0 R N L -3759 UC-34 - Physics

TID-4500 (37th ed.)

%4 b2gj

DETERMI NATION OF THERMAL-NEUTRO N

FLUX DISTRIBUTIONS IN THE BULK

SHIELDING REACTOR II BY COPPER

W I RE AC TlVAT IO N TECH N I Q UES

G. T. Chapman

UNION CARBIDE CORPORATION f o r the

U.S. ATOMIC ENERGY COMMISSION

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

L

C o n t r a c t No. W-7405-eng-26

N e u t r o n Physics D i v i s i o n

DETEXMINATION O F THERMAL-NEUTRON FLUX DISTRIBUTIONS I N T€E BULK SHIELDING FCEACTOR I1 BY COPPER

WIRE ACTIVATION TECHNIQUES

G. T. C h a p m a n

MARCH 1965

OAK RIDGE NATIONAL LABOFUlTORY O a k R i d g e , Tennessee

operated by UNION CARBIDE COKPORATION

f o r the U.S. ATOMIC ENERGY COMMISSION

I

Y P

5

> 3 t

A

TABLE OF C 0 " T S

c

-I-

DETERMINATION O F THERMAL-mmON FLUX DISTRIBUTIONS I N THE BULK SHIELDING REACTOR I1 BY COPPER

WIFE ACTIVATION TECHNIQUES

G. T. Chapman

ABSTRACT

The thermal-neutron f lux d is t r ibu t ion within the OWL s t a in l e s s s t e e l Bulk Shielding Reactor I1 has been determined by exposing copper wires a t selected locations i n the core during reactor operation. The gamma-ray a c t i v i t y resu l t ing from thermal-neutron ac t iva t ion of the copper was counted a s a function of posi t ion along the wire, and the r e su l t s were converted t o estimates of thermal-neutron f lux by the methods described i n t h i s report .

The method of analysis w a s checked by independently ex- posing gold and copper wires a t a common locat ion i n the reactor . The thermal-neutron fluxes obtained from analysis of both s e t s of data were i n agreement within - 3%. The method was fur ther checked by comparing the r e su l t s of a wire exposure with calculat ions of the d i s t r ibu t ion made by the PDQ reactor code. Agreement w a s good i n s t a t i s t i c a l l y important regions.

Several CE-1604A programs were wri t ten t o f a c i l i t a t e processing of the wire data, and are included a s an appendix.

I. INTRODUCTION 1

In measuring the gamma-ray spectrum of the Bulk Shielding Reactor I1 (BSR 11), a core composed of s t a in l e s s s t e e l f u e l e l emen t s , , i t w a s found

t h a t most of the higher-energy gamma rays had resul ted from thermal-neutron

captures i n the nuclides comprising the s t a in l e s s s t e e l f u e l cladding and

other portions of the core s t ructure . I n order t o s a t i s f a c t o r i l y in t e rp re t

the data it w a s necessary t o determine the d i s t r ibu t ion of the capture

gamma-ray sources by mapping the thermal-neutron f lux d i s t r ibu t ion through-

out the reactor core. This w a s done by inser t ing copper wires of length

grea te r than the depth of the core i n various locat ions i n the core, w i t h

1. G. T. Chapman -- e t al . , Neutron Phys. Div. Ann. Progr. Rept. Aug. 1, -, 1963 ORNL-3499, V O ~ . I, p. 93

-2-

the reactor operated at a nominal 2-W power level for controlled times,

then removing the wires and measuring the gamma-ray activity resulting from thermal-neutron activation of the copper. The method used in con- verting the measured activity to thermal-neutron flux is the principal

subject of this report.

Copper was chosen for the activation measurements for a number of reasons :

1. Its cross sections seems to follow a l/v law over a large

energy range, and there is no evidence of resonances near thermal energies.

The magnitude of the cross section is sufficient to produce reasonable activities in a reactor flux without excessively long exposures, yet is

not so great as to introduce large flux depressions.

2. Copper has only two naturally occurring isotopes: 63Cu (69.1%) and "5Cu (30.9%). twice that of the 65Cu at thermal-neutron energies, and its product nuclide

(64Cu) decays with a half-life of 12.8 hr, whereas 66Cu, the product

nuclide of 65Cu, has a half-life of only 5 . 1 min. only one relatively simple decay scheme need be considered in measuring

the activity.

tribution are widely separated in energy, with the lower one (0.511 MeV) much greater in magnitude than the higher one (1.34 MeV), facilitated analysis of the copper activity.

The 63Cu isotope has an (n,r) cross section which is

Thus, after just 1 hr,

The fact that the two gamma rays occurring in the 64Cu dis-

3. Finally, copper requires no special handling or preparation and may be disposed of, in a manner consistent with health physics requirements,

very soon after measurements are completed.

This report discusses only the methods developed for analyzing the data. The final results of the measurements will be reported later. In order to check the validity of the method of analysis, a gold wire and a

copper wire were activated at the same location in the reactor.

these two materials differ greatly in nuclear properties and since their

diameters differed by a factor of 2, a comparison of the results of the

two measurements should have been a satisfactory check. However, as an

additional check, the experimental data were compared with a calculated di s t rib ut i on.

Since

. -3 -

11. EXPERIMENTAL PROCEDURE

After the wires had been exposed in the reactor and then removed,

the activity was allowed to decay for a minimum of 1 hr before the count-

ing was started, in order to eliminate the activity resulting from the

disintegrating 66Cu nuclei.

100 min of the measured decay curve compared with the expected decay curve

for a natural mixture of 64Cu (T = 12.8 h) and "%u (T = 5.1 m) nu-

clei, the 1-hr waiting period was sufficient. Since the "two-component"

curve matches the measured curve so well, the wire can be assumed to be of

effectively pure copper, even though it was "off-the-shelf" material.

As can be seen in Fig. 1 showing the first

12 l. 12

For counting,the wire was mounted on the scanning mechanism shown

in Fig. 2. This mechanism moved the wire across the mouth of a collimator at an accurately controlled speed of 0.132 cm/sec. from the disintegration of the excited nuclei passed through the collimator

(shown schematically in Fig. 3) and were detected by a 3-in.-diam by ?-in.- long NaI(Tk?) crystal. The resulting counts were recorded by successively

"opening" the individual channels of a 400-channel pulse-height analyzer

as the wire passed over the collimator opening. Since each channel was open for 1 sec (controlled by a 1-kc oscillator in the analyzer circuit)

and since the speed of the wire was constant and known, each channel num-

ber corresponded directly to both the time elapsed since travel was initi-

ated and the total distance traveled in that time. The analyzer could be operated remotely, and so the time that the counting was started and the

time that it was stopped were both controlled by an arrangement of micro-

switches mounted on the scanning device, as shown schematically in Fig. 4.

The photons resulting

2

A brief explanation may aid in clarifying Fig. 4. The signal from the photomultiplier tube was first passed through a solid-state preampli-

fier, where the pulse shape was adjusted for compatibility with the

amplifier.

resistor from the same 1-kV supply used with the photomultiplier tube.

signal was then fed into a DD-2 amplifier

The power for the preamplifier was obtained through a dropping The

3 with a built-in single-channel

2.

3. E. Fairstein, Rev. Sci. Instr. 27, 476 (1956). Technical Measurement Corp., Model 40D.

-4-

2-01-058-905R

2

- C ._ E 105 \ u1 t

I)

0 0

t t 2 5 I-

0 a @ C, ( t ) = (1.0577.105) e- (9 .025 '10-4) + c u e 3 ( n, 7 1 c u 6 4

2

@ DATA P O I N T : ERROR IS L E S S T H A N T H E DIAMETER OF T H E ENCLOSING CIRCLE

40 50 60 70 80 90 100 104 10 20 30 0 t, T I M E A F T E R R E M O V I N G W I R E FROM NEUTRON F L U X ( m i n )

Fig. 1. Measured Decay Curve for a Sample of Activated Copper Wire Compared with the Theoret ical Decay Curve for Daughters of the Two Stable Isotopes of Elemental Copper.

.

I wl I

Fig. 2. View of the Wire Scanning Device Showing the Crystal Shield, Analyzer Control Switches, and Wire i n Place.

-6 -

2- 04 -058- 906 R

0 . 6 - c m L d i a m 4

0.2051-cm diam c A/

..-____

J

4.95 cm

Fig. 3 . Dimensions of the Collimator and Copper Wire.

.

-7-

SIGNAL - CRYSTAL n TUBE( h MONITOR

L - " I - " J o - J " , n

-CONTROL

- -1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - - I LIMIT SWITCHES MOUNTED ON I WIRE SCANNER !

