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1972

international book year

KFKI-72-65

/

3

. Pálfalvi SPECTRANS

P. Zaránd A COMPUTER C O D E

FOR STANDARDIZING NEUTRON SPECTRA

e f f c x i n g m a n < S 4 c a d m ^ o f (Sciences

CENTRAL RESEARCH

INSTITUTE FOR PHYSICS

BUDAPEST

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SPECTRANS

A COMPUTER CODE FOR STAND AR DIZIN G NEUTRON SPECTRA

J. Pálfalvi and P. Zaránd

Central Research Institute for Physics, Budapest Hungary Health Physics Department

September 1972

Work supported by the International Atomic Energy Agency under Research Contract

No. 1 1 1 5 /RB

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ABSTRACT

The DPSC code is written for comparison and evaluation of neutron spectra computed or measured by different techniques. The code calculates the spectra in 48 predetermined points independently from the original inter­

val distribution of the input spectra. The code computes kerma and rem-dose spectra as well as dose fraction from the standardized neutron spectra. The calculated spectra are written on a library tape and drawn by an off-line plotter.

KIVONAT

A DPSC program lehetővé teszi különböző módon számított és mért neutron spektrumok összehasonlítását és kiértékelését azáltal, hogy függvény- -interpolációk segítségével a spektrumokat egységesen 48 energia-intervallum­

ban adja meg. A program a standardizált neutron spektrumokból kerma és rem-dó- zis spektrumokat, valamint dózishányadokat számol. A spektrumokat könyvtár­

szalagon rögziti és plotteren kirajzolja.

РЕЗЮМЕ

Программа DPSC делавт возможным сравнение и оценну нейтронных спек­

тров, вычисленных и измеренных разными методами. Спектры с помощью интерполя­

ции приводятся к одному виду в 48 интервалах энергии. Из стандартизованных нейтронных спектров программа вычисляет спектры керма и бэр поглощенной дозы, а также вклад дозы в спектр. Спектры записываются на магнитных лентах и на самописце.

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I. Introduction

Neutron spectra calculated or measured by the different methods described in the literature often can only with

difficulty be compared with each other and used for evaluation of dosimeters, because they refer to different values; for instance, f /Е/ or Е.Ч* /Е/, etc.

The DPSC code, designed to simplify work wit£ the spectra,

ч

makes a neutron spectrum library by standardizing neutron spectra from either 'f /Е/ or E. V* /Е/ input spectra. The code also calculates dose and kerma spectra and dose fractions and has the standardized spectra drawn on a plotter.

II. Description of the program

The first task is to make a standardized spectrum from the input spectrum. This is done by Lagrange and linear interpolation.

The program determined both interpolations, compares the results, and the result which approximates the input function the better is used for the further calculation.

Lagrange interpolation

The function which is to be approximated, denoted by f/x/, is defined in the interval £ x^ ; x j . If ,xn are

different optional base points then the Lagrange polynomial is

• и Л _

р/х/ = X 'f /*к/ • T T ' 1/

ки i-'í хк-*|

K i + k

Generally it is not necessary to know the P/х/ polynomial in its explicit form aQ + a^x + a2* +..»+an_^xI_ ; the knowledge of its values at m discrete points ^ ^-s enouS^*

An algorithm for computer calculation of the P/Х/ values /here called А/ is given in [l] .

- 1 -

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2

In 1/ Р/х/ is a Lagrange polynomial of degree /п-l/ interval and has /п-2/ extremes. The positions of these extremes may all be inside the | x^ ; xn '| interval. In that case, if f/х/ has less

than /п-2/ extremes the interpolating polynomial is not a good approximation to the original function but oscillates. This happens, often, especially when f/х/ is monotonous in a large

interval within J^x-^ ; xnj . The oscillation increases when the value of

J

max f/х/ - min f/x/| in an energy interval £ x-L r; x j - or the energy interval itself - is large. Sometimes the value of P/х/ will be less than 0, despite the fact that x-j> 0 and f/x/> 0 in the whole j^x^ ; xn ^ interval.

Linear interpolation

(f/xn/ - f A i/) ./x - x±/

L/х/ « f/x^/ + --- 2 ^ xk “ x i

where x -4-

X

x

This interpolation results in large error when an extreme lies between x i and xk , but gives a good approximation if the function is monotonous and changing only slowly.

The standardizing procedure

To avoid the difficulties which have been mentioned above the following procedure is utilized.

Let f/х/ represent an input spectrum E.Y /Е/. If the input spectrum i s Y /Е/, then it is converted by the code to E . Y /Е/.

As a result the value of | max %/x/ - min f/x/j will be small, and x^ * log-j^E^ is used instead of E^ to decrease the length of the £x^ ; xn j interval.

The standardized output spectrum (e .Y / Е / ) is denoted by g/x/.

This is a combination of three different approximate functions:

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а/ g^/х/ computed by algorithm A using six base points.

These points are chosen on the basis of the conditions:

lxk+5 “ x ^- Iх “ xi' 1 » k,...,k+4 or (xk - x|>|x - x^\ i s k+l,...,k+5

* € [x k > Jk+5] ; V x k+5 €[xl ' xn]

b/ gg/х/ calculated also by algorithm A but for four base points, with

1хк+з “ х^- Iх - XJ i = k, k+1, k+2 or

|xk - x | > lx - x ± | i = k+1, k+2, k+3

x £ [xk ; хк+з] ; xk* x k+3 ^[Xl 5 xn]

с/ gj/х/ computed by linear interpolation.

Generally g^/х/ is the best approximation of f/х/. But at some points the Pg approximation may be deficient and the code

therefore replaces values of g^/х/ with values of g2/x/ or g-j/х/, such that at points where g-^/x/< 0, then g^/х/ = g2/x/, while points where g2/x/< 0, the value of g-j/х/ is used instead of g2/x/. Consequently g-^/х/ will be greater than 0 in the whole [X1 ’ xn] interval*

This optimalization is carried out with the expression

( c i = f ( * , ) - ( J , - * 4) ; C2 = f ( x k . , ) . ( S i t r xk) j 3 / which is put equal to D.^.

