ‘m-nucleonprocesses up to 300 MeV pion energy
has been enlarged to include the n-(p,y)n,oT (n,y)n, and T (p,~ )p channels.
The last channel is to represent the large absorption in the T = 1/2, J = 1/2
state. The use of a definite mass for the 0- is an approximation suggested by
the observed experimental width of the CJ-particle. The gamma-ray data require
El, Ml, and E2 multiples in both T = 1/2 and T = 3/2 states. The Ml multiples
occur in both J = 1/2 and J = 3/2 states. The multipole strengths are entirely
determined by the data; there are no theoretical inputs. The R-matrix approach
makes this feasible despite the limited amount of photoproduction and gamma-
emission data for this system.
The analysis is essentially completed and now allows reliable predictions of
m-nucleon scattering cross sections over the 0-300 MeV range, which, for the most
part, are more accurate than the individual
shifts are in reasonable agreement with the
shifts.
4
experimental results. The phase
most reliable single energy phase
.
.
D. Calculation of the39K(n,2n)
38K Cross Section from Threshold to 100 MeV (E.
D. Arthur)
‘1’he39 38K(n,2n) K cross section is used in pion radiotherapy to determine
the neutron dose arising from negative pion absorption. Because no experimental
data exist for this reaction above 23 MeV, we were asked by the biomedical
group at LAMPF to calculate this cross section up to neutron energies of 100 MeV.
For the calculations, the statistical model code GNASH1 was used, which included2
new preequilibrium routines based on recent exciton model efforts of Kalbach.
The (n,2n) cross section”represents only a few per cent of the
cross section; therefore, competition by proton, deuteron, and
included for each compound neucleus in the decay chain. Since
emission dominates, care was taken in the choice of the global3
sets used. Also, in the case of neutrons, slight adjustments
total reaction
alpha emission was
charged-particle
optical parameter
were made to
better reproduce the low-energy resonance data. The calculated results are
compared to representative experimental data in Fig. 3.
0 10 20 30 40 50 60 70
NeutronEnergy(MeV)
39Fig. 3.
Calculation of the K(n,2n) cross sectionto 100 MeV made using GNASH is shown.
0“0001 ! I I I I i ! i I
80 9k1
100
from threshold
E. Calculation of Proton Production From n +88,89X ~eaction~
. D. Arthur)
As part of a comprehensive effort to calculate neutron-induced reactions86-92Y and 89-90
on Zr from 0.001-20 MeV, we have investigated neutron and
proton optical-model parameters needed to calculate proton production induced
by neutrons on88Y and 89Y
. Recently, experimental data4 pertaining to these
reactions have become available through charged-particle simulation experiments90,91 89,90Y
employing the Zr(t,a) reactions. These reactions produce excited
systems, and the subsequent measurements of the proton decay can be used to de-
termine the relative proton production cross section for n +88,89Y reactions.
Previous calculations made using Perey proton parameters produce results for
n+89 Y, which are factors of 2-3 above the data for neutrons between 10 and 15
MeV. For the present calculation, we have used as a starting point a new de-
termination of the low-energy proton optical parameters in this mass region per-
formed by Johnson’ using sub-Coulomb barrier (p,n) reaction data. We have re-89
analyzed his Y(p,n) data8 making some adjustments to the proton parameters and
using a more realistic potential to describe the outgoing neutron channel. Pro-
ton production calculations made with these adjusted parameters for n +88,89Y
are compared with the charged-particle simulation results in Figs. 4 and 5. The
general features and magnitude of the experimental data are reproduced by the
calculations.
o
61 I I I I I
0.0 2.0 4.0 6.0 8;0 10.0 12.0 liO li.O 18.0 2[
Neu~ron Energy (kVI
Fig. 4.
.0
.
.
Comparison of calculated and experimental proton production crosssection resulting from charged particle simulation of n + 88Y.
o
o“ 1
lx
oG.o
0o“ -02
ao“ -a
oc5-V
0d-N
0
G h1 1 I I I 1
0.0 2.s 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 2!
Neutron Gtergy [MeVl
.0
m.?- cA-J-g, 2,
The total calculated proton production cross section for n +89Y
is compared to charged particle simulation results.
Fe Evaluation of the Tungsten T.sotopes [C. Philis (Bruy&es-le-Ch~tel)and E. D. Arthur]
As part of a cooperative effort between Los Alamos Scientific Laboratory,
Argonne National Laboratory, and Bruy&es-le-Ch~tel, we have begun a reevaluation
of neutron cross sections and gamma-ray production data for neutrons between
%3 and 20 MeV. As a first step, we have begun an extensive effort to determine
sets of sphertcal optical model parameters for neutrons in the range from 0.2 to
20 MeV suitable for use in statistical model calculations. Since the tungsten
isotopes are deformed, direct effects are important, and these must be accounted
for in the derivation of neutron optical parameters. Our approach has been
the following. Coupled-channel calculations with the JUPITOR code using the
Delaroche10 optical parameters for tungsten were made to determine the total
dtrect inelastic cross section from 0.2 to 20 MeV. This direct inelastic cross
section was then subtracted from the experimental total cross section, and the
results were used in the determination of spherical optical parameter sets.
By doing this, it was hoped that direct effects not accounted for in the spheri-
cal optical model could be separated, and the resulting data could be described
using realistic spherical parameters. In addition, other data such as the shape
7
elastic cross section, s- and p-wave strengths, and the potential scattering
radius were used in the optical parameter determinations.
The above procedure results in preliminary optical sets that fit the avail-
able total and elastic cross sections over the energy range 0.2-20 MeV.. These
parameters, when used in Hauser-Feshbach calculations, produce compound inelas->
tic cross sections which, after being added to calculated direct contributions,11give good fits to inelastic level excitation data for 182,184,186W .
. Prelimi-
nary GNASH (n,2n) cross-section calculations from threshold to 15 MeV also agree12well with the data of Frehaut for these nuclei.
G. n + 233U Evaluation (L. Stewart, D. G. Madland, and P. G. Young)
The preliminary ENDF/B-V evaluation that we provided to the National Nuclear
Data Center at Brookhaven National Laboratory used the Version IV evaluation of
the unresolved energy region, which included several discrepancies. During this
quarter we have reevaluated the data in the keV range, and matching unresolved
resonance parameters were obtained by F. Mann of Hanford Engineering Development
Laboratory. The tasks remaining are to merge the new data into the preliminary
file and to derive an energy-dependent fission spectrum representation up to an
incident-neutron energy of 20 MeV.