I

, I

52

+, SUPPLY LOCAL REMOTE

3 400-CHANNEL ANALYZER

I _ _ _ _ _

*SCA= SINGLE CHANNEL ANALYZER I

Fig. 4.. Block Diagram of the Electronics and Remote Control Used with the 400-Channelhalyzer for Scanning the Activated Wires.

A

-8-

analyzer (SCA) . The window-width, AE, and the base l ine, E, of the single- channel analyzer were adjusted t o pass only those pulses f a l l i n g i n the

peak of the d i s t r ibu t ion corresponding t o the desired gamma-ray energy.

The pos i t ive output of the SCA w a s used t o t r i gge r a coincidence gate i n

the multichannel analyzer, and the negative output was used t o monitor the

count r a t e .

input of the multichannel analyzer (PHA) through a length of "-2000 co-

axial cable, which delayed the s igna l about 0.75 psec. The analyzer, when operated i n the coincidence mode, would then accept only those pulses t h a t

f e l l within the desired peak of the pulse-height d i s t r ibu t ion .

The s igna l from the normal DD-2 output w a s fed i n t o the normal

The multichannel analyzer could be operated remotely by appropriate

connections through a multipin plug (5111).

be operated i n the "accumulate" mode, both pins C and F had t o be closed t o ground (p in E ) . With switch S1 i n the 'llocal" posit ion, pin C w a s closed t o ground a t 1 of Sla, the c i r c u i t from pin F t o ground w a s broken a t Slb

regardless of the conditions of S2 and/or S 3 , and a l l functions of the analyzer were controlled a t the analyzer control panel. With S1 i n the "stop" posit ion, only pin A w a s closed t o ground (through 2 of S la ) and

the analyzer w a s held i n the stop mode t o prevent an accidental destruction

of' the data.

a l l times through 3 of Sla. only i f the wire scanner had moved away from the end posit ion, thus r e -

l i ev ing the pressure on S2 and S3 and causing them t o switch t o the normally closed (NC) posi t ion.

(NO) posit ion, which occurred when the wire scanner w a s a t e i t h e r end of

the t r a v e l length, then the e l e c t r i c a l path from pin F t o ground w a s broken

and the analyzer went i n t o the "stop" mode.

I n order f o r the analyzer t o

With S1 i n the "remote" posit ion, p in C was a t ground a t Pin F w a s closed t o ground through 3 of S lb

If e i t h e r S2 o r S3 w a s i n the normally open

With the semiautomatic method described above it w a s found t h a t

e ight t o ten wires could be exposed and scanned i n a period of 8 hr, with two people required f o r operation.

ac tor check-out time a t the start of the day, the required 1-hr decay time,

and a t l e a s t three ca l ibra t ion checks during the scanning of the wires.

This period included the normal r e -

C

-9 -

A

111. THEORY

The theory f o r converting the data recorded i n each channel of the

analyzer t o thermal-neutron f lux as a function of posi t ion along the wire

w a s the following:

1. Assume, f o r the present, t h a t a wire has been exposed t o mono- energetic neutrons i n the water between the f u e l p la tes . i s removed from the flux, the a c t i v i t y i n the wire will continue t o decay,

and a t some subsequent time, t, i n a s m a l l volume of the wire it w i l l be

After the wire

- A t A ( t ) = v C T(1 - e-At) e ? where

A ( t ) = a c t i v i t y a t time t (d/sec),

v = volume (em3),

Z = macroscopic absorption cross section f o r the wire mater ia l (em

@ = average neutron f lux along the diameter of the wire (neutrons

-1 ),

- -1

cmm2 sec ), -1 A = decay constant (see

T = exposure time ( see ) ,

t = decay time ( see ) .

),

The average f lux i n the wire i s expected t o be somewhat lower i n

magnitude than the f lux i n the water before the wire w a s inser ted. This

"flux depression," which i s discussed i n d e t a i l i n the l i t e r a t u r e ,

requires the appl icat ion of the f ac to r

4 -6

f = T/g , ( 2 )

4. R. V. Meghreblian and D. K. Holmes, pp 244,260 i n Reactor Analysis, McGraw-Hill, New York, 1960.

5. R. J . Royston, The Absorption of Neutrons by a Small , Strongly Ab- sorbing Rod, AERE T/M 117 (1954).

6. Reactor Physics Constants, m-5800, Sect. 5.2, p 387 (1958).

4

-10-

where f i s a function of the wire radius a and the absorption cross section

C and L i s defined as the unperturbed neutron f lux.

Since the wire moves constantly while the a c t i v i t y i s being measured,

the volume of wire passing a given point i n a time T sec ( T

-11-

seconds, there will be recorded i n channel i a t o t a l number of counts, Cy corresponding t o the number of gamma rays emitted i n s m a l l volume v a t x.

The length of l i n e sources v i s ib l e through the coll imator i s 25, where 6 i s the distance measured from the coll imator ax is . There i s some point,

51, where the "edge" of the coll imator w i l l s t a r t shadowing the sources

so t h a t the number of gamma rays passing through the coll imator from

sources a t E > E 1 w i l l be monotonically reduced and approach zero a t 5 = 52. Thus the e f fec t ive so l id angle f o r the l i n e of sources i s

where p(E) = the coll imator "self-shadowing" f ac to r f o r a constant distance

from the shield ( see Sect. IV), and a( 5 ) = the so l id angle subtended by a c i r cu la r area (coll imator aperture a t the c rys t a l ) f rom a point source a t

5 . an even function, Eq. 6 may be wri t ten as

Since both p ( 5 ) and Q ( 5 ) a re even functions, and thus t h e i r product i s

The number of nuclei d i s in tegra t ing per second w i l l give r ise to A ( ~ ; ) T photons emitted per unit s o l i d angle per disintegration. Of these, only vvA(E) photons w i l l leave the wire without having a t l e a s t one co l l i s ion i n the wire, resu l t ing i n e i t h e r an absorption or energy degrada- t ion.

second from the source a t 5 i s Thus the t o t a l number of photons passing through the coll imator per

If the c r y s t a l i s against the coll imator e x i t aperture and i f the

radius of the c r y s t a l i s equal t o or grea ter than the radius of the e x i t

aperture, then Eq. 8 a l s o gives the nmber of uncollided photons incident on the c r y s t a l surface. O f these only E photons w i l l have a t l e a s t one

-12-

in te rac t ion i n the c rys ta l , with a probabi l i ty p t h a t the t o t a l photon

energy w i l l be given up i n the c rys ta l , thus causing a pulse with the ap-

propriate magnitude t o be recorded i n the peak of the pulse-height d i s -

t r ibu t ion . The t o t a l counts recorded-in channel i due t o the length of

wire UT passing the coll imator i n T second therefore is:* \

Ci(X) = - UT S A k ) TiT de) N e > E P T d5 , 0

( 9 )

where C.(x) = counts recorded i n channel i due t o photons or iginat ing i n the small volume of wire a t x, and a l l other terms have been defined. If the a c t i v i t y does not vary grea t ly over the distance UT, Eq. 9 may be wri t ten as

1

2 A(x,t) q v E p a' c . ( x ) 1 = U ,

where R ' i s defined i n Eq. 7 and the e x p l i c i t dependence of the a c t i v i t y A on the decay time and distance along the wire i s shown. Solving Eq. 10

f o r the a c t i v i t y and equating the results t o Eq. 5 gives

from which i s obtained

3. The methods used t o approximate or otherwise determine the ap- propriate values f o r appl icat ion i n Eq. 12 were the following:

*Actually, V , p ( 0 , E, and p a re a l l functions of the photon energy, bu t here t h i s dependence i s neglected since the discussions a re con- cerned with monoenergetic photons.

c

Y

-13-

Decay Time and Distance. - In a l l cases the decay time and distance along the wire were adjusted t o the center of the analyzer channel current-

l y "open." Since the time required t o br ing the reactor t o the nominal 2 - W

power l e v e l w a s short compared with the length of time t h a t the wires were

exposed i n the reactor, the time d is t r ibu t ion of the neutron f lux was as-

sumed t o be t h a t shown i n Fig. 5. It i s seen from the f igure tha t the t o t a l exposure time i s

T = T - T1 see , (13) 2

and the t o t a l decay t i m e through one-half the counting period f o r channel i

i s

t = (T3 - T,) + T i + 0.5 T

since T w a s constant for a l l channels. The distance the wire has t raveled a t t h i s time i s

x = u T ( i + 0.5) cm ,

where i may take on values from 0 t o 399 i n Eqs. 14 and 15.

The i n i t i a l processing of the data consisted of converting the data t o

C i ( X )

c I (x) 1 = - A t ) - A t ~ ( 1 - e e

by means of the Fortran-63 program WIREDAT, wr i t ten fo r a CDc-1604A com- puter. This allowed an intermediate inspection of the data for correc t

alignment and consistency. A second program, WIREDAT2, performed an

averaging over a 1-ern wire length i f desired and accomplished the conver-

sion t o thermal-neutron flux. List ings of both programs are i n the

Appendix.