In the approximation the values of g-Д^ ^ /i increases from 1 until m/ are tested for each i.

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4

Fig. 1.

In Fig. 1 x k is the nearest to and if 0< i < 4

if 4 — i if i = m

then j = 4 then j = i+1 then $ = m

and

When g-^ ^ in 3/ is replacedby g2(fi) or ЬУ ±j » we Set the different values D^ and D^.

If is the smaller quantity among Dg and D^, then g-j^

will not be changed; if is minimum, then let g]|jfj^ = g2 ( ^ i) >

and if is minimum, then g^(^ will be equal to 6 3( ^3]* the next step /when tested/ the changed value of Si(^i+i) is taken. Finally let g/х/ be equal to g-^/x/. In this procedure the code uses uncorrected values for calculation of g(f1 'j and g ^ 2 j * Although this may result in an error, the error is not significant when f/х/ is a neutron spectrum /since the function in the low energy range is smooth/. The difference of the limits of summarizing also gives an error. The total error of inter­

polation is, in fact, less than the error which may derive from the measurement of calculation of "the input neutron spectrum.

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Further calculations

From the calculated E. T /Е/ spectrum the Y /Е/ spectrum can be recorded. Kerrna and rem-dose spectra are computed from this by applying conversion factors obtained by graphical interpolation from [2] and [з]* /see Appendix 8/. After this the Е.У /Е/

kerma and rem-dose spectra are normalized to unit area as follows.

If h/х/ denotes the spectra to be normalized and h /х/ denotes the normalized spectra then

_____ h±/x/

h./х/ = _________ 1=1... m 4/

1 ÍI1

h ./х/

i»l 1

The dose fractions are computed by the expression 5/ k+L

dosisi /E/.E^.lethi i=k

*

5/

m

dosis^ /E/.E^.leth^

i-1.

Where lethm equals the length of the lethargy interval. The boundaries of standard energy intervals, /Е/ the energy base

points / Ve ..E. / , the length of the lethargy intervals and the energy intervals in which the dose fractions are calculated are given in Appendix 2 and 3.

III. Users* manual Program name: DPSC

Program language: ICL-1900 FORTRAN

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Peripheriala: 1 tape reader - 6 -

1 line printer

3 magnetic tapes: DPSC- LIBRARY PLOTTER tape Scratch tape 1 off-line plotter

A core of 19.000 words is needed.

The running time for the preparation of a spectrum is about two minutes.

Input data

The input data must be given in records.

1./ The first record contains a variable ICARD /format 10А8/

defining the mode of operation. ICARD may contain the following characters, written into the first character positions of the record /the rest character positions are left blank/:

- RUN The input spectrum is standardized and the output is given on the line printer and on the plotter.

- ADD As in RUN mode but the input and output spectra are also written into the library.

- EDIT Prints the input and output spectra requested from the library.

- LIST Lists the contents of the library from a given identification number.

- DELETE Deletes the spectrum identified below.

- PLOT Output on the line printer as in EDIT mode and the output spectrum is also plotted. /Description of the plptter code is given in /4//.

- ENDEND - NEY/TAPE

Terminates the program.

Deletes the whole library tape.

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The mode of operation determines the content of the other records.

2. / In EDIT, LIST, PLOT and DELETE modes the second record contains the spectrum identification number in A8 format. No further record is needed in these cases.

3. / In RUN and ADD modes the second record is the same as 2.

Information about the spectrum may be placed in the next five records 3-7 /format 10А8/.

Record 8: N, Kl, KN /format 310/

N: Number of input points 6^ N — 200

Kl, KN: Serial numbers of the standardized energy points. The interpolation begins from K1 and is terminated by KN. An

arbitrary value may be given to K1 and KN in the input list, provided the condition 1— K l - K N 48 is fulfilled. If

ESTAND /K1/<EIN/1/, then the current value of K1 is increased by 1 until ESTAND/KV<EIN/1/. Similary, if ESTAND/Kll/> EIN/N/, then KN is decremented by 1 until ESTAND/KN/< EIN/N/.

If ESTAND/Kl/> EIN/l/ and ESTAND/KN/< EIN/N/, then the calculations described above are made in the energy interval ESTAND/K1/ Ar- ESTAND/KN/.

Record 9: ZZ /format Р0.0/. If ZZ>0, then both EIN/I/ and Р/1/ must be given in the input list. If ZZ-<0, then only

Е/I/ must be specified; in this case the previous set of EIN/I/

will be used in the calculations. Variable Е Ш /I/ gives the energy base points of the input spectrum /in eV/ in increasing order (6— Iá. N-í- 20o). Variable Е/I/ gives the input spectrum, which may be either Т /E/, E . T /Е/ or flux per GY length lethargy interval ( 6 — 1 — N — 20o). If ZZ is greater than 0, then

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Record IQ;

11:

Record N+9:

N+10:

N+ll:

Е Ш / 1 / /format FO.O/

EIN/2/ "

EIN/N/ "

F/l/ "

Р/2/ "

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Record 2N+9:

2N+10:

If Z > 0 , then Р/I/ is identical with E.T /Е/ ; if Z < 0 , then Р/1/ is identical with Y /Е/;

Record 2N+11: GY /format FO.O/

GY is the length of the lethargy interval in which the input spectrum is given. If the form of the input spectrum (p/I/) is

Y /Е/, then GY value is arbitrary, if^F/I/)is Е . Т / Е / , then G Y = 1 .0

Record 2N+12: KU,KUK /format 210/

KU respectively KUK may be equal to 1,2,3,4,5,6 or 7 correspond to this the first grades of linear E.T /Е/ and E.KER/E/ axises may be either 0.2, 0.1, 0.05, 0.04, 0.025, 0.02 or 0.01

If KU=0, then the code chooses the appropriate grade of axises If zz is less than 0, then

Record 1 0: Р/1/ /format Р0.0/

1 1: Р/2/ tl

Record Д+.9 8 F/N/ ft

N +10: Z If

N+ll: GY 1»

N+12: KU, KUK /format 210/

F/N/

Z

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In RUN and ADD modes no further record is needed. The modes mentioned under points 2 and 3 юау follow each other in any order.