H. n + 242Pu Evaluation (D. G. Madland and P. G. Young)
A new evaluation of n +242
Pu cross sections has been completed for the
neutron energy range 10 keV to 20 MeV. The evaluation is available on the
photostore file FS=LASL407 (MAT 107, 0AC=T02PGY) and has been processed for
use in TD Division.
The only242
Pu reactions for which experimental data exist above 10 keV
are fission and radiative capture, and the capture data only extend to 100 keV.
It was therefore necessary to rely heavily upon nuclear model calculations for
the present evaluation. In particular, model calculations were used to derive
and/or evaluate elastic; inelastic; (n,2n); (n,3n); (n,Y); and first> second,
and third chance fission cross-section components, as well as the elastic and●
inelastic angular distributions. The model calculations were performed using
LASL versions of the Hauser-Feshbach statistical reaction code COMNUC13 (3/29/78 .
version) and the direct reaction coupled-channel code JUKARL.14
All calculations
utilized the LASL preliminary global actinide optical potential.15
Pertinent de-
tails of evaluated and calculated quantities are summarized below.
8
1.242
Pu(n,f) Reaction. The evaluated fission cross section is based upon16
averages of the measurements by Auchampaugh below 100 keV and upon the data of
Behrens et al.17
from 100 keV to 20 MeV. The ENDF/B-V evaluation of235
U fis-
sion18242PU
was used to convert the Behrens’ ratio measurements to absolute
cross sections. In Figs. 6 and 7, the evaluated results are compared to the ex-16,17,19-22
perimental data. The (n,f), (n,nf), and (n,2nf) cross sections were17
calculated subject to the constraint that their sum equals the measured total
fission cross section. Discrete fission channels (up to 12 each for first, sec-
ond, and third chance fission) and deformed level continuum fission channels were
employed. The calculated and measured total fission cross sections agreed to
within ~ 5%.
n
-.
#Yi?
+
>; x xx xx@x x x ‘- x -xt- X x RUCHFrMPFrUGtio 1971
m xxxx x + BERGEN. 1970x
: XxXx%x e BEHRENS. 1976
x o BUTLER, 1960r? xx xx
A FOMUSHKIN, 196S
x1
104 e Y 4 S6 7 6 9 10-’ t? 9 4 5
NCUTRON ENERGY, MEV
Fig. 6.
Experimental and evaluated242 -
Pu(n,f) cross sections between 10 and500 keV. The solid curve is the present evaluation (LASL-78).
.
s
PU-Z42 FISSION CROSS SECTION b-f t
+ BERGEN. 1970x aucwinmum. 1971● BEtiRENSo 1976Q BUTLER. 1960● fOIWSliKIN. 1969x auctifltlPFluoll. 1971* FOIIUSHKIN. 1967
Experimental and0.1 and 20MeV.
NEUTRON ENERGY, MEV
Fig. 7,242
evaluated Pu(n,f) cross sections betweenThe solid curve is the LASL-78 evaluation,
The evaluated
tures approximated
fission spectrum
by23
T = 0.50 + 0.43 F
is represented by a Maxwellian using tempera-
● (1)
With this representation, the average energy of fission neutrons induced by l-MeV
incident
The
8 and 9.
The most
neutrons is 2.031 MeV.
different evaluations of the fission cross sections are compared in Figs.
The LASL-78, HEDL-78,24
and ENDL-7625 evaluations are quite similar.26
significant difference occurs for the ENDF/B-IV evaluation, which is
.
.
substantially higher than the other data sets below 200 keV and between 2 and 8
MeV.
10
.
u
l--uwU3
inI
.
- PU-242 FISSION CROSS SECTION
N
70mm r -4t-
+
-..40 ---
wl‘-.
---------
- .
m ENoF/B-4‘- -- - ./”-—--
1’Ill 0
. Q
-i- ● J,
NEUTRON ENERGY. MEV
Fig, 80
Evaluated242Pu(n,f) cross sections from 0,1 to 20 M&,
b
2. Average Number of Neutrons Emitted Per Fission (~). There were no242
Pu experimental data available for the determination of ~p, the average number
of prompt neutrons emitted per fission. To determine ~ , the substantial exper-P
imental data available for the case of neutrons incident on240
Pu were analyzed,242
and the resulting data were corrected to Pu by adjusting for the systematic
variation of U with mass number.P
A comparison of the different evaluations of Vp(En) is given in Fig. 10.
Below 6 MeV, the LASL-78, ENDL-76, and ENDF/B-IV evaluations are in good agree-
ment, whereas the HEDL-78 values, which are based upon a phenomenological27model given in the Manero and Konshin review article, are 3-4% higher than
the other data.
11
NEUTRON ENERGY. MEV
Fig. 9,
Evaluated 3P F42Pu) for neutron energies between 0,1 to 20 MeV,
6
5
1:
4
3
I I I 1
‘2PuPROMPTV
ENDL-76
/
4
Evaluated 1P (242Pu) for
8 12 16 20En(Mel/)
Fig. 10,
neutron energies between O and 20 MeV.
J
12
3.242 242
Pu(n,Y) Reaction. The Pu radiative capture cross section was
calculated using the COMNUC model code and a gamma-ray strength function adjusted28
to agree with the measurements of Hockenbury. For energies above 4 MeV, the
capture cross section was calculated using a preequilibrium cascade process with
gamma-ray emission probabilities calculated at each stage.
The evaluated cross section is compared to the Hockenbury data and to other
evaluations in Fig. 11. Large differences exist, particularly above 3 MeV. A
~ 1 mb near 14 MeV, is supported by recent238
value of 0 , U measurements at then,
Los Alamos Scientific Laboratory.29
- I I [I
mzccccm
.
u
U-3
‘t ‘.. \
ENDF/B-4 Z; ‘=s
CROSS SECTION
\L #
Q
?o I I 1 u
104 ~ y c S678910-’ 4 S678910° 29 4 S676S10’ z
NEU;RCi ENERGY. MEV
Fig. 11.