2-01 -058 - 908 T, : EXPOSURE STARTS

T3: WIRE SCAN STARTS 7,: CHANNEL i OPENS AND REMAINS

NEUTRON INTENSITY 1 T2: EXPOSURE STOPS OPEN FOR T sec

i

I

Fig. 5. Assumed Time Distribution of the Neutron Flux and Wire Activity .

3

- 15-

Flux Depression Factor. - The f lux depression factor , f , i s d i s - cussed exp l i c i t l y and i n d e t a i l i n r e f s . 4, 5, and 6. however, t h a t the nwnerical values of the escape probabili ty, Po, calculated

by Case, deHoffman, and Placzek7 agreed with the values of f f o r long

cy l indr ica l rods given i n r e f s . 2 and 3, as shown i n Fig. 6. (This i s probably the r e s u l t of the neutron sca t te r ing i n the absorbing materials

being neglected i n the l a t t e r references.) Based on t h i s it w a s assumed that , t o a f i r s t approximation, the escape p robab i l i t i e s discussed i n

re f . 7 could be used f o r f . f o r small-diameter gold and copper wires since the cross sections f o r

these mater ia ls a re predominantly absorption cross sections a t neutron

energies near thermal.

It was found,

Such an approximation should not be too bad

The Probabi l i ty of Photons Escaping Without a Collision. - The escape probabili ty, Po, mentioned e a r l i e r i s a function only of the a t t enua t ion propert ies of the mater ia l and the radius of the wire.

ray in te rac t ions a re a l so functions of the at tenuat ion propert ies and

geometry of the material , the escape probabi l i t i es7 might equally as well

be used t o give the probabi l i ty t h a t a gamma ray born i n the wire with a

given energy w i l l escape without undergoing a co l l i s ion .

the r e l a t ive ly small s ize of the wires used i n the experiment compared with

the mean f r e e path of the charac te r i s t ics gamma ray, t h i s factor , v, w a s taken t o be uni ty ( t o an accuracy of about 23).

Since gamma-

However, due t o

S o l i d Angle and Collimator. -As w a s mentioned e a r l i e r , the con-

t r ibu t ions from sources located beyond a ce r t a in distance 51 would be

reduced because of self-shadowing by the collimator. This shadowing re -

sults i n an e f fec t ive reduction o f the so l id angle subtended by the e x i t

aperture of the collimator.

the so l id angle for cyl indr ica l coll imators w a s described. coll imator used i n t h i s experiment w a s conical, it w a s necessary t o

extend the method t o conical coll imators having the source a t a distance

l e s s than the distance t o the apex of the cone.

8 In a previous report , a method of correct ing

Since the

7. K. M. Case, F. deHoffhann, and G. Placzek, Introduction t o the Theory of Neutron Diffusion, Vol. I, p 17, Los Alamos Sc ien t i f i c Laboratory (1953).

8. G. T. Chapman, Neutron Phys. Div. Ann. Progr. Rept. Aug . 1, 1963, OWL-3499, Val. I, p 188.

IT 0 I- o 2 Z 0 u-3 u-3 W LT a W a x 3 _I LL

z 0 IT I- 3 W Z

k

-

c

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

r 4- 0 1 i

\

-16 -

2 - 01 - 058-909R

F R O M CASE, D e H O F F M A N A N D P L A C Z E K ( R E F 8 )

0 V A L U E S F R O M A . E . R . E . T / M 117 ( R E F 5 1 o V A L U E S F R O M FIG 5.2, A N L 5800 -

( R E F 6 1

\ 1 A

\

0 1 2 3 4 5 6 7 as, , WIRE R A D I U S (mfp )

Fig. 6. First-Approximation Flux Depression Factors for Long Slim Cylinders.

.

-17-

r

Figure 7 shows a r ight-conical coll imator truncated a t a length 1 and with r a d i i rl a t the entrance (source) aperture and r2 a t the e x i t

( c rys t a l ) aperture. It w i l l be noticed t h a t r2 i s greater than rl. For

any i so t ropic source located on the l i n e between 0 and 51, the so l id angle

subtended by the e x i t aperture a t the locat ion of the source i s Q ( E ) as tabulated i n r e f . 9 . However, a t any distance grea te r than 51, some of the photons emitted i n t o the so l id angle Q ( 5 ) of the entrance aperture and never reach the e x i t aperture.

angle i s reduced and only the hatched area i n the f igure i s illuminated by the photons.

illuminated area t o the t o t a l e x i t aperture area.

a r e intercepted by the edge

Thus the so l id

The self-shadowing fac tor i s defined as the r a t i o of the

For any displacement l e s s than or equal t o (1 the t o t a l e x i t aperture area i s illuminated and the self-shadowing f ac to r i s

d E 5 51) = 1 9

but f o r 5 grea ter than E 1 the illuminated area becomes

where

2 -1 2 2 -1 - r2 s i n h,(E) - r ,B s i n h,(5)

a @ = I - + - Z J

E2 - 5 1 5 2 * ?

B - 1 5 h2(5) =

9. A. V. H. Masket and W. C . Rodgers, Table of Solid Angles, TID-14975 (July 1962).

*P, hl , h2, and A are a l l functions of z, the distance from the coll imator entrance, but t h i s distance w a s held constant for t h i s experiment.

-18-

2-04 -058-940R

4

SOURCE LINE

I

/ /

/ /

/ /

/ I , / /’

’ / / /

/ /

PROJECTION OF ENTRANCE APERTURE \

Fig. 7. Geometry of a Conical-Shaped Collimator wi th the source Located o f f the Collimator Axis.

I

= point at which shadowing first occurs,

B rl + r2 b = B - 1

= point at which the source becomes "invisible" through

collimator;

and the self-shadowing factor* becomes

In order to perform the integration indicated in Eq. 7, it was de- sirable to have an analytic expression f o r n(!). small displacements from the collimator axis, an applicable expression was

It was found that, for

where

Q(0) = solid angle subtended by the collimator aperture from a point

at the collimator axis,

k = constant,

x = E h = normalized displac ment . A simple linear leastysquares fit to the values given in ref. 9 for

the geometry of the collimator used gave a k value of 0.1755. lated values are compared with the published values in Fig. 8. integration

The calcu-

The

*By setting rl = r2, the equations discussed here reduce to those previ- ously reported (ref. 9) for a straight collimator.

-20-

0.4190

0.4180

0.4170

0.4160

0.4150

0.4140 0

I A- A-A-A-

2-01 - 058-9AjA

x=- E r2

I

0 EXACT VALUES FROM MASKET -

AND RODGERS, TID-14975 (1962) - I

0.1 0.2

E 0.3 0.4

Fig. 8. Calculated Values of the So l id Angle f o r All Displace- ments Compared with the Exact Values.

I

I

A

w a s performed on the CDc-1604A computer using Eqs. 19 and 20. the program ( LOMEGO) i s given i n the Appendix.

A l i s t i n g of

I n t r i n s i c Crystal Efficiency. - The i n t r i n s i c c r y s t a l efficiency, E, i s defined as the f rac t ion of those photons of a given energy incident on the c r y s t a l face t h a t have a t l e a s t one in te rac t ion i n the c r y s t a l t o

produce a measurable pulse. If the photons a re collimated i n t o the face of

the c r y s t a l so t h a t the average path length through the c r y s t a l does not

d i f f e r grea t ly from the length of the c rys ta l , t h i s eff ic iency may be taken

as

where p = p(E ) = t o t a l gamma-ray absorption coef f ic ien t (cm-l) and L =

c r y s t a l length. Y

Correction of Window Distr ibut ion t o a Gaussian Distribution. - Though not spec i f ica l ly mentioned i n the previous discussion, the d is t r ibu-

t i o n of pulses i n the window (&E) of the single-channel analyzer did not

represent a Gaussian d is t r ibu t ion below the channel containing the maximum

counts and a t the l imits of the window width. This i s shown graphically i n

Fig. 9. A correction, 1

area of the equivalent Gaussian g = 7 area of the d i s t r ibu t ion i n the window

w a s applied by multiplying the counts i n each channel (i) by g.