4./ It should be noted that:

The input list should begin with NEWTAPE if it is necessary to delete the whole library or to begin a new library tape. In every case the input list must finish with ENDEND. A sample input list is given in Appendix 7.

When there is a mistake in the input list, then the code writes the following text: "Error in input date" and writes out the faulty data, too. The program is continued from the next operation defined by the variable ICARD.

Output data

We demonstrate a complete processing of a spectrum by DPSC code in Appendix 1-11. The presented sample spectrum is published in [ б ] .

In RUN mode the output data are printed on line printer /see Appendix 1, 2 and 3/.

In ADD mode the output data are printed on line printer,

as in RUN mode, and the following data are written on the library tape: identification number and comments about the input spectrum, the input spectrum in its native form and the standardized

spectrum obtained from it. /see Appendix 5 and 6/. Beside these data E . Y /Е/, kerma and rem-dose spectra are drawn on an off-line operated plotter, /see Appendix 9, 10 and 11./

In EDIT and PLOT modes the datß are read from the library tape and written by line printer, /see Appendix 5 and 6/.

In PLOT mode the E.Y /Е/ spectrum is drawn, /see Appendix 9/.

In LIST mode the content of the library is printed /see Appendix 4 / .

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- 10

Motes

The identification number of the DPSC-library is ‘1677. The tape was opened on 15th Jan, 1972.

Time of the preservation is 3 years.

The program language is ICL-1900 FORTRAH, this differs from AN SI-FORTRAN.

The DPSC code used the following differences: /see [ 5 J/

- Names with up to 32 characters.

- Subscripts formed from any INTEGER expression.

- Named common blocks differing in size in different segments.

- Text constans in DATA statements initializing several array elements.

- Operators and / combining elements of type:

INTEGER and REAL

- Zero statement labels in computed GO TO and arithmetic IF.

- INTEGER expressions as the parameters of a DO statement.

- TEXT constans as actual arguments replacing dummy arrays.

- TEXT constans as actual arguments of external function references.

- A MASTER statement is required.

- FORMAT of READ and WRITE may be 10 and FO.O .

- Four spetial segments for handling of characters and data C0MP8 compare two strings of eight characters for equality.

G0PY8 copy eight characters.

DATA writing of data.

TIME writing of time.

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References

[*lj I.N. Bronstein, K.A. Semendiaev: Mathematical Handbook Ж . Budapest, 1963. pp. 723-724. /in Hungarian/

[2] J.A. Dennis, H.J. Delafield, P.D. Holt, S.J. Boot: AERE-R 6498, June, 1970.

[ 3] D. Nachtigall, P. Rohloff: JÜ1-213-ST /1964/.

[4] ICT 19OO Series, Graph Plotter, Technical Publication 4087, ICT, Letöhworth, Hertfordshire, Great Britain, 1968.

£5] Technical Publication 4261, ICL Printing Service, at Letchworth, Hertfordshire.

[б] ORNL-RSIC-29. PP* 42-57.

1

*

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Appendix 1

NFUTRON SPFCTRUM TRANSFORMATION

0 0 0 0 0 0 1 2

ORNL-RSIC-29 . P . 51 .

RFACTOP SPECTRUM . FF , Db90C.M POKER CODE (A.W.R.F.HPIMK) INPUT SPECTRUM!E*PHI (F)

* *

MUMBER of thf INPUT

ENFRGY FV

1 0.17320F 00 2 0 .547/00 00 3 0.22360F 01 4 0.7 41 6 0 F 01 5 0.18170F 02 6 0.42430c 02 7 0,0 4870 F 02 8 0.74490F 03 9 0.63250c 03 1 0 0.12250F 04 11 0.1 7 3 2 0 F 04 1 2 0.28280F 04 13 0.4M990F 04 1 4 0.7 7 4 6 0 F 04 1 5 0.1 1 4 0 0 F 05 1 6 0 . 1 M 2 0 F 05 17 0.22360F 05

1 8 0.P7390F 0 5 19 0.4 2 4 3 0 F 05 20 0 ,69?80F 05

?1 0.89 44 Or- 05 22 О. 1 1 400F 06 2 3 0.1 39 6 0 F 06 74 0.1 A 4 3 0 F n6 25 0.2 7 4 5 0 F 0 6 26 0.3 7 4 2 o 0 6

?7 0.7071 OF 0 6 28 0.1 2 6 5 0 F 07 29 0 . ? 1 9 1 о 07 50 0,42430c 07 11 0.67050c 0 7 12 0.79370c 07 1 3 0.11220' 0 8

F N E R G Y G R O U P S !

INPUT DATA

77

f n f pGY*FLUX

0.18000000F 07 0.1AOOOOOOF 0«

O.SOOO0000F 0«

0.O00O0000F 08 0.120000 OOF 0<?

0.16000000F 09 0.1 7000000F 09 O.lfiOOOO'OOF 09 0.21OOOOOOF 09 0.280000OOF 09 0.-S2000000F 09 0.400000OOF 09 O.AAOOOOOOF 09 0.1 80 0 00O0F 09 O.AOOOOOOOF 09 0.60000060F 09 0.10000000F 10 O.^OOOOOOOF 0«

O.lflOOQOOOP 09 0.20000000F 09 0.1400000OF 09 O.2AOC00O0F 09 0.18001)0 OOF 09 О.4/OOOOOOF 09 O.^SOFiOOOOF 0 8

0.160000 OOF OH 0.8 О О 0 о О О 0 F 0 7 0.1 2 О О О О О 0 F 00 (). 1 О О о о 0 о 0 F 0 5 О . ?. О О О О О О О F О А 0.00000000F 00 О . о 00''000 О F 0 0 (1 . О о О л О ООО F 0 0