Evaluated242
Pu(n,y) cross section from 10 keV to 20 MeV.
13
4.242
Pu(n,n’) Reaction. Hauser-Feshbach calculations were carried out
for the discrete compound inelastic scattering for 19 levels up to an excitation
energy of 1.152 MeV. Above this excitation, continuum compound inelastic scat-
tering was calculated using a deformed nucleus level density. Direct coupled-
channel inelastic scattering was calculated for the first five members of the
ground state rotational band assuming an axially symmetric rotor model. Quadru-
ple and hexadecapole deformations were taken from Ref. 30.
Figure 12 compares the total inelastic cross section from the various eval-
uations. Numerous differences exist among the data sets; one of the more signif-
icant is the fact that the maximum in the ENDL-76 cross section is broader and
occurs some 1-3 MeV lower in energy than for the other data sets. The average
emitted neutron energy from inelastic scattering is given in Fig. 13 for each of
the evaluations. The ENDL-76 (n,n’) spectrum is significantly softer below 1 MeV
than the other evaluations, and large differences exist among all the evaluations
above 1 MeV.
o .
.
In..
0 .
u).0
0 .
I I I
PU-Z42 INELfKTIC CROSS SECTION
●
✏
W#,-e,
● ENOL-76 c)/o HEOL-7E /
m
B-
●
w
\
c)”
% :
J,\
44? “.
@ ---
y@m
●
0-’ 1 c1S67S91O”’ c y 4 S678S10° 23 4s676910 2
*
.
NEUTRON ENERGY. MEV
Fig. 12.
Evaluated 242Pu inelastic cross sections from threshold to 20 MeV.
14
I 1 I I I
ENDF/B-4
1
#/ 0_.. - --
2.0 - //
—--Lo -
0.5 -
:
zw
0. 1- 1 x-ENDF/B-42%
0.05 :1
I
‘1
0.02 1 I I I 1
0 2 4
En(MeV)
Fig. 13,,..,.
The average emitted neutron energy from ‘4ZPU inelasticscattering calculated from several evaluations for inci-dent neutron energies between O and 5 MeV.
5.242
Pu Elastic Cross Section. The elastic cross section was determined
by subtracting the sum of the evaluated nonelastic cross sections from the eval-
uated total cross section. The evaluated elastic cross sections from 10 keV to
20 MeV are compared in Fig. 14. The present (LASL-78) evaluation differs from
the calculation by at most ~ 100 mb. The LASL-78 elastic and inelastic angular
distributions include both compound and direct contributions.
6.242
Pu(n,2n) and242PU n Sn ~eaction~o
9 Hauser-Feshbach calculations
of the (n,2n) and (n,3n) reactions were carried out with discrete (10 levels) and
continuum (deformed level density) contributions included in each case. The cal-
culations are compared to other evaluations in Figs. 15 and 16.
.co
● ‘\* r I 1I
\\ \a. PU-242 ELflSTIC CROSS SECTION
w \
4)●
p .. ,& \am
jti
+ \(J \LLl” .mm ‘\
‘\K’
!9 -
.w
● EuOL-76
. I t 1 J-l@ ~ 3 4 Stasal(y”’ f s 4s 670810” c S 4 S679810’ 2
NEUTRON ENERGY. PIEV
Fig, 14,
Evaluated242
Pu elastic cross section from 1.0keV to 20
loq
‘1PU-242 (N.2N) CRO$S SECTION
‘2ofga Qm~ ●
o HEDL-78e ● ENDL-76
. eo e
z~ ● ttapu . . . * /
wENoF/B-4 “\— K. ● \
1 I I I IW
.
0 -2\
* \t L-
------ ---8 I
.
‘4. 6. 6. 10. 12. 14. 16. 18. 20.
MeV,
NEUTRON ENERGY. tlEV
Fig, 15.
Evaluated 242pu(n,2n) cross sections f~om~threshold to 20 Mev .
16
00 .
o
m@l
.
0
00 .
PU-242 (N,3NI CROSS SECTION
ENDF/B-4
.
● ENDL-76Q HEOL-78
! I I
‘4.J/ I 1 1
6. 8. 10. 12. 14. 16. 18. 20.
NEUTRON ENERGY. MEV
Fig. 16.
Evaluated242
Pu(n,3n) cross sections from threshold to 20 MeV.
7.242
Pu Total Cross Section. The 242Pu total cross section was obtained
in an ad hoc fashion. The deformation effects (inelastic scattering in the
coupled-channels formalism) were combined with the total cross section calculated15
with the preliminary LASL (spherical) global actinide potential in the follow-
ing manner. Calculations with this potential for actinides (uranium isotopes)
of measured total cross sections showed that the differences between calculation
and experiment were approximately equal to the calculated total direct inelastic
scattering using the coupled-channels method without modification of the absorp-
tive potential. Since no inelastic scattering data exist by which the change in
the absorptive potential could be determined, the total direct inelastic scatter-
ing was simply added to the calculated (spherical) total cross section to obtain
the final total cross section. [The LASL preliminary (spherical) global optical15
potential for the actinides is presently being used as the starting parameter
set to obtain a global (deformed) potential in coupled-channel calculations that
include inelastic scattering data.]
17
.
s
%-—-—’- ‘ I v-r—
[
\\ PU-24Z TOTRL CROSS SECTION.
● 2,*to.-+- \\*~-
I ENDF/13-4--& -y
0 IICOL-78● ENCIL-76
.&-..=l, I Iz Y 4 5670910-’ t
.u.~Y 4 5678910” ? Y 4s6?0910” z
NEUTRON ENERGY. MEV
Fig. 17.
Evaluated242
Pu total cross section from 10 keV to 20 MeV.
The total cross sections from 10 keV to 20 MeV for
pared in Fig. 17. The peak in the ENDL-76 total near 1
in the (n,nf) cross section shown in Fig. 12,
four evaluations are com-
MsV results from the peak
I. Addition of the Fission Channel to the GNASH Code (E. D. Arthurj
As part of a program to upgrade the preequilibriuwstatistical model code
GNASH1 we have incorporated a fission channel so that multistep particle emis-
sion cross sections and spectra can be calculated for nuclei in which fission
occurs. The fission barrier is represented by a harmonic oscillator hetght EB
and curvature liu. The fission transmission coefficients are then given in the
Hill-Wheeler31
formulation as
1 .‘F(E) - 1+ exp [21T(E-EB)/liU]
For
eluded.
each fissioning system, up to 50 discrete fission channels can be in-
These can be supplied by the user or, as a default, the levels of the
.