Gaussian corresponding t o the measured d i s t r ibu t ion w a s obtained by a

method suggested by Zimerman.

t r i bu t ion about &, with a standard‘deviation a i s

The

10 The general equation of a Gaussian d i s -

~. -

02/27;

10. W. Zimerman, Rev. Sci. I n s t r . 32(9), 1063 (1961).

-22 -

105

5

2

io4

5

2

103

5

2

I O 2

5

2

IO’

2-01- 058-912R

/ GOLD: 411.8 keV I p 3 x 3 i n . N a I ( T I ) If- COLLIMATOR I I I n

m I

1 I I I I I I

45 50 55 6 0 65 7 0 75

CHANNEL NUMBER

Fig. 9. Measured and Corrected Distribution of Fulses in the Single-Channel Analyzer Window (&) .

-23-

and i f

X I = x - 1,

where X i s a rb i t ra ry , then Eq. 25 reduces t o

Then, upon taking the logarithms of both sides of Eq. 27,

2 an Q ( X ) = - ( X - &) 8

2 2 & + - X , = - -

a2 a2

which may be wri t ten as

Z ( X ) = A + b X i

, !

i

= constant,

= constant.

-24 -

Equation 29 is linear in X and may be used to determine u from the slope and the central value (G) of X from A and 6.

If Q(X) is interpreted as the measured count in each channel* and X as the channel number with the analyzer operated in pulse-height analysis

mode, a straight line will not necessarily result when the values are ap-

plied in Eq. 29, because of the nonuniformity of the measured distribution mentioned above. However, a portion of the distribution above X, will prob- ably give a straight line. A simple least-squares fit to this portion will give the best values of A and B. Figure 9 shows the corrected Gaussian normalized to the experimental distribution for the 411.8-keV gamma ray from lS7Au.

Peak-to-Total Ratio. - The ratio, p, of the area under the peak of the pulse-height distribution to the total area under the distribution for a particular gamma-ray energy is a measure of the fraction of the total

photons that deposited all their original energy in the crystal.

ratio is normally determined from the experimentally measured distribution

as shown in Fig. 10. The area under the peak is again approximated as described above.

This

Probability, 7, of Emission of Gamma Ray of Desired Energy per

Disintegration per Unit Solid Angle. - Copper-64 and gold-197 decay accord- ing to the schemes given in Fig. 11, which are based on data in ref. 11. The gamma ray of interest in the 64Cu measurements was that which originated

With the annihilation of the positrons ( @ ) in the copper.

are two such photons (0.511 MeV each) emitted in each annihilation and since a is emitted 19% of the time, the number of 0.511-MeV photons emitted per unit solid angle per disintegration is

+ Since there

+

= .4 0.19 x 2 = 3.023 x io -2 . VCU 2-r

*A pulse-height channel (X) 11. K. Way -- et al. (Comp.),

Academy of Sciences of

is not to be confused with a time channel (i) . Vol. 5 (set l), National

the National Research Council, Washington, 1962. 8

-25 -

I I I

T O T A L DISTRIBUTION

1 o4

5

2

1 o3

5

2

l o 2

5

2

IO ’

-

0

2-01 - 0 5 8 -91 3 R

, - I -

TOTAL A R E A = 14.91 3 x lo4 I 1 P ( E ) = 0 . 4 6 8 II I u

4 I

W IR E S C A N N ER; C R Y S T A L : G O L D : 411.8 k e V

3- in.-DIA x 3- in . -THICK; C O N I C A L C O L L I M A T O R

10 20 30 40 50

C H A N N E L N U M B E R

i 60 70

4

Fig. 10. Pulse-Height Distribution for 411.8-keV G m a Rays.

A

-26 -

0.41.18 MeV

2- 04-058-944R

12.8-hr C U ~ ~

I

1.34 MeV

STABLE Ni64

b8 '70

p+, 43% E STABLE Zn64

,

Fig. 11. Decay Schemes for lS8Au and 64Cu. (Based on data in K. Way s t2bles. 11)

n

-27-

An experiment12 t o determine the number of posi t rons escaping the copper

without being annihilated w a s made by placing a sample of act ivated cop-

per wire i n an unactivated copper sleeve with an inside diameter compar-

able t o the wire diameter. No d is t inc t ion could be made between the num-

ber of 0.511-MeV gamma rays recorded with the bare wire and with the

covered wire.

would have been annihilated i n the sleeve and thus have produced a grea te r

number of gamma ray than those produced i n the wire alone, it w a s assumed

t h a t e s sen t i a l ly a l l the posi t rons were annihi la ted i n the wire.

Since any positrons which might have escaped from the wire

The 0.4118-MeV photons shown i n the decay of lS8Au were measured t o

determine the a c t i v i t y of the gold wire. Two paths i n the decay scheme give r i s e t o a photon of t h i s energy. One percent of the decays are t o

the 1.087-MeV l e v e l of s tab le lS8Hg, with a subsequent 82% probabi l i ty of

t he t r ans i t i on t o ground being through the 0.675-MeV l e v e l t o cause the f i n a l emission of the 0.4118-MeV photon. The other path a r i s e s through

the 99% of lS7Au decays t h a t go d i r e c t l y t o the 0.4118-MeV l e v e l of lS8Hg. The transmission from t h i s l e v e l t o the ground s t a k i s by the emission of

the 0.4118-MeV photon. Consequently, the number of 0.4118-MeV photons

emitted per un i t so l id angle per d i s in tegra t ing lS7Au nucleus i s

= 7.943 x . - 0.01 x 0.82 + 0.99 rlAu - 4fl

Neutron Cross Sections;. - The thermal-neutron cross sect ions used13 for “%u and lS7Au were 4.3 - + 0.2 barns and 98 - + 10 barns, respectively. When averaged over a Maxwellian d is t r ibu t ion , the macroscopic absorption

cross sections were 0.2234 cm-I and 5.157 cm-l, respectively.

R a t i o of Thermal Neutrons t o A l l Neutrons. - An approximation for %, the r a t i o of thermal neutrons t o a l l neutrons, w a s obtained from the r e su l t s of a PDQ c a l c ~ l a t i o n ~ ~ previously done for the design study of

12. M. S. Bokhari (Om), pr iva te communication. 13. D. J. Hughes and R. B. Schwartz, Neutron Cross Sections, BNL-325

2d ed., ( Ju ly 1, 1958). 14. E. G. S i lve r (Om), pr iva te communication.

-28-

t h i s reactor . It i s emphasized t h a t the following does not normalize the

data t o the calculat ions.

Experimentally, one would measure such a parameter as the cadmim

r a t i o defined as15

neutron f lux measured with the bare detector R = (32)

C neutron f lux measured with the detector covered with cadmium

The numerator of Eq. 32 i s a measure of the number of neutrons of

a l l energies, while the denominator includes only those neutrons above a

ce r t a in cutoff energy (about 0.4 eV f o r cadmium). the thermal-neutron f lux can be obtained by the relation15

From such measurements,

thermal flux resonance flux

Rc - 1 = (33 1

The previously mentioned PDQ calculat ions used four energy groups of

thermal, thermal t o 0.6176 eV, 0.6176 t o 9.118 x lo3 eV, and neutrons: above 9.118 x 16 eV. a t the center of the reac tor by a successive addi t ion of the t o t a l neu-

t rons of each group as a function of posi t ion. A l s o shown on the f igure

are the data obtained through the ac t iva t ion of a gold w i r e and a copper

wire i n comparable locat ions a r b i t r a r i l y normalized t o the calculat ions.

The two sets of data have been corrected f o r the ac t iva t ion and decay

times. It w i l l be noticed t h a t the copper-wire d i s t r ibu t ion matches, t o

a fa i r approximation, the shape of the calculated d i s t r ibu t ion for neutrons up t o 0.6176 eV.

only up t o about t h i s energy. It w a s not possible, however, t o match the

gold-wire data with e i t h e r of the calculated groups. Based on these ob-

servations, a parameter

-29 -

E

e

n

w a s obtained f o r gold.

follow a possible experimental procedure.

In the discussion t o follow, an attempt i s made t o

If it i s assumed t h a t copper i s sens i t ive only t o 0.6176 eV, then the bare copper wire would "see" a t o t a l neutron flux,

TH + 'RES ' ' = '

where @TH = calculated s p a t i a l d i s t r ibu t ion for the thermal group, and 'RES = calculated s p a t i a l d i s t r ibu t ion f o r the group THE3MA.L - < E, - < 0.6176 eV, as shown i n Fig. 12. Now

by Eq. 33. From Eq. 352

cu D

r e fe r s t o the r a t i o taken from the calculation* and Rcu i s de- where %DQ n

fined by Eq. 4.

Having obtained $& -' 1 f o r copper, the r a t i o of thermal neutrons t o resonance neutrons (as defined by Eq. 33) may be obtained from the r e l a t i on16

($EQ - 1) = -1) ,

where R I i s the "resonance i n t e g r a l i n the pa r t i cu la r reactor neutron spec-

trum" and CdD, t he "cadmium difference," i s defined as the difference

*Since the neutron spectrum changes with locat ion i n the reactor, Rn and

16. Reactor Physics Constants, ANL-5800, 2d ed. ( Ju ly 1963). RPDQ a re functions of the posi t ion.

i

-30-

U

s cu

rc)

In

2

f

W

cu (u

9

.