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dumber of тир

standard energy

E V

1 0 . 2 1 7 0 1 t 0 0

г 0 . 3 5 3 5 6 E 0 0

3 0 . 2 0 7 1 5 E 6 0

4 0 , 1 4 6 6 3 E y i

5 0 * 3 1 6 1 9 6 01

4 0 . 6 8 1 9 1 6 11

7 0 . 1 4 6 6 3 E 0 2

8 0 3 1 4 l 9 t o 2

9 0 . 6 8 1 9 1 E •'2

1 0 0 . 1 4 6 6 3 E 0 3

11 0 . 3 1 6 1 9 E 0 3

1 2 0 . 6 8 1 9 1 6 0 3 1 3 0 . 1 4 6 6 3 E 0 4 1 4 0 ] 3 1 6 1 9 E 0 4 1 3 0 . 6 8 1 9 1 6 u 4

1 6 0 1 1 2 2 0 E 0 5

1 7 0 . 1 4 1 2 5 6 0 5 1 8 0 . 1 7 8 1 6 E 0 5

1 9 0 . 2 2 3 8 5 E 0 5

2 0 0 . 2 8 1 8 2 E 0 5

21 0 . 3 5 4 7 8 E 0 5

2 2 0 4 4 6 6 3 E 0 5

2 3 0 . 5 6 2 2 6 E 0 5 2 4 0 . 7 0 7 6 2 E 0 5 2 S 0 . 8 9 1 1 7 6 0 5

2 4 0 1 1 2 2 0 E и 6

2 7 0 1 4 1 2 5 6 0 6

2 8 0 . 1 7 8 1 6 6 0 6 2 9 0 . 2 2 3 8 5 6 0 6 3 0 0 2 8 1 8 2 E 0 6

31 0 * 3 5 4 7 8 6 Л 6

3 2 0 4 4 6 6 3 6 о б 3 3 0 j 5 6 2 2 6 E о б 3 4 0 . 7 0 7 8 2 6 0 6

3 5 0 , 8 9 1 1 7 6 1)6

3 6 0 . 1 1 2 2 0 6 0 7

3 7 0 . 1 4 1 2 5 E 07

3 8 0 . 1 7 8 1 6 6 0 7

3 9 0 . 2 2 3 8 5 6 07

4 0 0 2 8 1 8 2 6 0 7

41 0 3 5 4 7 8 E 0 7

4 2 0 . 4 4 6 6 3 6 0 7

4 3 0 . 5 6 2 2 6 6 07

4 4 0 . 7 0 7 8 2 6 97

4 5 0 . 8 9 11 7 E 07 4 6 0 . 1 1 2 2 0 6 0 8 4 7 0 . 1 4 1 2 5 6 0 8 4 8 0 . 1 7 8 1 6 6 0 8

S T A N D A R D E N E R G Y G R O U P S ; и Я

L I M I T S O P T И F 6 N F R G Y G R O U P S L E T H A R G Y i nT F P V A L S P l U X O U T E * p w I ( F )

6 6V

0 . 1 8 8 4 5 6 n o

6 6V

0 . 2 5 0 0 0 6 O u л . 2 7 1 л 0 . 1 1 9 4 7 t •j M 0 . 2 5 9 < * ( 0 7

0 . 2 5 0 0 0 6 o o 0 . 5 0 ( 1 0 0 6 0 0 0,* 0 3 0 0 . 2 0 0 S 2 E 9 * 0 . 7 0 * 9 / 1 0 7

0 . 5 0 0 0 0 6 O n 0 , 1 0 0 0 0 6 0 1 0 . 6 9 3 0 •Ci

4\J

О

0 4 0 . 1 7 4 0 0 5 0 8

0 . 1 0 0 0 0 6 0 1 0 . 2 1 5 0 0 ' 0 1 л .7 * 6 0 0 , 2 2 9 0 4 6 O b 0 . 3 3 5 * 8 6 0 8

O . 2 1 5 0 0 6 0 1 0 . 4 * 5 0 0 6 0 1 0. 7 * 6г 0 [ 1 8 0 7 5 6 9 * 0 . 5 7 1 8 0 ' ( »8

0 . 4 6 5 0 0 6 л л 0.1 0 0 0 0' 0 2 0. 7 и А11 0 . 1 * 5 2 7 6 0* C . 8 5 3 9 1 6 0 8

0 , 1 0 0 0 0 6 0 2 0 . 2 1 5 0 0 ' 0 2 0, 7 * * п 0, 7 5 1 6 7 6 0 7 0.1 1 0*2' 9 9

0.2 15 0 0 6 о г 0 . 4 4 5 0 0 ' 0 2 0 . 7 4 6 0 0 * 6 4 9 * 4 6 0 7 0 , 1 4 * 1 7 ' 0 9

0 . 4 6 5 0 0 6 0 . 1 0 0 0 0 6 0? Г . 7 * 60 0. С 4 1 8 4 6 0 7 0 . 1 * 4 9 1 6 0<3

o ! 1 0 0 0 0 6 0* 0.2 1 5 0 0c 0 3 0 !7* 60 0 . 1 1 8 2 9 6 ,7 0 . 1 7 5 4 5 ' ;. V

0 . 2 1 5 0 0 6 л * 0 . 4 6 5 0 0 6 0 3 Л ^ 7 <ч А) Г) 0 . 5 8 6 7 4 6 Oft 0 . 1 » 5 5 2 6 l-v

0 . 4 6 5 0 0 6 0 * 0.1 0 0 0 0' 0 4 о , 7 47)0 0 . 3 1 6 5 7 6 0 6 0 . 2 1 5 * 4 ' 0 9

0 . 1 0 0 0 0 6 п и 0 . 2 1 5 0 0 ' l ) L 0. 7*4Г» 0. *039<.fc " 6 0 . 2 9 9 0 4 ' 0 9

0 . 2 1 5 0 0 6 0 4 0 . 4 6 5 0 0 ' 0 4 0. 7 4 6 0 0 . 1 2 * 5 4 6 O Ó (1. 4 0 6 4 5 ' 0 9

0 . 4 6 5 0 0 6 0 4 0 . 1 0 0 0 0 6 0 5 0 . 7 * 6 0 0. 3 8 8 1 Л6 O S 0 . 2 6 4 * 5 ' 0 9

0 . 1 0 0 0 0 6 ö S 0 . 1 7 5 * 9 6 0 5 0.2 * 0 0 0 . 3 4 6 * 5 * } 0 . 3 8 9 1 6 ' i*9