,
.
.
18
compound
discrete
ture and
supplied
system compressed by a given input factor can be used. Above the last
fission channel, a continuum level density based on constant tempera-
Fermi-gas forms is used. Barrier heights and curvatures are generally
as input, although the option exists for default values based on syste-
matic to be used.
Comparisons have been made between GNASH and the statistical code COMNUC
with identical parameter sets for n +242
Pu, and good agreement was obtained for
the (njf) cross section. We are presently using GNASH to calculate (n,xn) reac-
tions on235U and 238
U, to provide spectral efficiency correction data for recent
measurements of Lynn Veeser of LASL Group P-3, and to compare with other available
(n,xn) data. Usi~g neutron transmission coefficients based on a recent actinide32
optical-model parameter set of Madland, the fission-barrier parameters of Back
et al.,3334 235U
and the preequilibrium model of Kalbach, we have calculated the
and 238U fission cross section from 4 to 21 MeV. The calculated curve is compared
in Fig. 18 to recent measurements of the235
U and 238U fission cross sections by
Leugers et al.35 in the energy range from 1 to 20 MeV.
, 1 , , I , , I , I 1 1 r 1 1 I # i I ‘ t
235U(n,f) .*b..2.0 - ●e
●
●* .*● .
●9●
n.●-%.
“! 1.0 -0
238U(n,f)$
rQr~ma
m P4mo
G I.o -
:.●
0’ ‘:’ ! 1 , I I
o 5 10 15 20
En(MeV)
Fig, 18:The GNASH calculated fission cross sections are compared with theexperimental data of Leugers for 235u and 238U0
19
J. Gas Production and Activation Cross Sections (L. Stewart and E. D. Arthur)
Many of the cross sections required for ENDF/B-V have not been measured,
and a few are virtually impossible to determine experimentally. For example,
hydrogen and helium production cross sections for structural materials such as
stainless steel have not been measured above a few MeV except at 14 MeV.
A paper36 discussing the problems associated with providing gas production
and activation data for ENDF/B was presented at the June San Diego American Nu-,
clear Society Meeting. Examples of calculations of hydrogen and helium produc-
tion cross sections with the GNASH nuclear model code were presented.
II. NUCLEAR CROSS-SECTION PROCESSING.
A. Integral Testing of Methods and Data (R. B. Kidman)
The 50-group library LIB-IV,37 38
generated with the MINX processing code
using ENDF/B-IV39 data, has been extensively tested on all 17 of the Cross Sec-
tion Evaluation Working Group fast reactor benchmarks.40
Results from this test-
ing have been compiled in a LASL report.41 Every experimental measurement is
compared to 1-D and 2-D diffusion theory and S P16 1/2
transport theory results.
Several comparisons with other laboratories are also presented. In general, the
results do not show any outstanding improvements or discrepancies over previous
calculations. The main benefits of the study are the introduction of the pack-
aged bench mark concept, which provides a convenient tool for rather complete
testing of data and methods, and the establishment of a reference set of calcu-
lations that can be used to assess MINX and measure future data and code
improvements.
B. Phase 11 Testing of Preliminary ENDF/B-V Data (R. B. Kidman)
Phase II testing of preliminary ENDF/B-V data consists of having
laboratories process the data into multigroup cross sections and then
several
to test
the processed data in the calculation of several assigned benchmark problems.
LASL has just recently received the preliminary ENDF/B-V data tapes. We
have decided to process the data with the new code NJOY. Also, in order to make .
the processed cross sections applicable to fast and thermal reactors, fusion,
weapons, and shield calculations, new 185-group neutron and 48-group photon .
structures and a new weighting function were programmed into NJOY. This proces-
sing is currently under way with high priority. It will require setting up,
debugging, and “pushing” through the computer approximately 100 runs.
20
When Phase 11 testing of ENDF/B-IV was carried out, LASL provided 50-group
cross sections to several laboratories. We intend to collapse the 180-group
data to 50-groups to minimize-any changes required to repeat the bench mark
calculations.
co Power Reactor Cross-Section Processing Methods (R. E. MacFarlane)
The new generation of thermal reactor codes sponsored by the Electic Power
Reseach Institute (EPRI-CELL, EPRI-CPM) use the same background cross-section
approach to self-shielding as is used in fast-reactor codes. A detailed investi-
gation of the effects of the approximations used in this method on thermal reac-
tor problems is npw under way with the goal of improving both the libraries and
the analysis codes. Some early results were reported in a paper42
entitled
“Data Processing for Power Reactor Fuel Cycle Codes,” presented at a symposium on
Nuclear Data for Thermal Reactors held at Brookhaven National Laboratory. Some
effects of non-1/E flux, intermediate resonance parameters, elastic scattering
self-shielding, transport correction, and heterogeneity were discussed.
D. The MATXS/TRANSX Cross-Section System (R. E. MacFarlane, R. J. Barrett, andR. B. Kidman)
The MATXS cross-section interface file is under development as a comprehen-
sive file for use in the CCCC system. Recently, capabilities to store and re-
trieve thermal cross sections and self-shielding information have been added to
the format, to the MATSXR formatting module of NJOY, and to the TRANSX retrieval
code.
Thermal data are stored in a special “data type” that allows for free-gas
and bound-scatterer incoherent and coherent group-to-group matrices of arbitrary
Legendre order. For each nuclide, several different binding states can be in-
cluded in the same library. This would allow, for example, the construction of
cross sections for both water and polyethylene without having to duplicate the
high-energy cross sections of hydrogen, whtch are not altered by the binding.
In practice, the TRANSX user specifies the number of thermal groups desired
(e.g., 40) and the names of the thermal coherent and incoherent scattering reac-1
tions desired (e.g., “H20”). The code then replaces the static H elastic scat-
tering group-to-group cross sections for the lowest 40 groups with the cross
sections for lH in H20
requires setting “NUP”
up and down scattering
and adjusts the total cross section accordingly. This
greater than zero; TRANSX will consistently truncate both
if necessary in forming the transport tables.