-31-

between the a c t i v i t y induced i n the detector by neutrons of a l l energies

and the a c t i v i t y induced by thermal neutrons only. Thus

(38

Since the wires used i n the experiment were not of the same diameter and since the a c t i v i t i e s of the wires were a measure of the average neutron

flux i n the wire ra ther than the t rue, unperturbed neutron f lux i n the

reactor, then f o r a u n i t length of the wires the r a t i o of the "cadmium

differences" of the two % i r e s may be wri t ten as

TH (2) (2)

A u -- I TH dDAU - CdDCu

cu

c

( 39)

where

N = number of atoms/cm3,

om = microscopic absorption cross sect ion a t thermal-neutron a energy,

f = f lux depression fac tor (Eq. 2 ) ,

v = volume of wire per u n i t length of wire. I

Finally, from Eqs. 39 and 37;

Use w a s made of a calculated spectrum14 t o determine the approximate

resonance in t eg ra l s f o r the gold and copper. Brief ly , the absorption cross

sect ion for copper w a s assumed t o vary as E

t o about 34 eV.

-1/2 (% = neutron energy) up The same assumption w a s made f o r the gold cross sect ion

n

-32 -

below 1 eV.

energy increment occurring i n the spectrum calculat ion i s

h7ith these assumptions, the average cross section over an

J” El

w h e r e E2 and E l represent the upper and l o w e r l i m i t s respectively of the

energy increment.

Above 1 eV a numerical in tegra t ion of the gold cross sect ion as 13

given i n BNL-325 Thus

w a s performed t o obtain the average cross section.

(42)

where

E = neutron energy a t the middle of the - nth energy increment of n width h n ( D E n < E2 - E l ) ,

us ( En) qq= r a t i o of sca t te r ing t o t o t a l cross sect ion as given i n BNL-325.

The neutron energy spectrum and the averaged cross sections a re shown i n

Table 1. Another numerical in tegra t ion of the flux-weighted averaged

e

n

-33 -

Table 1. The Calculated Neutron Energy Spectrum and Averaged Cross Sections Used i n Determining the Approximate

Resonance In tegra ls for Copper and Gold

,cu ,bu %(E,) J 0 0 E1 E2 Neutron Flux a a (4 (ev) per Unit Energy (barns) (barns)

i

a

3.075 x lom2 3.756 x 4.587 x 5.603 x 6.843 x 8.358 x lom2 1.021 x 10-l

1.247 x 10-1 1.523 x 10-1 1.860 x 10-l 2.272 x iom1 2.775 x 10-l 4.140 x 10-I 6.176 x 1o-l 9.214 x 10-1 1.375 x 10' 4.564 x loo 1.016 x lo1 1.515 x lo1

3.756 x 4.587 x 5.603 x 6.843 x 8.358 x 1.021 x 10-l

1.247 x 10-1 1.523 x 10-1 1.860 x 10-1 2.272 x 10-l 2.775 x 10-1 4.140 x 10-1 6.176 x 10-l 9.214 x 10-1 1.375 x 10' 4.564 x 10' 1.016 x io1 I 1.515 x lo1 3.372 x lo1

1.35 x lo1 1.20 x lo1 1.06 x io1 9.32 x 10' 8.08 x 10' 7.06 x ioo 6.06 x ioo 5.24 x 10' 4.42 x 10' 3.80 x 10' 3.16 x 10' 2.50 x 10'

1.80 x ioo 1.29 x ioo 8.89 x 10-l 4.00 x 10-1 1.53 x 10-1 9.79 x 5.51 x l'j2

3.68 3- 50 3.32 3.16 3.00

2.85 2.71 2.58 2.45 2.33 2.22

2.01

1.83 1.67 1 - 5 3 1.19 1.03 0.96 0.84

83.92 79 * 77 75.78 71.99 68.40 64.99 61.78 58.71 55.84 53.16 50.65 45.92 41.73 37 * 99 35.89 68.06

261. 240. 206.

cross sect ion between 3.085 x lom2 eV and 3.372 x lo1 eV gave the approximate resonance in t eg ra l . Thus

R I = f @(Ei) ;(E.) mi 1

i= 1

= 1.320 x 103 barns f o r gold

= 5.403 x 10' barns for copper. (43 1

-34-

Observing t h a t the volume per un i t length (v) of wire i s numeri-

c a l l y equal t o the cross-sect ional a rea of the wire as l i s t e d i n Table 2

and using the value of the flux depression from t h a t table, one c m now

Table 2. The Constant Parameters Used i n the Wire Analysis

Numerical Value

Description of Parameter Symbol Copper Gold

Wire speed, cm/sec U 1.32 x iom1 1.32 x iom1 Count time per channel, sec T 1.0 1 .0

Wire radius, cm a 1.03 x iom1 4.06 x Area, cm2 S 3.32 x 5.18 x iom3 Decay constant, sec-l A 1.50 x 2.97 x Photons. d i s - l . ( u n i t so l id angle) " 7 3.02 x iom2 7.93 x Positron annihi la t ion probabi l i ty 1.00 (not applicable)

Probabi l i ty for photon escape

I n t r i n s i c eff ic iency of the

from wire V 1.00 1.00

c r y s t a l E 9.19 x 10-I 9.54 x 10-1 Peak eff ic iency of the c r y s t a l P 3.11 x 10-l 4.45 x ioe1

a Integrated so l id angle,

Macroscopic absorption cross

Flux depression f ac to r f 9.71 x 10-1 7.86 x 10-1

cm/s teradian n' 1.69 x 10-1 1.55 x 10-1

-1 2.23 x 10-l 5.14 section, cm 'a

Window correction

b Total e f f e c t

g 9.84 x 10-l 9.56 x 10-l

K 4.69 x io4 4.39 io3

a. Entrance aperture corrected f o r penetration.

g b. K = 2 7 v E p R ' s Z a f

I

. -35 -

I-

T

write the f i n a l expression f o r the r a t i o of thermal neutrons t o resonance

neutrons as measured by the gold wire r e l a t ive t o the r a t i o as measured

by the copper wire:

The r a t i o of thermal neutrons t o a l l neutrons as measured by the gold wire i s

(45)

which of course implies the un rea l i s t i c condition t h a t the resonance i n t e -

gra l s a re constant throughout a l l regions of the measurement. This d i -

vergence from rea l i t y , however, should not be important i n the power-

producing volume of the reactor and should become s igni f icant only near

the edges of and external t o the core of the reactor .

IV. RESULTS AND CONCLUSION

The values chosen f o r the many parameters discussed above a re l i s t e d

i n Table 2 f o r gold and copper, along with the value computed f o r the " t o t a l

effect" factor , K. the data by K and Rn i s shown i n Fig. 13. sents the ari thmetic average.of seven or e ight measurements made over a

1-ern length of wire.

i n 1 em.

A typ ica l experimental curve obtained by multiplying Each experimental point repre-

The e r ro r bars r e f l e c t only the t o t a l counting e r r o r

The calculated thermal-neutron d is t r ibu t ion , normalized t o 2 W of

reactor power, i s a l so shown i n Fig. 13. The experimental data compare favorably with the calculat ion through the fuel-bearing region of the

reactor and f o r some distance above t h a t region.

begin t o deviate from the calculat ion a t about 44 em, which may be due t o the existence of s t ruc tu ra l mater ia ls i n the ac tua l reactor which were not considered i n the calculation.

copper-wire data and the calculat ions a t about 40 em.

The copper-wire data

The gold-wire data deviate from both the

This i s qui te

-36-

2-04-058-946R

I I I I I I 1 + COPPER WIRE MEASURED DISTRIBUTION 1 l I I l 1 + GOLD WIRE MEASURED DISTRIBUTION I I I I I 1 I

THE 1 1 1 I I I I CALCULATED DISTRIBUTION IS NORMALIZED TO AN ABSOLUTE TWO WATTS OF

REACTOR POWER WHILE THE MEASURED DISTRIBUTIONS WERE OBTAINED WI THE REACTOR OPERATING AT A NOMINAL TWO WATTS. EACH DATA POINT SHOWN IS THE AVERAGE OF AT LEAST SEVEN READINGS OVER A ONE CM LENGTH OF WIRE AS SHOWN BY THE HORIZONTAL BARS. THE VERTICAL ERROR BARS REFLECT THE COUNT- RATE STATISTICS ONLY. THE CALCULATED AND GOLD WIRE DISTRIBUTIONS HAVE BEEN ADJUSTED TO AGREE WITH T H E COPPER DATA ONLY IN THE LINEAR DIMENSION ( x

I I 1 I I I I I I / l /

TH

) .