0 . 1 2 5 8 9 6 O S 0 . 1 5 8 4 8 6 0 5 0, < í*OP 0 \ .4 8 4 9 > 6 c 5 0 . 5 1 5 * 7 ' «.’9

0 . 1 5 8 1 . 8 6 O S 0 . 1 9 9 4 1 6 0 5 0 . 2 3 0 0 0 . 4 8 9 4 ' 6 Ö P 0 . 6 7 1 7 9 6 и 9

0 * 1 9 9 5 1 6 O S 0 . 2 5 1 1 7 6 0 5 0 . 2 * 0 0 0 . 7 1 1 3 5 6 o s 0 \ 1 5 9 2 3 ' 1 fi

0 ! 2 5 1 1 7 6 o s 0 . 3 1 6 2 0 6 0 5 0.с 3 0 0 0 . 6 3 5 3 2 6 0 4 0 . 6 6 3 1 9 - O ö

0 . 3 1 6 2 0 6 0 5 0 . 5 0 * 0 5 6 0 5 С . 2 3 0 0 0 . 3 5 10 16 0 4 0 . 1 2 4 5 3 6 0 9

0 3 9 3 0 5 6 O S 0 . 5 0 1 1 2 ' 0 5 0 . 2 1 0 0 0 . 4 0 6 7 4 6 0 4 0 . 1 8 1 6 6 6 0 9

0 . 5 0 1 1 2 6 0 5 0 . 4 7 0 3 6 6 0 5 0 . 2 3 0 0 0 . 3 3 * 4 ‘ 6 0 4 0. 1 9(5 2 8 t 0 9

0 . 6 3 0 8 6 6 O S 0 . 7 9 4 1 8 6 0 5 0 . 2 3 0 0 0 . 2 7 6 2 4 6 0 4 0 . 1 9 5 8 3 ' O V

0 . 7 9 41 8 6 O S 0 . 1 0 0 0 0 ' 0 6 о . 2 3 0 0 0 . 1 5 8 1 8 6 0 4 0 . 1 4 0 9 6 ' 0 9

0 . 1 0 0 0 0 6 0 * 0 . 1 2 5 8 9 6 0 4 0 . 2 3 0 0 0 . 2 * 3 ® 9 6 0 4 0 . 2 5 1 2 1 ' u 9

0 . 1 2 5 8 9 6 0 * 0 . 1 5 8 4 8 6 0 6 0 . 7 * 0 П 0 , 1 2 6 9 * 6 0 и 0 . 1 7 9 3 3 ' ü 9

0 ! 1 5 8 4 8 6 0* 0 . 1 9 9 5 1 6 0 6 0 . 2 3 0 0 0 * 8 1 8 5 1 E Q A 0 . 1 4 5 8 3 ' 0 9

0 ] 1 9 9 5 1 6 0 * 0 . 2 5 1 1 7 6 0 6 0 . 2 3 0 0 0 . 2 9 5 4 4 6 0 3 О .6 6 4 4 4' 0 8

n 2 5 117 6 o<s 0 . 3 1 6 2 0 6 0 6 0 . 2 3 П 0 0 . 1 6 4 0 7 6 0 3 0 . 4 6 2 > 8 6 0 8

0 . 3 1 6 2 0 6 0 * 0 . 3 9 8 0 6 6 0 6 0 . 2 3 0 0 0 .*6301 5 6 0 2 П * 4 2 3 5 7 6 o b

0 . 3 9 8 0 6 E 0 * 0 . 5 0 1 1 7 * 0 6 0 . 2 3 0 0 0 * 2 9 4 9 1 6 0 2 0 . 1 - И 7 2 ' O b

0 ! 5 0 1 1 2 € 0 * 0 , 6 3 0 * 6 6 0 6 0 . 2 * 0 0 0 [ 1 5 3 9 5 6 0 2 0 . 8 6 5 * 1 6 Ü 7

0 . 6 3 0 8 6 6 Ofc 0 . 7 9 4 1 8 6 0 6 0 . 2 3 0 0 0 ! 4 * 3 3 1 6 0 1 0 . 2 9 9 * 3 6 0 7

0 . 7 9 4 1 8 6 0 6 0 . 1 0 0 0 0 ' 0 7 0 . 2 * 0 " 0 . 2 3 0 0 1 6 0 1 C . 2 0 4 9 8 ' 0 7

0 . 1 0 0 0 0 6 0 7 0 . 1 2 5 8 9 6 0 7 0 . 2 * 0 0 0 7 6 4 6 * 6 00 0 . 8 5 8 2 0 ' v/6

0 1 2 5 3 9 6 -fi7 0 . 1 5 8 4 8 ' 0 7 0 . 2 3 0 0 O ! 7 5 2 2 * 6 .- 0 1 0 . 1 0 3 4 3 ' 0 8

0 . 1 5 8 4 8 6 0 7 0 . 1 9 9 5 1 6 0 7 0 . 2 3 0 0 0 . 3 4 7 Я ? Е - и 1 0 . 6 1 9 8 0 6 O S

0 . 1 9 9 5 1 6 0 7 0 . 2 5 1 1 7 6 0 7 0 . 2 3 0 0 0 . 7 0 0 2 9 f.• 0 2 0 . 1 5 6 7 6 6 O S

0 . 2 5 1 1 7 6 0 7 0 . 3 1 6 2 0 6 0 7 0 . 2 * 0 0 0. 4 15 9 л 6 - 0 2 0 . 1 1 7 2 1 6 0 5

0 . 3 1 6 2 0 6 0 7 0 . 3 9 8 0 6 ' 0 7 0 . 2 3 0 о 0 . 1 9 0 0 * 6 ..0 7 0 . 6 7 4 5 1 ? (1 4

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0 . 4 3 0 3 6 6 0 7 0 . 7 9 4 1 8 6 0 7 0 . 2 3 0 0 0 . 0 0 0 0 0 6 00 0 . 0 0 0 0 0 ' 00

0 . 7 9 4 1 * 6 0 7 0 . 1 0 0 0 0 6 0 8 0 . 2 3 0 0 0 . O O O O O E ü u 0 . 0 0 0 0 0 ' 00