21
The traditional method of representing resonance self-shielding effects has
been to use “f-factors,” defined as the ratio of the cross section for one par-
ticular temperature T and background cross section 0.0
to a reference case (often
T=Oanda .mo ). MATXS departs from this tradition by storing AU = C(T,CO) -
a(ref). This representation requires less storage in the retrieval code since
only the accumulating cross section and AU are in memory at once, whereas the
traditional method requires the accumulating cross section, the f-factor, and
the reference cross section. The Aa method allows TRANSX to shield each element
of the scattering matrix without excessive use of memory. Provisions are in-
cluded to shield the heat production cross section and the photon production
matrix. .
TRANSX allows for group and nuclide dependent 00 values for each mixture.
The values can be determined by iterating the total cross section of a mixture
to convergence (the 0o-iteration), by using a simple buckling, or by specifying
a single escape cross section.
Once T and 00 have been determined for each nuclide, the code interpolates
using multipoint Lagrangian interpolation with special branches for very large
and very small ~. values. This approach requires only one material to be in
memory at any time and is therefore well suited to reading through a material-
order file like MATXS. These new schemes have been investigated with the use of
an auxiliary plotting program that has graphically caught several errors. The
latest iteration is still under investigation.
To make use of the new thermal and shielding capabilities, the TRANSX user
must supply some additional information. An example for a simple three-region
pin cell follows.
YRANSXMATXS TO TRAN$PORT 3Q,QAISS
OPTIONS..W.O.9
IPRINT 0IOUT 01PR08 0ISET t:FOQU 1ITIME 1IFPART BlTRC 0ICOLL =1IFLLJX e
PARAMETERS,W.,w-e.mqNGN zNGG 0
(8/lxL’oNG/snoRT)(k311/s/3/u=~ONEILASL/TD/FIDO/ANISN)[Otl=DII?ECT/AOJOINT)(1/?/3zNN/GG/COUPl.ED)C1/2=MAT~ISE/G20UPdISE)(1/~=sTEAOY-STATE/2QOM2T)(fl/tSNO/yEs)(0/1/2/3/u=NO TQANspoRT COaR/CONS,~/DIAG/B_HWS/INFLOUl(=1/0/NFINE=LIR FLux/NO COLLAPSE/QEAD FLUX)(0~1/2xN0 FLUX cALCULATIfJN/Ba/Bl)
t4EUTRON GROUPSGAMMA GRouPS
.
?.
.
.
22
NL TABLEsNTABL d! POSITIONS IN TABLENUP UP SCATTER GRoupsNMIX : MIXE$ OR t447kR1ALsNMIXS 5 MIXTURE SPECIFICATIONSNED AA EXTRA EDIT POSITIOVSNCDS 3 EDIT SPECIFICATIONS
MIX NAHES HETEROCENIETY,W-wava.v 99.99w.-089--
(1) 1 FUEL l,0173E+0Ei 0,2 w;5 1! 0, 0,3 0 2), 0,
NIX SPEcS DENSITY TEMP (K) SIGZERO REG THERMALW*9?OW9V8 99----- 9.9-9-.. we-.,-m w-w ..m.w-,
(2) 1 Llz35 6,253E;a/1 3,000E+Fj? 0, i aa FREE
U23B 4,721E-02 3,809E+a~ 0, 40 FREE
; ALz1 6,025E.k3i? 3,E’H0E+a2 l*kli30E+10 ; 48 FREE
(?)3 Ml 6,676Eo02 3000L3E+a2 l,nO@Et!n 3 40 H203 016 3,336E=B2 3,~@~L40~ loOi)@E+lB J 40 FREE
.
EDIT NAMES9*m-*-mv-w
CHI
: F2383 F2354 C236
EOIT SPECIFIC~710NSWUa----.woa.-.w-.992 NFTO1 l,a@OE+aB u231J
3 NFTOT l,L3B9E@fin UZ35
a NG i,000E+Dk3 U232J
COLLAPSE SPECIFICATIONS..wqa-=.w.---.w . ..-”...
45 24
FILE ID MATXS T2LASL NJOY VERs 1
THERMAL TEST●
●
●
CDMPUTEO SIGMA ZERO ?ALOES BY FINE GQOUP-*--*-=----- . . . . . . . . . . . . ..--=.m-m.-- -v--GROUP 1 UI?35 ~ J238.“-99 89-...9-. . ..9.---=
2,13E+03 2.16E+M1; 2,21E+93 .s,i7E+@l
POSITIONg9*0w.*.
1 CHI2 F238S F2354 C231)5 AOS6 NuSIGF7 TOTAL8Q INGRP
to
.:.
GROUp 1● *-..9”-.l,a?aE+noU,317E.n35,669E.M~3,33ZE.g2~,975E-o122,577E-mz5,Z09E.nlV.363E.~0AJ,609E=@lo,
GROUP z.9.8 . . . . .
0,0,l,8A3E-017,170E.az7,228E.31u,u99E.all,15uE+0aJ.u,3B7E.Or
2,536EoI?u
Line (1) indicates that mix 1 is to have an escape cross section correspond-
ing to a mean chord of 4.915 mm. The other two regions are infinite and homo-
geneous. Line (2) specifies that in mix 1,235
U is to have a given density and
temperature, that 00 is to be calculated, that mix 1 is in region 1, and that 40
groups of free thermal scattering are to be used. In mix 2 and mix 3, U. = ~ is
adequate. Note on line (3) that the thermal scattering appropriate to water is
used for the hydrogen in the moderator region. The results are collapsed to two235U fis
groups (0.625-eV break), and special activity edit cross sections for238
sion and capture and U capture are provided for calculating the standard spec-28 28
tral indices p , 825, and 6 . The resulting cross sections for the three mixes
are directly avai~able for use in a standard transport code.