BOTT2M OF REACTOR I I

8 42 46 20 24 28 32 36 40 44 48 52 4

56 60 0 4 x. DISTANCE ALONG THE COPPER WIRE ( c m )

e

Fig. 13. A Comparison of the Distr ibut ion Measured Along the Reactor Center Line with the Gold and Copper Wires and a Calculated Distr ibut ion Using the PDQ-4 Reactor Program.

.

-37-

8

n

probably the r e s u l t of assuming a constant resonance in t eg ra l f o r gold

even i n t h i s region, where the neutron energy spectrum i s expected t o

change rapidly.

i n determining the power of the reactor.

This pa r t i cu la r volwne i s not of much importance, however,

It i s d i f f i c u l t t o quote an overa l l e r r o r f o r t h i s system of estimat-

ing the reaction r a t e s i n a reactor from the a c t i v i t y induced i n copper

wires since the analysis u t i l i z e s values from published tabulat ions where

e r rors a re seldom quoted. However, the r a t i o of the thermal-neutron f lux

as determined by the gold-wire measurement t o the thermal-neutron f lux as

determined by copper wire i s 1.023 + 0.121 within the reactor core. This suggests t h a t the method i s probably accurate t o within - +lo% o r l e s s . It i s concluded, therefore, t h a t the use of copper-wire ac t iva t ions i n con-

junction with a method of data in te rpre ta t ion such as the one presented

here affords a convenient method f o r measuring neutron in te rac t ion r a t e s

i n a reactor .

-

!be author i s g ra t e fu l f o r the assis tance given by K. M. Henry and

J. M. Miller, who operated the reactor and ass i s ted during the measure-

ments, and a l so f o r the advice given by F. C. Maienschein, W. Zobel, and

T. V. Blosser, and a l l members of the BSF staff .

-38-

Appendix

FORTRAN PROGRAMS

The three Fortran-63 programs used i n the data analysis a re l i s t e d

i n t h i s section, with a b r i e f discussion of each.

p i led f o r use with the CDC-1604A computer a t ORNL and use only standard I/O tapes.

The programs are com-

Program WIREDAT

Program WIREDAT ca lcu la tes the posi t ion along the wire and the t o t a l

decay time corresponding t o each channel.

the "open" time f o r each channelto give the count r a t e i n the channel and

i t s associated e r ro r and then by the product of (1 - e-hT) e i n Eq. 16 (Sect. 111) t o give the spec i f ic ac t iv i ty .

The input data are divided by

- A t as shown The l i s t e d output

s h o w s both the count r a t e and the specif ic ac t iv i ty , along with the posi-

t ion .

f o r fur ther use.

The spec i f ic a c t i v i t y and/or the count r a t e may be punched on cards

The following def in i t ions a re per t inent :

Input Constants

XLAM = decay constant,

SPEED = wire scanning rate,

T I = t o t a l time each channel i s open for counting,

I D = unique iden t i f i ca t ion number for each wire,

TML* = date and time the ac t iva t ion s ta r ted ,

TI@* = date and time the ac t iva t ion stopped,

TM3* = date and t i m e the scanning s tar ted,

BPC = f ac to r t o cor rec t f o r incomplete inser t ion of the

wire i n t o the reactor,

POS = locat ion of the wire i n the reactor .

~~

*See discussion of Subroutine TIME.

-39 -

i

Control Characters

URD - < 1 r e su l t s i n the output of two decks of cards, the f i r s t containing the posi t ion and count r a t e and

the second containing the posi t ion and the spe-

cific activity.

r e su l t s i n the output of one deck of cards con-

ta ining the posi t ion and the spec i f ic ac t iv i ty , - > 2

IQUIT = -1 i f program i s t o process another s e t of data with

a d i f f e ren t decay time, speed, and count time,

= 0 i f program i s t o process another s e t of data

with a d i f f e ren t decay time, speed, and count time,

= +1 i f the next s e t of data i s the l as t s e t t o be

processed.

Subroutines

TMC (ID,SPEC,IRR) - This subroutine reads i n a one-dimensional array containing the number of counts i n each channel. The

data were taken from the analyzer on punched paper tape a t the

BSF and converted t o punched cards through the use of an ex-

t e r n a l program supplied by W. Zobel of the BSF staff . TMC

reads each card and checks it f o r word alignment. the identification,number punched on each card i s checked

against the I D number above (see "Input Constants").

e r ro r i s detected i n the deck of cards, the s e t of data i s

processed; otnerwise the s e t of data i s re jected.

TIME (TX,SEC) - The t i m e s TM1, TM2, and TM3 (see "Input Constants") a r e read i n as one word, each giving the number of elapsed days and the hour, minute, and second i n 24-hr notation.

v e r t s each number t o the equivalent number of seconds. For example, assume t h a t an exposure w a s s t a r t ed a t 4:30:32 PM and w a s terminated a t 6:42:20 PM. Assume f u r t h e r t h a t the s ta r t

of the scanning w a s delayed u n t i l lO:52:OO AM the following day. The appropriate numbers t o be read i n a re

I n addition,

If no I

TIME con-

-40-

T M ~ : 00163032

TM2: 00184220

m: 01105200

Program WIREDAT2

Program WIREDAT2 averages the output of WIREDAT i n 1-ern in t e rva l s

through the whole length of the wire. ( see "Ratio of Thermal Neutrons t o All Neutrons," Sect. 111) and K ( see Table 2, Sect. 111) for each in t e rva l .

SHAPE(1) i s the product of R n

Program LOMEGO

Program LOmGO calcula tes the integrated so l id angle as given by

Eq. 21.

the input required. It i s believed t h a t the included comments will adequately explain

n

.

C C****

C

C

C

C C****

C

C

C

1 0 3 1 0 0

1

2

1 0 1

1 0 2

3

4

5 6

7

PROGRAM W I R EDAT

FOR USE I N REDUCING THE DATA TAKEN B Y EXPOSING WIRES

I N THE REACTOR FOR NEUTRON F L U X MEASUREMENTS.THIS

PROGRAM G I V E S THE S P E C I F I C A C T I V I T Y AS A F U N C T I O N OF

P O S I T I O N ALONG THE WIRE.

PROGRAM NUMBER 6 4 0 2 0 6 - 0 1 0 2 (RO) / 1 6 0 4 - 6 3

D I M E N S I O N S P E C ( 4 2 0 ) , X ( 4 2 O ) , E R R ( 4 2 0 )

READ INPUT TAPE 5 0 , 1 O O l , X L A M , S P E E D , T I READ I N P U T TAPE 5 0 , 1 0 0 0 , I D , T M l ,TM2,TM3,EPC,POS,LCRD, I Q U l T

C A L L TMC( ID,SPEC, I R R ) I F ( I R R ) 1 5 , 1 , 1 5

I OUT=l

DO 2 J = 1 , 4 0 0 S P E C ( J ) = S P E C ( J ) / T I

ERR ( J)=SQRTF ( S P E C ( J) 1 X ( J = S P E E DJrT I * ( F LO A T F ( J -0 . 5 )+E P C W R I T E OUTPUT TAPE 5 1 , 1 0 0 2 , I D , S P E E D , P O S , T I , B P C

I F ( IOLT-1 ) 3 , 3 , 4 WT? I T E OUTPUT TAPE 5 1 , 1 0 0 3 GO TO 5 WR I T E OUTPUT TAPE 5 1 , 1 0 0 4

L= 1 LL=L+49 W R I T E OUTPUT TAPE 5 1 , 1 0 0 5

DO 7 J=L, LL J l = J - 1 $ J2=J+49 $ J3=J+50 WR I T E OUTPUT TAPE 5 1 , 1 0 0 6 , J 1 , X ( J ) , SPEC( J) ,ERR (J ) , J2, X ( J3 ) .

GTC-OR NL

1 S P E C ( J 3 ) , E R R ( J 3 )

I F (LL-350)8,9,9 8 L=L+IOO

I -

.