0 . 1 0 0 0 0 6 O Ä 0 . 1 2 5 8 9 6 0 8 0 . 2 3 0 0 O . ü O O O O E 0 9 0 . 0 0 0 0 0 ' 00

0 . 1 2 5 8 9 6 0 A 0 . 1 5 8 4 8 6 0 8 0 . 2 3 0 0 0 . 0 0 0 0 0 6 00 0 . 0 0 0 0 0 6 0 0

0 . 1 5 8 4 8 6 0 A 0 . Ю 9 . 5 1 6 0 8 0 . 2 3 0 0 0 . 0 0 0 0 0 6 0 0 0 . 0 0 0 0 0 6 0 0

(18)

D U 3 i S /2 l */ w и ffi jэ o S (s )

8 0 = 8 / 9 9 4 * 2 < 8 ) M 3 b • 3 D i b 0 i 0 4 3 0 0 3 8 v 0 0 i * i t 3 > e 3 >« 3 D i b O i J f J

H»j jO »3fl ilNfi ül «Oi0«i ONl/CiVWaO*

un3

к u ü о 0*0 Л3и8■8 .-Лзw ‘ 8

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SNOliOtöi 3S0«

Оч/ a l ' D Ú Ú U ’ Ö Ü 1‘ a U O O U v * Ü

0 0 3 0 0 0 0 0 * 0 0 З О О о О С

' (>

0

о о з о о о о о ' о 0 0 3 0 0 0 0 0 0

» 7

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U V а о о о 00 * Ü o ü 3 0 о о 0 0 ' ’ 0 0 0 3 0 0 0 0 0 " 0 У 7 и 0 a t* и 0 ü 6 V 01» 3 0 0 0 0 9 * 0 Z 7

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u u * z О к z к * ö O l ä к 9 9 6 1 ■ Ü 0 о Э 1 0 2 2 2 ' 0 6 t b V - a 7 u £ £ Z ' V 9 0 - 3 ‘ £ 8 8 4 *0 0 2 k u - a Z O O O k ' O 1 0 • d Z 9 . Z V 0 0 3 8 8 ‘ 2 ‘ * 0 В i k O - d V i t f t f к ■ 0 9 ’ - 3 8 8 0 4 1 *0 6 к k O - d k í 2 C>£ *0 lU bavutv ' и К - 3 / 9 9 W * 0 Z t

£ Ü - d O V Ü i t ' 0 5 о - 3 / 9 ‘ £ 8 ' и Ь к к v - з k 7 J k Z * U U ^ d t Z y b c * 0 ‘ '’- 3 / 4 2 4 8 * 0 9 i

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8 ' ' » - 3 2 4 8 8 8 * 0 V к

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£ 0 - d 6 k t f k * * Ü 7 0 « * d k 0 O 6 t 4 0 2 0 - 3 6 8 2 9 2 * 0 к k O - d f t O & z Z ' V 9 0 - 3 6 0 8 2 9 0 7

k O - d k i ó 2 k 4 и 7 0 - 3 7 S 0 i Z 4 0 80-3 8 4 SB 6 * 0 г w u - d « k k W c'и 4 0 - 3 8 9 6 8 6 и £

k U . a 6 7 z t t'W 7 C « ^ V b y 9 ^•и £ 0 - 3 2 4 ‘v i * 0 t k v - d O V e Z Z V 8 0 - 3 6 8 0‘ ‘ 0 г

I d > d S Ü O * d ö * a ( 3 ) íWÍ 3 3-3 83) lwá*»:

k U “ d $ 7 k k к' и 9 1 - 3 0 1 8 8 8 * 0 к

» э Ö V 1 1 N n ui из;n i «W309 C 6 1 D3 Í1 I d ) d b OUr* a Ö l a ) V r » d d ^

Z xxpnsddy

(19)

• I D E N T I F I C A T I O N NU MP к R NUMBER’ Of I N PU Г P OI N T S NUMBER OP OUTPUT POI NT S

Л () 0 0 0 0 0 U

w UM 00000004

51 * 0 5 - 7 ?

MELEKFs,7969,PROB.JA$CS.6,P.lS4

REACTOR SPECTRUM P 0 L V T H F N D s í í С M

I NPUT PTA A R f REAP FROM' THf c rURVfc I N R Fl aTtVf U N I T , P h ! f t )

I 0 F M T I F I CaT I ON NUMBER 0 0 0 0 0 0 0 5

NUMBER OF I NPUT POI NT S ? 5

NUMBER OF OUTPUT POI NT S 4ft

0 0 0 0 0 0 0 5 1 ? - 0 a ■ 7 ? ,

F I S S I 0 ,f N F. U T R 0 R S P F C T R U Mf F F , D * 5 0 C M Г A I Г. и I A 7 E 0 BY V E R T E S , 1 9 6 8 . I X . THERMAI. NEUTRON f LUXUS I 1 . 5 9 / E - O A

i n p u t f*p h i<l> i n ^.7 7 l f t h a r g v i n t e r v a l

I D E N T I F I C A T I O N Ni.iMP.ER 0 0 0 0 0 0 0 5

NUMBER of I N P U T POI NT S 25

NUMBER OF OUTPUT POI NT S Aft

О О О 0 0 0 0 5 1 P - 0 6 - 7 2 .

f i s s i o n n e u t r q n s p e c t r u m,f e,d«5о cm OALCUt ATf cO BY V E R T E S , 1 9 6 8 . I X . Th e r m a l n e u t r o n ft их u s . i . 5 9 7 E - 0 6

1 Mp и T Е * P 8 I f t ) IЫ ),77 L FT M A R G Y I N T E RV AL

I D E N T I F I C A T I O N NUMBER 0(100 001 ?

NUMBER of I N P U T POI NT S 35

NUMBER OF OUTPUT POI NT S 48

o o o o o n 1 2

o r n l” R s 1 c - 2 9 . p . ь 1 .