E. Thermal Reactor Cross Sections (R. E. MacFarlane and R. M. Boicourt)
A library of multigroup cross sections for thermal reactor applications has
been prepared from ENDF/B-IV evaluated nuclear data using the NJOY processing
system. The library uses the 69-group structure of EPRI-CPM,43
which has 27 fast
groups (above 4.0 eV) and 43 thermal groups. The nuclides included are listed
in Table I. Note that temperature and background-dependent self-shielding fac-
tors are included for the heavy isotopes. Most nuclides include complete sets of
cross sections and P3 group-to-group matrices versus temperature (usually 300 to
2100 K), although only transmutation cross sections are given for the indicated
isotopes. All nuclides have had prompt heat production cross sections (KERMA
factors) and free gas thermal scattering matrices constructed for them. In addi-
tion, bound thermal scattering matrices are included for lH in water,1H in Dolv-
2 9ethylene, H in heavy water, Be in beryllium metal, and12C in graphite. Coher-
ent scattering is given for beryllium metal and graphite. Although this library
was originally produced to be converted into a job library for the CPM code (a
reactor cell code using the collision probability method), it can also be used
in standard diffusion and transport codes after appropriate reformatting.
111. FISSION PRODUCTS AND ACTINIDES: YIELDS, YIELD THEORY, DECAY DATA, DEPLETION,AND BUILD-UP
A. Fission-Yield Theory [R. Pepping (University of Wisconsin), C. W. MaynardUniversity of Wisconsin), D. G. Madland, T. R. England. and P. G. Youngl
Fission-product yields have been computed,based on the assumption of oblate
fragments at the scission point. This is done by constraining either the center-
.
.
.
●
to-center or end-to-end separation. Such a constraint is consistent with the
24
TABLE I
ISOTOPES IN THERMAL POWER REACTOR CROSS-SECTION LIBRARY
Nuclide Nuclide (with(complete) (transmutationonly)
H-1H-2He-4B-10C-12
N-140-16Na-23Mg -Al-27Si
KCaCrMn-55FeNi
Ru-103Ru-105Rh-103Rh-105A$3--1O9
1-135Xe-131Xe-133Xe-135CS-133CS-134
Pr-143Nd-143Nd-145Nd-147Pm-147Pm-148
Nuclide (withresonance only)
Th-232Pa-233u-233u-234U=235
U-236U-238NPF237Pu-238Pu-239Pu-240
Pu-241Pu-241Pu-242Am-241Am-243Cm-244
Zircalloy-2 Pm-148mMo Pm.149
Pm.151Sm-149Sm-150
Sm-151Sm-152Sm-153Sm-154Sm-155
44nmdel proposed by Jensen and Dossing. The general features of the yield do not
differ greatly from those previously reported.45
In some cases the space of al-
lowed shapes appears to be too restricted, the minimum potential energy occurring
tor shapes of maximum allowed oblateness.
A persistent feature of the yields computed,assuming both oblate and prolate
configurations,is an enhancement of the yield of fragments with odd Z. Recent46,47
measurements show an enhancement of about 25% of fragments with even Z.
There are two possible sources of this effect: the level density and the ener-
getic. The level density, with the parameters reported previously,48
shows an
25
odd-Z enhancement, while the energetic (G-function) favor even-Z. The effect of
energetic is then not sufficiently strong to overcome the level-density effect.
As an independent check, level densities have been computed with a code devel-49
oped by Moretto for a few test cases, confirming the odd-particle number en-
hancement. A reevaluation of the shell and pairing terms is under way.
B. ENDF/B-V YIELDS [T. R. England, J. Liaw (University of Oklahoma), W. B,Wilson, D. G. Madland, and N. L. Whittemorel
Subject to data testing results, Version VE yields will be supplied to re-
place those values currently being used in ENDF/B-V. The target date for com-
pletion of this effort is August 15, 1978.
The new yiel~s correct several known, but minor, errors in Version VD, and
include more delayed neutron branching fractions (92 vs. 57) and measured data.
Currently,the isobaric chains are being extended to include all nuclides in
the decay data files, and the yields and their uncertainties put into the new
ENDF/B-V format structure. Data testing will begin about August 1, and the re-
sults will determine whether or not the new values will be used.
c. Decay Heat Standard [T. R. England, R. E. Schenter (Hanford EngineeringDevelopment Lab), and F. Schmittroth (Hanford Engineering Development Lab)
An extensive report50
on integral decay-heat comparisons with ENDF/B and
generation of the nominal values for use in the ANS 5 Decay-Heat Standard has
been prepared. The results were presented in an invited talk at the seminar on
Nuclear Data Problems for Thermal Reactor Applications held at Brookhaven Nation-
al Laboratory on May 22-24, 1978.
In this report, results from recent integral decay-power experiments are
presented and compared with summation calculations. The experiments include
the decay power following thermal fission of233U 235U and 239PU
9 1 . The sum-
mation calculations use ENDF/B-IV decay data and yields from Versions IV and V.
Limited comparisons of experimental beta and gamma spectra with summation cal-
culations using ENDF/B-IV are included. Generalized least-squares methods are235 239
applied to the recent U and Pu decay-power experiments and summation235U
calculations to arrive at evaluated values and uncertainties. Results for
imply uncertainties less than 2% (1 0) for the “infinite” exposure case for all239
cooling times greater than 10 s. The uncertainties for Pu are larger. Ac-235U 238U
curate analytical representations of the decay power are presented for s s
.
●
✎
and 23’Pu for use in light-water reactors and as the nominal values in the new
26
ANS 5.1 Standard, accepted by the
inal values with ENDF/B-IV and the
eluded. Gas content, important to
on decay power are reviewed.
The importance of this report
ANS on June 21, 1978. Comparisons of the nom-
1973 ANS Draft Standard in current use are in-
decay-heat experiments, and absorption effects
is that it documents all comparisons and con-
tains a detailed summary of the nominal values and uncertainties used in the
Most of the effort toward understanding the239
standard. Pu decay-heat discrep-
ancy between IASL and ORNL and calculations made during this quarter are dis-
cussed in the report.
D Spectral Comparisons (T. R. England, R. J. LaBauve, and N. L. Whittemore),
During this quarter, we have compared239
Pu and233
U gamma spectra recently
measured at LASL by E. Jumey and P. Bendt with calculations using ENDF/B-IV
data. The results are generally as good as the earlier235
U comparisons.51
E. Status of Fission-Product Data for Absorption Calculations (W. B. Wilsonand T. R. England)
The status of fission-product data for absorption calculations was described
in a paper presented at the seminar on Nuclear Data Problems in Thermal Reactor
Applications held at the Brookhaven National Laboratory on May 22-24, 1978. In
addition to the summary of the development of methods and data, a study of the
fission-product nuclides and parameters most significant to parasitic absorption52
calculations was described. The sensitivity of the fission-product absorption
rate to each of the nearly 300 nuclide parameters was examined at a number of
irradiation periods of 33 GW days/MT light-water reactor fuel.