-42 -

WRITE OUTPUT TAPE 5 1 , 1 0 0 7

GO TO 6 9 IF (LCRD- IOUT)~O,YO, 1 2

90 WRITE OUTPUT TAPE 5 2 , 1 0 0 8 , I D

M=1 $ MM=4

l F ( M M - 4 0 0 ) 1 1 , 1 2 , 1 2

i o WRITE OUTPUT TAPE ~ Z , ~ O O ~ . ( X ( J ) , S P E C ( J ) , J = M , M M ) , I D

1 1 M=M+4 $ MM=MM+4

1 2 I F ( IOUT-1) 1 3 , 1 3 , 1 5 1 3 IOUT=IOUT+l

GO TO 1 0

C A L L T I M E ( T M 1 , T 1 )

CALL T IME (TM2, T 2 )

CALL T I ME (TM3, T 3 D O 1 4 J=l,400

TD=T3-T2+T I * ( F L O A T F ( J - l ) + O . 5 > TA-T2-TI +TD E J=E XPF ( -X LAM*TD 1 -EX PF ( -X LAM*T A 1 S P E C ( J )=SPEC( J) / E J

14 ERR ( J ~ E R R ( J) /EJ GO TO 1 0 1

1 5 I F ( I Q U I T ) 1 0 3 , 1 0 0 , 1 6

1 6 STOP C C C**** FORMAT STATEMENTS

C C

1 0 0 0 FORMAT ( 1 0 0 1 FORMAT ( E l 2 . 4 . 2 F 8 . 4 )

1 0 0 2 F O R M A T ( 6 5 H l

I 6 , 3 F 1 0 .O, F 6 . 3 . 1 A 8 , 2 13)

l S C A N DATA/

239X,8HRUN NO. , I6,3X, 14HSPEED ( CM/SEC) , F 8 . 4 / 3 3 8 X , g H P O S I T I O N , 1 ~ 8 , 3 x , 1 5 H C 0 U N T T I M E ( S E C ) , F 6 . 3 / 4 4 1 X , 25HGACK-PLATE CORRECT I ON (CM) , F 8 . 4 / )

WIRE

n

-43 -

1 0 0 3 FORMAT(SOX, 17HMEASURED A C T I V I T Y / )

1 0 0 4 F O R M A T ( 5 O X , 1 7 H S P E C I F I C A C T I V I T Y / )

1005 FORMAT(8H CHAN,8X,3HCMS, 5 X , 1 0 H CTS/SEC , 1 1 1 X, SHERROR, 12X,4HCHAN,8X, 3HCMS, 5 X ,

2 1 0 H CTS/SEC , l l X , 5 H E R R O R / )

lF6 .2 ,3X ,E12 .5 ,6X ,E12 .5 ) 1 0 0 6 FORMAT(5X. I 3 , 6 X , F 6 . 2 , 3 X . E l 2.5,6X, E l 2.5, I O X , I3,6X,

i o 0 7 F O R M A T ~ H I 1 1 0 0 8 F O R M A T ( 7 2 X . 18) 1 0 0 9 F O R M A T ( 4 ( F 6 . 2 , E l 2 . 4 1 , 18)

C C

END W IREDAT

-44 -

SUBROUTINE TMC( ID,SPEC, I R R )

C C**** FOR USE WHEN CHANNEL ZERO CONTAINS DATA OTHER THAN

C T I M E . T H I S PROGRAM READS CARDS PUNCHED V 1 A MARK I V

C AND R E S H I F T S THE CHANNEL ZERO FROM THE L A S T TO THE

C F I R S T . T H I S I S REQUIRED FOR DATA TAKEN I N THE M U L T I -

C SCALER MODE O N THE TMC A N A L I Z E R . C PROGRAM NUMBER 6 4 0 2 0 6 - 0 1 0 1 ( R 0 ) - 1 6 0 4 / 6 3

C D IMENS I O N D A T A ( 4 2 0 ) , S P E C ( 4 2 0 )

C

IRR=O

KCRDm1

M 5 1

L= 1

M L e l O 1 R E A D INPUT TAPE 5 0 . i o o . i I D , I C H N . ( D A T A ( J ) , J = L , M L ) , I C R D

I F ( I I D - I D ) 7 0 , 2 , 7 0 2 I F ( K C R D - I C R D ) 7 1 , 3 , 7 1 3 NCHK=( I C R D - l ) * l O + l

4 I F ( I C H N ) 6 , 7 2 , 7 2 5 M=M+lO

L=L+ lO

ML=ML+lO

KCRD=KCRD+l

GO TO 1

I F ( I CHN-NCHK) 4 . 5 . 7 2

6 I F ( I R R ) 7 3 , 6 1 , 7 3 6 1 S P E C ( 1 ) = D A T A ( 4 0 0 )

DO 7 b 1 . 3 9 9

GO TO 74 7 S P E C ( J + l ) = D A T A ( J )

70 W R I T E OUTPUT TAPE 5 1 , 1 7 0 , ICRD, I I D GO TO 73

7 1 WRITE OUTPUT TAPE 5 1 , 1 7 1 , ICRD. I ID

GT C-OR NL

-45 -

...

b

c

r-,

GO TO 73 72 W R I T E OUTPUT TAPE 51 , 1 7 2 , ICRD, I I D 7 3 l R R = l

GO TO 5 74 RETURN

C

C**** FORMAT STATEMENTS C

100 FORMAT( 16, 1 6 , 1 0 ( F 6 . 0 ) , 18) 1 70 FORMAT ( 3 9 H ERROR ON CARD, 1 3 , 4 H OF , 16,

i 2 6 ~ , I.D. NUMBER DOES NOT MATCH) 1 7 1 FORMAT ( 3 9 H ERROR ON CARD, 1 3 , 4 H OF , 16,

118H,CARD OUT OF P L A C E ) 1 7 2 FORMAT ( 3 9 H ERROR ON C A R D , 1 3 , 4 H OF ,16.

1 1 7 H . CARD PUNCH ERROR) C

END

-46 -

SUBROUTINE T I M E ( T X , S E C )

C C****

C C

CALCULATES THE REQUIRED T I M E S FOR DECAY CORRECTIONS.

PROGRAM NUMBER 6 4 0 2 0 6 - 0 1 0 2 ( R 0 ) - 1 6 0 4 / 6 3 GTC-OR N L

I D A Y = T X / 1 0 0 0 0 0 0 . 0

TEMPI =TX-(FLOATF ( I DAY >*I OOOOOO. o 1 IHOUR=TEMPl / lOOOO.O

TEMP2=TEMPl - (FLOATF ( I H O U R ) * 1 0 0 0 0 . 0 ) I M I N = T E M P 2 / 1 0 0 . 0

TSEC=TEMPZ-(FLOATF(IMIN)*IOO.O) SEC=(FLOATF ( I DAY )*86400 .O ) + ( F L O A T F ( IHOUR )*3600.0

1 + ( F L O A T F ( IMIN)*GO.O)+TSEC

RETURN

C

END

-47-

PROGRAM W I R E D A T 2 C C**** AVERAGES THE SATURATED A C T I V I T Y DATA OVER A ONE

C CM LENGTH AND CONVERTS THE DATA TO THERMAL NEUTRON

C F L U X . C

C**** PROGRAM 6403~5-0100(R1)/1604(63) GTC C

C D I MENS I ON X ( 5001, D A T A ( 5001, SHAPE (5001, XA( 5001,

DATAV ( 5 0 0 1, DATNOR (500) 1 C

C

1 0 0 0 READ READ

1 READ

NPUT TAPE 5 0 , 1 0 0 , NGPS NPUT TAPE 5 0 , 1 0 1 , ( S H A P E ( I ) , 151 NPUT TAPE 5 0 , 1 0 2 , P O S , X M I N , B P C ,

NGPS 1 DENT, NPTS, MOR

R E A D INPUT TAPE ~ O , ~ O ~ , ( X ( I ) . O A T A ( I ) , I=I,NPTS) IF ( B P C ) 2 , 4 , 2

2 DO 3 I = l , N P T S 3 X ( I )=X( I )+BPC 4 TEMPmO.0 $ N=O $ D l V ~ 0 . 0 $ K1-1

DO 1 1 I = l , N G P S

I F (B-X ( NPTS A=XM I N+F LOATF ( I -1 1 $ B=A+I . o

6,5,5 5 B = X ( N P T S ) 6 K2=K1+9

X A ( I )=A+(B-A) /2 .0 DO 9 K=K1 ,K2 I F ( X ( K ) - A ) 9 , 7 , 7

7 I F ( X ( K ) - B ) 8 , 1 0 , 1 0 8 TEMP=TEMP+DATA ( K )

N=N+I $ D I V = D I V + l . O 9 CONTINUE

1 o DATAV ( I )=TEMPID I v DATNOR ( I )=DATAV ( I )*SHAPE ( I 1

-48-

TEMP=O.O $ DIV=O.O $ K I = K l + N $ N=O 1 1 CONTINUE

L2=0

l F ( N G P S - 5 0 ) 1 2 , 1 2 , 1 3

1 1 5 WRITE OUTPUT TAPE 5 1 , 1 0 4 , P O S , IDENT

1 2 L l = l $ L2=NGPS $ GO TO 1 4 1 3 L l = L 2 + 1 $ L 2 = L 1 + 4 9 1 4 WRITE OUTPUT TAPE 5 1 , 1 0 5

I F ( L2-NGPS) 1 6 , 1 6 , 1 5

1 5 L2=NGPS 16 DO 1 7 I = L 1 , L2 1 7 WR I T E OUTPUT TAPE 5 1 , 1 0 6 , XA( I ,DATAV( I ) ,SHAPE( I ) ,DATNOR( I ) , XA( 1 )