REACTOR S P E C T R U M , F f , 0 = 9 0 Cm P о V t R COLE ( A . i J . i í . F , ) ( P I N К ) i n p u t s p e c t r u m• F > P H I (f) E и I) I N D

(20)

Appendix 5

IDFNTIFiс ЦТ I ON NUMBER 00000012

n u m b e r OF INPUT POINTS 33

NUm bFR OF OUTPUT POINTS 48 o o o o o m 2

ORNl-RS I 0 2 0 . P .51

REACTOR SPECTRUM, FF,0*90CM POKER C 0 í)F (A. W. R .c .1(PINK)

i n p u t Sp e c t r u m ! E * P Ч I (F)

**

e n e r g y FV

1 1 . 7 3 2 0 0 E-01 1 . 8 0 0 0 0 E 06

? 5.47 70ЛЕ -01 1 . 40000F 07

? 2 . 7 3 6 0 0 F on 5.OOOOOF 07

4 7. /,1 60')F 0 0 9.OOOOOF 0 7

s 1 . f t 1 7 0 0 F 01 1.2ЛО00Е 0Я

6 4 . 2 4 3 0 0 F. 01 1.6OOO0F 0Я

7 0.4 Я 7 0 о E 01 1.70000F 0Я

Я 2 . 4 4 0 0 0 E '0 2 1.80000F OR

О 6. 1?50OF 02 2.1OrtOOE 0Я

1 о 1.22500F 03 2.flOOOOF 0Я

11 1.732OOF 03 3.2O0O0F 0Я

1? 2. H?ftO )F 03 4. 0 0 0 0 0 F OR

15 4 . «OO0OF 03 4. 40000«= 08

1 4 7 . / 4 6 0 0 F 03 1. ЯПОООЕ 08

1 5 1 . 1 4 0 0 0 E 04 4. OOOOOF 08

16 1.o120op 04 6 .OOOOOF OR

17 2.2 3 6 0 0 F 04 1.6OOO0F 09

1ft 2. 7 3 9 0 0 F 04 6. OOOOOF 07

10 4 . ? 4 3 0 о E 04 1.ЯООООЕ OR

20 6 .O7Ö00E 04 2.OOOOOF On

21 8.0 4 4 0 0 F 04 1. 40000E 08

2? 1. 14000E 05 7 .60000F OR

2? 1. 30600E 05 1 . ftOOOOF OR

24 1 . 6 4 3 0 0 F 05 1.7OOOOE C 8

2 5 2. 2 4 5 00 F 05 6. 5 0 0 0 0 R 07

26 3.7 4 2 0 0 F 05 1 . 60000F 07

27 7. 071 ONE 05 3 .OOOOOF 04

2ft 1 . 7 6 5 0 o F 06 1.20O00F OR 20 2 Л 010 о E 06 1 . 6 0 0 0 0 F 0 4 50 4 . 2 43 09 E 06 2.0 0 0 0 0 F 03 31 6.2 0 5 0 0 E 06 0.OOOOOF-■0 1 37 7 .V 3 7 0 0 F 06 0.0O000F-•01 3 3 1 . 1 2 2 0 " F 0 7 0 OOOOOF-.01

1 К1 p и т SPFCTRItM

(21)

F N F R G Y f V

1 2.1701 OF-01 3.61 465F-04

2 3.5356OE-01 9.88448F-04

1 7.071 5 0 F- 01 2.42592F-OT

A 1.46630F 00 4.68280F-O3

S 3.1619 OF 0 0 7.96787F-03

6 6.81910F 00 1 .19052F-02

7 1 . <+66 3 0 F 01 1 .53665F-0?

Я 3.1 61 9 0 E 01 1 .98721F-02

9 6.8191 OF 01 ? . 29922F-0?

1 (1 1 .466 3 OF 02 2.41825 F-O?

1 1 3.1 619 оE 02 2. 5 6 650F-0?

1 ? 6.81910 F 02 3.00922E-0?

1 3 1 4 6 6 3 0 F 05 4.1A9 20F-0?

1 4 3.1619 о F 03 5 .66675F-0?

TS 6.819 1 OF 0 3 3.66975F-6?

16 1 . 1 ? 2 0 0 E 0 4 5.42574F-0?

1 7 1 . 4125OF 0 4 7.18667F-02

1 Я 1.7Я160Е 04 1 . 2 1 5 4 6 F - 01

19 2.,'385 OF 04 2. 22006F-O1

20 2.81«20F 04 9.?46?7F~03

21 3.5 4 7 8 0 F 04 1 . 73623F-0?

22 4,.466 3 OF 0 4 2.5 T276F-02

23 5 ! 6 7 2 6 0 F 0 4 2.66?8SF-0?

24 7.0782OF 0 4 2.72609F-02

2 s 8.9117 0 E 0 4 1 .96 5 29 F-02

26 1 . 1 220OF 05 3.5n?3?F-0?

27 1 . 412 5 o f 0 5 2.5OC26F-02

28 1 .7816 о F 05 2.03311F-0?

29 2.2 3 8 5 0 F OS 9.2 2 042 F-03

30 2.81 8 2 0 F 08 6.446S3F-03

31 3.5 4 7 8 о F 05 3.1 1 69 7F-03

3? 4.4 6 6 3 0 F 0 5 1 .83639F-03

33 5.6226 OF 0 8 1.20684F-05

34 7.0782оE ()8 4.17744 F-04

35 8 . <> 11 7 0 F 0 5 2.8‘■784 P- 04 36 1 .1? 2 0 л F 06 1 .1 9 6 5 0 P - 0 4

37 1.4125 >F 06 1 . 44209F-OS

38 1 .7816о F 06 8.6 4 1 3 2 F - 0 6

39 2.2 3 8 5 0 F 06 ?. 18565F-0A

40 2.8182op 06 1 . 6 3 4 1 3 P - 0 6

41 3.5478oF 06 9.40126F-07

4? 4.46 6 3 0 F 06 2.471 06F-0 7

43 5.6 ? 26 0 F 06 8.2771 3 F-0 8

44 7.0782 OF 06 O.OOOOOF-01

45 8.9117 0 F 06 0.0O000F-01

46 1 .1? 2 0 о F 07 O.OOopOF- 0 1

47 1 .412 5 о F 0 7 0.0O000F-01

48 1.7 816 0 F 0 7 O.OOOOOF-01

N OR MA L I Z I N G f a c t o» TO U N I T aBfA o f F + p h i(f) SPFCTRUM 7 . 1 / 2 5‘ 3 r MO 22 / 0 1 /зб

if * * * a x f л м US PM On 1 9 / 0 0 / 7 7 AT 7 2 / 0 2 / 6 4

(22)

Appendix 7

ADD

00000012

ORNL-RSIC-29.P.51.