F. Library for Processed ENDF/B Aggregate Fission-Product Spectra (R. J.LaBauve, T. R. England, and D. C. George)
The library of processed ENDF/B aggregate fission product multigroup pulse
spectra (PEFPYD), the code for collapsing to a broad-energy group structure and
fitting the resulting broad-group pulse spectra with analytic functions (the
code FITPULS), and the application of these fitted functions in the calculation
of decay-energy spectra for finite irradiation times were described at the June
American Nuclear Society Meeting.53
To date, we have obtained parameters for
pulse fits in 11 broad-energy groups for 5 ENDF/B-IV fission-yield sets.
27
The parameters for the fits, shown in Table II, are in an ENDF-like format233 235U ~herml 238U fast 239PU themal and 232~ fast
and are for U thermal, 9 s s
neutron incident energy for both beta- and gamma-decay energy spectra.
In the ENDF-like format, columns 66-70 contain the “MAT-No.” that is used
to identify the target nucleus. The MAT-Nos. used in the listing are the same
as those used in ENDF/B-IV and are as follows.
MAT No. Target Nucleus
1260233U
1261235U
1262238U.
1264239PU
1296232m
A zero in column 70 signifies the end of the data for that MAT. The next two
columns, 71 and 72, are used for the MF-No., which identifies the energy of the
incident neutron. Here only two numbers are used; MF=80 denotes “thermal”
neutrons, and MF=81 denotes “fast” neutrons. A zero in column 72 signifies the
end of the data for that MF.
. Columns 73-75 contain the MT-No. that is used here to identify whether the
parameters are for a fit for the beta decay energy spectrum (MT=802) or a fit
for the~amma decay energy spectrum (MT=803). A zero in column 75 signifies
the end of the data for that MT.
The data for a particular MAT, MF, MT combination are given in field widths
of 11 and are organized as follows.
1. The sixth field on the first data card (number 11 in this case) gives thenumber of broad-energy groups for which the pulse fits are given.
2. On the next card, the first two fields give the energy bounds for thegroup in MeV; 0.1 to 0.9 MeV for group 1, for example. The sixth fieldgives the group number; 1, 2, 3, 4, etc.
3. The first two fields on the third data card give the cooling-time range
in s over which the fit was made; 0.1 to 1 x 109 s for group 1, for ex-ample. The sixth field gives the number of pairs of parameters used inthe fit; 16 for group 1, for example.
4. Next follows a number of cards containing the ai and Ai used for the pulsefit.
28
For example, for group 1, six cards are needed to contain the sixteen16
parameters needed for the pulse fit fc(t) =z
aie-Ait .
. i=l
TABLE 11. .
USEFUL FITS IN 11 GROUPS
11 GROU? FITS FROM EpT/TIHE DECADE PEFPYD D474tJUN78tRJL/DCGoLASL -0-0 ●00, 0 0 u ll126u8@8ezI,naaot?- 1 hnwul- 1 B e B l12bBB08@i?1,921?(3R- 1 l.dndk!u+ 9 0 161?bti8~80ZI,17887w 3 1.31789*0 7,3@fJZ3W; 1,23996-1 3,3S156=i l,b?269= Z12b~8~8024,191!917- 5 3oi(154@- 3 ~,9s31?8* 5 1,fj9729- 3 8,50174- b 4, 1fG?89-, U12b~8@6023,93218- b 1.U3197- Q“Y.872U~- 7 4.15921- 5 4,88582- 7 1,537949 5126B8080~6,2S912- 8 qo5z95H- 6 3c25ai6- o 1,~7531- 6 7,57565- 9 U,985913- 7126080802U,ZZ?OID 9 ~m2flu67- 7 6,7995U-10 7m57b4cjw 8 3,61435-11 l,b148ti- 81~6i~8@8@21,8i2686011 8.87199-!0 0oO’dk3@0+ i! 0.’d’?iUa0+ O 0p00aL4@+ a @otii$U@d+ U1260808a2am~aeaa- 1 9.afiaf10- i a c1 a Z12b08ti8f12lo~dd?n- 1 loil@dUti* 9 c1 u 171?6U8t?8tiZ7,89~lb- S lmU8bf45+ 8 1,695599 z 2,99261- 1 ~,95b7Z- 3 l,i?286b- ll~ba838k121,79883- 3 1,85960- I? ZmIJZ225W u 3,97993- 3 1,03123= 4 l,3t3779w 3i2bldB08023,45265- 5 4.54434- 0 1.23831- 5 l,b741S- U i?,la957= 6 4,42Zli3- 5126ti8@6@2l,U7@U5- b 1.7flu84- 5 2.f1228b- ~ 5,76BU3W 6 s,8594d- 8 l,Q41?b- b12bfi6ti8~29,13u35R- 9 IJ.62132- 7 6,85P99w 9 2.031U7- 7 1,23372- 9 8,a9713= 81~b~8~802l,0@fl~3wli3 2.11370- 6 l,5z75u*ll 8,b2735-lfl O,@fdOWO+ : ti#OaWM+ ai26aS@Bu29,fld3iJ!?- 1 1,35ABO+ 0 a nl,aa3uL3- 1 j.00auO+ 9
31260B@8fif217126flfJB13Bz