I F (NGPS-L2) 1 9 . 1 9 , 1 1 5 1 9 I F ( M O R ) 1 0 0 0 , 1 , 2 0 20 STOP

C C C**** FORMAT STATEMENTS C

C

100 FORMAT( I 3 1 1 0 1 FORMAT(8E10 .4 )

1 0 2 FORMAT ( 1 AS, 2F6.3,3 1 6) 103 FORMAT ( 4 ( F 6 . 2 , E 1 2 . 4 1 1 0 4 F O R M A T ( 6 9 H l

1 NEUTRON F L U X / 6 7 H

2 VERT I CAL T R A V E R S E / / s b H 3 L O C A T I O N , 1 A 8 , 6 H RUN ,161

1 0 5 FORMAT(86HO X ACT I V I T Y

1 0 6 FORMAT(27X, F6.3.3 ( 5 X . E 1 0 . 4 ) , 5 X , F6.3) 1 ACTOR F L U X X / / 1

C

THERMAL

F

C

END W IREDAT2

-49-

PROGRAM LOMEGA

C**** CALCULATES THE REDUCED S O L I D ANGLE FOR A L I N E SOURCE

C LOCATED ALONG THE DIAMETER OF THE COLLIMATOR ENTRANCE C APERTURE.

C**** THE ASSUMPTION IS MADE THAT, FOR SMALL DISPLACEMENTS C FROM THE COLLIMATOR A X I S , THE S O L I D ANGLE MAY B E

C O B T A I N E D FROM THE EQUATION C OMEGA(X) = OMEGO"(1 . O - A * ( ( X / R 2 ) * * E ) )

C WHERE

C X = D I S T A N C E FROM COLLIMATOR A X I S C R 2 = COLLIMATOR R A D I U S A T E X I T (DETECTOR) C OMEGO = S O L I D ANGLE AT THE COLLIMATOR C A X I S ( S E E T I D 1 4 9 7 5 ) C**** OTHER I N P U T SYMBOLS

C R 1 = COLLIMATOR R A D I U S AT ENTRANCE (SOURCE) C Z = D I S T A N C E FROM COLLIMATOR ENTRANCE C C L = COLLIMATOR LENGTH C X l N C = INCREMENT OF DISPLACEMENT C

C**** PROGRAM NUMBER 640203-0100(R1)/1604(63)

500) , RHO

NC, OMEGO E , A , IQU I T

B E T A l = l . O + ( C L / Z ) $ B E T A 2 = B E T A l - I . O AREA=3.1415927" (RZ**Z) $ ALPHA=1.5707963*(((Rl*BETAl)**Z)+(RZ**Z)) R O = ( B E T A l * R l - R 2 ) / B E T A Z $ R M = ( B E T A l * R l + R 2 ) / B E T A Z $ R=RO*RM RB l = B E T A Z / ( Z . O * B E T A l "R 1

R R l = ( R l * B E T A l ) * * Z $ RRZ=R2*"2 $ K L I M = R O / X I N C DO 1 I = l , K L I M X ( I >=X I NC*FLOATF ( I A X ( I )=AREA

$ RBZ=BETAZ/ (Z.O*RZ) $ RB3=R 1 " B E T A l " B E T A 2

i RHO(I)=I.O

-50-

L I M=F LOATF ( K L I M)+ ( ( 2.O*R2 / ( B ETA2"X I NC) $ L=L I M+l K K = K L I M + l $ K K I = K K + l $ X(KK)=RO $ X(L)=RM F 1 ( K K ) = l .O $ F 2 ( K K ) = - l .O $ F 1 ( L ) = l .O $ F 2 ( L ) = 1 . 0 0 DO 2 l = K K l , L I M

K= I -KK x ( I )=RO+FLOATF(K)*XINC Fl(I)=RBl*(X(I>+(R/X(I)))

2 F 2 ( I ) = R B 2 * ( X ( I ) - ( R / X ( I ) ) ) DO 3 I = K K , L

AX( I )=ALPHA-RB3*X( l ) *SQRTF( l .O-F1 (I)**2)-RRl*ASINF(Fl(I)) 1

3 RHO( I su M=o DO 7 I F ( I -

4 DELX( GO TO

- R R 2 * A S I N F ( F 2 ( 1 ) ) = A X ( I ) / A R E A 0 = l , L

) = X I NC 6

)5,4,5

5 D E L X ( I )=x ( I 1-x( 1-1 1

SUM=SUM+RHO( I )*OMEGA( I ) *DELX( I 1 6 OMEGA(I)=OMEGO*(l.O-A*((X(I)/R2)**E))

7 CONTINUE WRITE OUTPUT TAPE 5 1 , 1 0 0 1

WRITE OUTPUT TAPE 5 1 , 1 0 0 2 , R l ,R2,CL,Z ,SUM

K l m l $ K2a.50 8 WRITE OUTPUT TAPE 5 1 , 1 0 0 3 9 I F ( K 2 - L ) 1 1 ,l 1 , 10

1 0 K2=L

1 1 DO 1 2 I = K l , K 2 1 2 WR I TE OUTPUT TAPE 5 1 , 1 0 0 4 , X ( I 1, AX( I ,RHO( I ),OMEGA( I 1, X ( I

I F ( K 2 - L ) 1 3 , 1 4 , 1 4 1 3 K l = K 1 + 5 0 $ K 2 = K 2 + 5 0

WRITE OUTPUT TAPE 5 1 , 1 0 0 5 GO TO 8

1 4 I F ( I Q U I T ) 7 3 , 1 0 0 , 7 3 73 STOP

1

-51-

t

C

C**** FORMAT STATEMENTS C

1000 FORMAT(bF8.4, F6.3, E 12.6.2F7.4, 13) 100 1 FORMAT ( 70H 1

10R SOLID ANGLE/64H

2 L INE SOURCE) 1002 FORMAT(48HO

110H R2=. F7 .4 / 248H

3 Z=, F7.4165.H 4SOLID ANGLE=,E10.5)

1003 FORMAT (86HO

1004 FORMAT(29X,F6 .4 ,3X ,E10 .4 ,2 (6~ ,~10 1 RHO OMEGA X / 1

i o05 F O R M A T ~ H I 1 C

C

END LOMEGA

X

4 ) ,2X,F6.4)

COLL IMAT

R 1 = , F7 .4 ,

L=,F7.4,10H

INTEGRATED

AREA

L

".

.

ORNL-3759 UC-34 - Physics

TID-4500 (37th ed.)

I"AL DISTRIBUTION

1. Biology Library 2-4. Central Research Library 5. Reactor Division Library

6-7. ORNL - Y-12 Technical L i b r a r y Document Reference Section

8-57. Laboratory Records Department 58. Laboratory Records, ORNL R.C. 59. E. P. Blizard 60. T. A. Butler 61. C. D. Cagle 62. G. T. Chapman 63. R. D. Cheverton 64. W. H. Cook 65. R. A. Costner, Jr. 66. J. A. Cox 67. F. F. Dyer 68. R. L. Ferguson 69. E. B. Johnson 70. W. H. Jordan 71. B. C. Kelley 72. L. Jung 73. C. E. Larson

74. M. Leimdorfer 75. G. H. L l e w e l l y n 76. W. S. Lyon 77. H. G. MacPherson 78. F. C . Maienschein 79. B. F. Maskewitz 80. J. M. Mil ler 81. R. Pee l le 82. J. J. Pinaj ian 83. J. W. Poston 84. C. A. P re sk i t t 85. R. T. Santoro 86. M. J. Skinner 87. L. E. Stanford 88. W. J. Stelzman 89. J. G. Sul l ivan 90. D. K. Trubey 91. A. M. Weinberg 92. R. C. Weir 93. G. Dessauer (consultant) 94. M. L. Goldberger (consul tant) 95. R. F. Taschek (consultant)

EXTERNAL DISTRIBUTION

96. A. M. Sarius, Centro D i Calcolo, C", V ' a Mazzimi 2, Bologna, I t a l y

97. V. B. Bhanot, Physics Department, Panjab niversity, Chandigarh-3, India

98. Research and Development Division, AEC, OR0

I 99-743. Given d is t r ibu t ion as shown i n TID-4500 (37th ed.) under Physics

category (75 copies - CFSTI)