REACTOR SPECTRUM,FE,D=90CM POKER CODE (A.W.R.E.)(PINK) INPUT SPECTRUM:E*PHI(E)

**

33 1 48 О.13

О .17З2 0.5477 2.236 7 . 4i6

18.17 42.43 94.87 244.9 632.5

1225.0 1732.0 2828.0 4899.0 7746.0

1.14e 04 1.612E 04 2.236E 04 2.739E 04 4.243E 04 6.928E 04 8.944E 04 1.14E 05 1 .396E 05 1.643E 05 2.245E 05 3.742E 05 7.071E 05 1.2б5Е Об 2.191E Об 4.243E Об 6.205E Об 7.937E 06 1.122E 07

Continuing in the secund column.

1 .8e Об 1 .4E 07 5.0E 07 9.0E 07 1 .2E 08 1 .6E 08 1 .7E 08 1 .8e 08 2 • 1 E 08 2.8E 08 3.2E 08 4.0E 08 4.4E 08 1 .8e 08 4.0E 08 6.0E 08 1 .6e 09 6.0E 07 1 .8e 08 2.0E 08 1 .4E 08 2.6E 08 1 .8e 08 1 .7E 08 6.5E 07 1 .6e 07 3.0E Об 1 .2E 05 1 .6e 04 2.0E 03 0.0 0.0 0.0 0.15

1.0 0 0 EDIT 00000012 DELETE 00000012 ENDEND

****

(23)

Conversion factors

Но. Kerma rem-dose

— 1 2

/rad.n .cm / /rem.n .cm'

1 6.99E-12 1 .12E-09

2 5.53E-12 1.15E-09

3 3.90E-12 1.16E - O9

4 2.72E-12 1.21E-09

5 1 .88E-12 1 .24E-09

6 1 .29E-12 1 .27E-09

7 9.90E-13 1.32E-09

8 9.00E-13 1.34E-09

9 1.09E-12 1.38E-09

10 1.75E-12 1.35E-09

11 З.ЗОЕ-12 1.31E-09

12 6.70E-12 1.ЗОЕ-09

13 1 .47E-11 1.24E-09

14 3.16E-11 1.21E-09

15 6.70E-11 1.21E-09

16 1.12E-10 1.59E-09

17 1.40E-10 1.88E-09

l8 1 .7О Е - Ю 2.2ŐE-09 19 2.10E-10 2.65E-09 20 2.5О Е - Ю 3.20E-09 21 3.05Е -10 3.75E-09 22 3.65E-10 4.50E-09 23 4.3О Е - Ю 5.38Е-09

24 5.20E-10 6.37E-09

25 6.10E-10 7.67E-09

26 7. Ю Е -1О 9. Ю Е-09 27 8.20E-10 1.1O E-08

28 9.50E-10 1.29E-08

29 1 .09E-09 1.52E-0Ö

30 1 .23E-09 1.85E-O8

31 1.40E-09 2.14E-08

32 1.59E-09 2.54E-08

33 1 .79E-09 2.92E-08

34 2.00E-09 3.09E-08

35 2.20E-09 3.64E-08

36 2.38E-09 3.86E-08

37 2.50E-O9 4.00E-08

38 2.90E-09 4.08e-08

39 З Л О Е - 0 9 4.14E-08

40 3.40E-09 4.17E-08

41 4.20E-09 4.17E-08

42 4.20E-09 4.19E-08

43 4.50E-09 4.21E-08 44* 5. Ю Е - О9 4.22E-08

45 4.90E-09 4.22E-08

46 5.45E-09 4.25E-08

47 6.80E-09 4.25E-08

48 7.30E-09 4.25E-08

(24)

E*PHI(E)

Appendix 9

10

-1 10

-2 10

-3 10

-4 10

10

-6

10

~1 1 I I I I Г

NORMALIZING FACTOR 0. 717E 10

ч---1— I I---г Г ' ' 1 Г 1 1 1

*«* X х х

_L__ L I I i l l __I__ 1__1___1__ 1...1.___1__ L__ 1___ L

10U 101 102 103 104 105 10b i

ООП! 10017

ENERGY(FV)

(25)

E*PHI(E)

C. 250

0.225

0.200

0. 175

0. 150

0. 125

0. 100

0.075

0.050

0.025

0.000

Appendix 10

ENERGY(EV) 00000012

(26)

ЕжКЕН(Е),E*DO(Е)

A ouendix 11

0 . 2 5 0

0 . 2 2 5

0.200

0 . 1 7 5

0. 150

0 . 1 2 5

0. 100

0 . 0 7 5

0 . 0 5 0

0 . 0 2 5

0.000

1 I I I I I I I I i I I I I— I---1— I— I---1— I— г

_ KERMR=+

_ D0SIS=0

+

0 +

Q +

+ .0 + +0

a 0 0 0 + + *

9 1 7 '° 1 ? I I I I 1 I I I I 4 I t l--- 1-- 1-- 1--- 1-- 1-- 1--- 1

10 10 1 0' 10 10 10'

ENERGY(EV)

10 10 10

0 0 0 0 0 0 1 2

(27)
(28)

3 S 7

Kiadja a Központi Fizikai Kutató Intézet Felelős kiadó: Szabó Ferenc, a KFKI

Reaktor Kutatási Tanácsának elnöke Szakmai lektor: Kulcsár Katalin

Koblinger László Nyelvi lektor: T. Wilkinson

Példányszám: 205 Törzsszám: 72-7457 Készült a KFKI sokszorosító üzemében, Budapest, 1972. október hó

Figure

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References

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