1,571B6w 2 l,606ab+ a 4,61113= ! 3,54381= ; 7,bla68* f l~27003=ll~b~0~S~22,9g6b?J- 3 Z.51209- 2 3,61966- U 4,49169- s l,22~b6- 4 10U@394- 3126be08023.73b73- 5 a.73914- 4 l,3uS4b- 5 1,78L353v (l ?,b193b- b 5.48139- 5126UBtf8ib21;48189- 6 2.31377= 5 1.27872- 7 7.abi6L4- b 1,19771- 0 l,336bl- 612b08ti8023,33251= 9 2,98222- 7 2,1zU19- 9 104093KP 7 bOU3U93-ia 5,93584- [email protected] 2.19179- 8 1.89017-11 8.S4770-19 8,ma@@@+ a kl.aOOCiO+ 0120WB08’d21.35330+ a 108t+a14a+ 0 0 0 IA 412bd81?8f121,nan314w I 1.an300+ 9 1712bfi8ti8022,515u1- z l,6933b* a.8.l?767- : 3,24759- : 1,05374= : l,3619iI- l12b~808@23,9287?- 3 2.17891- 2 3.68696- 4 4,51fl!u- 3 1,UQ071= 4 l,U44f16W 312b~8~ti~23,bi36~l- 5 0,7S951=Q 1,031136=5 I,715U59~ l,73b\T- b 5,D49uU= 512b~8fi0~2l,b1758- 6 Z.7R9~5- 5 8,5s165- B 9.20376- 6 u,f?b210- 9 l,U53f39* b12bW8a8ai?U,3u?690J~ 209UQt0- 7 4,au202-11 5Q85841- 8 U,19332-13 2,B3529m 81?bd906024,22!)93=11 2a~U31b- 8 1,483ZU-11 7,82~OW*lti “0,0301)0+ d klotl@ak3L?l+ 312b~8@8U2
l,~a2aa+ R 2.2va3u+ n 0 B u 51Zbd9d802l,aat4tifl= i I.OaafiO+ 9 0 ii 161?6’@8~8’d22.679~7- 2 1,758?5+ 0 9.79129- : 3.97575w 1 l,2B35vi- i? I,U1739- ilZbUOOBO~3,65?4?- 3 Z.381’J3- 2 3,81235- u 6,1!2!3- 3 1,152514- 4 1,s3819- 312b88~JJ@23,2bb4b. 5 S.2U298- 4 4,77b7~- b 1.748(I8w 4 1,29386- 6 4,76461- 512b~80b~2l.l~nl(l- 6 30135131~ 5 600~!!b9- 8 l,lJb94- 5 5,21521-10 1,’d059bo b12b#808022.33656-12 1.8?bbZ- 7 3.66U27-10 2,77694- 8 ?.h3892-14 7,73643- 9126f19f1802a,la29n-la 7,832’afl*10 m,flaliltin+ a 0,k3vlakl@+ fi .a,OaOLi(.#+ a k1,000aa+012b#8f180z2.ZZY339+ 0 ~.bP3~0+ 8 a 0
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SC*1660- 3 o.7dtfJ3= u l,rn1017m S l,8!796~ U 8,635S0= 7 5,51538- 51262818S21,S7733T 6 3.a04~5- s Q.~?342- b 9,71a58- 6 5,04098- 9 1,53196- 61?6281002S,1917b=10 2.J76b8- 7 l,93ZSbmlti 2.4~312- 8 U.29b00ul13 2,63340- 812b2B18f122,41377-!1 z.4173b- 8 703U?03=l~ 7,8aa2b-lfl ‘d,Gli4~@0+ ‘d 0.OBOaa+ 01i!b2B10@2l,8i101acl+ k! 2.a@i?an+ 0 (d 8 @ 51262818021,’aa?fja- 1 1.td910f10+ 9 j6i262B180~1,2182?= 1 1.674aa+ a 6,715??= ! U.4~0661D : 2,1il184m ~ 9,79773- 212b2518a25,I)?381o 3 ~,0b433- 2! U,OflSS?D u S0071aD=3 1,24747-u 1,49232-31262018023,83982-~ a.4;b37mU 4,88170-6 1,98849-4 S,54439-7 4,244159512b281801!•,33b7@~ 7 3.b174ti- S 7.68902- D l,l~993m S 7,8S048.10 1,37681. 6126?81802l,a7515=19 u.3@b6b- 7 5.2617b=l@ ?,5S611- 8 ~,78392-12 ltu82~Q~ 512b2818B?2m@2893-la 7,83408=10 0.?l@OOfl+ a O,a@OflO+ B f1,00V1@fl+ R 0,ag090+ 01?62818022,aa8ea6 o 2.60af10+ @ 0 e a b12628180al,BWW i i.aflaOa+ ~ ~612b28180Zl,lBQb5m 1 1.72670+ @ 1,00788- ; S,UT4111P : 2,4560$- : l,B9i30= l12bZ810024.94003= 3 Z.219~mm ~ 5.697939 4 5,78Z313= 5 1,12438- u 1,S587EW 31262818023,09993= 9 S,8~090- a 2.66004- b 2.ll130Q 4 s,lS608= O S,010600 5126?818029,fj~86~0 ~ 3,82860- s 2,4s419- S 1,2B9YIw $ l,lb787-10 3,87879- 7126i?13180aZ,*ltillmlfl 2.4Y37ti= 8 2,37?68-11 8,69907- 8 2,01270-11 2,4S36B- 812b28180Z1076u10=14 1096B3W Q 0,06000+ u 0.O~eam+ 0 O,GIOOOn+ 0 B,tiOOOO+ 012b2fJ180a2,600s0+ o 3.00000+ @ e o 0 7126281802i,OaOOa- 1 l,OwaOO+ Q 1512b28100aI,2B735w 1 1.09558+ ~ 6,5s667- : S.20294= : ~,6b05Sm : $,29667= 112620160~4,4795?= ~ ~,37821~ 2 5.67751- 4 b,12419- 3 8,4i1430= 5 1,7039S- 312625180Z3,129439 g b.48b73- 4 l,31abb= T 3,7t~fJ1- G 2,14065= O U0030919 S1266?818021.6B41s- 6 s.3f1285- $ 1.?73aU- 8 l,4f147~ S 1,60230-10 l,a6i27- 61262810021,OU823=1O 2.2!1906= 8 2.21337-11 3.32754- 8 2,2731?-17 l,1877flw 9126?1310fda3,eae0a+o O,soaflo+0 0 n B 812b251e0?i.12000s-1 1.0000a+9 1S12b2UlS0a2,384130 1 1,8$105+ @ 1,1T61811 ; U,7*8*b- ; 3,70757=; 1,15181-11262818026,00884= 3 ~.2T0$00 2 6.07918- u 6.6$S2b~ 3 :,3866$- U 1,78724- 3126281802
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34
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0 912628180214126281802
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35
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REFERENCES
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45