Some neutron resonance-absorption integrals

J. Nucl. Energy, II 1959. Vol. 9. pp. 20 to 27. Peqamon Press Ltd., London. Printed in Northern Ireland

SOME NEUTRON V. B.

RESONANCE-ABSORPTION INTEGRALS* and V. M.

KLIMENTOV

GRIAZEV

(Received 10 May 1958) Abstract--Observed resonance abs,orption integrals are reported for 42 elements, ten of which have not heen examined hitherto. The method involves an accurate measurement of the reactivity of a reactor when the specimen is inserted into the core, and gives the resonance absorption integral for the epicadmium spectrum of the reactor.

THE

REACTOR

DURING the years 1955-6 we carried out a series of measurements of neutron resonance-absorption integrals using a swimming-pool reactor. The reactor consisted of a heterogeneous system of enriched uranium, containing 10 kg of 235U in a core of height 60 cm and critical radius 35 cm. Ordinary water was employed, and the ratio of the numbers of nuclei of hydrogen and mu was ~330; the reflector was composed of natural uranium in addition to the ordinary water. The uranium rods were situated at the vertices of equilateral triangles of side 5.2 cm. In the centre of the core, the cadmium ratio indicated by a 0.05 g cm-2 gold foil was 3.18. The reactor was operated at low power levels, corresponding to thermal neutron fluxes at the centre of less than 108cm-2sec-1. The automatic flux-recording and control system made it possible to use it as a measuring instrument. When one of the two pairs of boron-loaded control rods was fully withdrawn from the core, the other pair remaining in position, the power level rose with a period which may be called T. The reactivity p is determined by the doubling time T as indicated by a potentiometer reading of the current in an ion chamber. As shown in Pile Neutron Research,(l) /

204

535 2036 0~62+~+~+2~19+~+6~50+~+31~7+~+80~3 20’3

787

with T = 144T. In our experiments the reactivity was in the range (35-30) x 10-5, corresponding to doubling times between 162 and 190 sec. Non-linear effects such as poisoning and the temperature effect were insignificant at the low powers employed. The reactivity was, moreover, independent of atmospheric pressure. The excess reactivity was such that accuracy of measurement was Ap = &O*OSx 1O-5 with the specimens employed, this figure being. fixed by the uncertainties of determining the doubling time. A cadmium tube of wall thickness 6 = 0.5 mm was inserted into the central cell of the core and functioned as a neutron filter, being effectively opaque to neutrons of energy below 0.49 eV.(2) METHOD The resonance absorption integrals were determined by measuring the change in reactivity when a specimen was introduced into the middle of the core. In practice,

* Translated from Atomnaya

Energiya 3, 507 (1957). 20

Some neutron resonance-absorptionintegrals

21

the effect of the specimen alone was obtained as the difference Ap between the reactivities observed with the prepared sample and with an empty ahuninium container. This method, R3) of course, depends on the linear relation between reactivity and the

I

0

1

2

3

Microscopic I-The 2-The

4

5

6

absorption cross-section

7 NV&,

cm-’

FIG. 1.-Calibration of the reactivity. effectiveness of specimens containing different amounts of Li,CO,, without taking into account neutron slowing down. same results after applying aApo correction = Ap _ AfP.,or the effects of slowing down:

macroscopic absorption cross-section concerned. Experiments with a number of samples containing different concentrations of L&CO, indicated that Ap = BNVJ, + C, with B = 0.684 x 1O-5 and C = 0.16 x 10-5. In this equation, N is the number of 2.0

30

40

50

60 Height,

Fig. 2.-The

70

80

90

cm

diminution in reactivity caused by a specimen of graphite in the tube. (&VJ, = 21 cm-l).

nuclei cm-3, Vis the volume in cm3 and J, is the resonance absorption integral in barns. C is not zero, because the specimen is itself effective in slowing down neutrons, so that those which are scattered from it are somewhat more easily absorbed in the cadmium than before. The observed magnitude Ap is therefore the sum of two parts, Ap, due to true absorption and a term Aps which arises from scattering.

22

V. B. KLIMENTOV and V. M. GWEV

The significance of neutron slowing-down in the specimen can be judged from Fig. 2, which shows the diminution in reactivity brought about by a graphite sample situated at various heights within the cadmium tube. Naturally the effect is greatest when the graphite is in the centre of the core. The correction for neutron slowing down which was required in the subsequent absorption-integral measurements was determined experimentally. Various amounts of weakly absorbing scattering materials such as graphite, BeO, MgO, NaBiO, and PbO were added to specimens containing a constant quantity of the substance under investigation. There was virtually no absorption in the filling material, and the geometry of the experiments remained unchanged. Fig. 3 shows results obtained in this way for antimony, iodine, strontium,

0

1

2

3

4

5

Slowing-down FIG. 3.-The

reactivity

6 power,

7 SNVJ,,

8

9

10

II

cm-1

change as a function of the slowing-down cross-section The absorbing power NVJ,is constant. l-antimony; 2-iodine; 3-strontium; 4-titanium; 5-zinc.

of the specimen.

titanium and zinc. It was found that the reactivity loss was linearly proportional the scattering power: Ap = At-NVJs + D,

to

with A a constant of proportionality, E the mean logarithmic energy loss per collision in the appropriate moderator, and J, the resonance scattering integral in barns. D = Ap, is the term giving the true absorbing power of the specimen. A and D were derived by a least-squares fit to the complete collection of data, using values of J, given in Table 1. A was in fact the same for all the elements studied, and came to (0.070 + O-030) X 10-6. The final corrections ApS were small; a macroscopic crosssection of &VJ8 = 1 barn cm-3 gave rise to Ap, = 0.07 x 10m5. All samples were carefully dried to exclude the possibility of neutron slowing-down by adsorbed water. Elastic neutron scattering fr0m.a specimen in the centre of the core, being isotropic, had no effect on the experiments. For the elements with strong resonances a preliminary investigation was necessary to ensure that self-screening did not influence the results. Figs. 4, 5 and 6 show measurements of Ap for indium, hafnium, silver, osmium, wolfram and bromine as a function of the concentration of these substances; the linear dependence is found over a limited range only. When the substance is strongly absorbing, quite small amounts

Some neutron

23

resonance-absorptionintegrals

of material are needed for a reliable measurement; for example only 50 mg of the compounds of In and Sm was required. The desired absorption integrals were derived by comparison with the results of Fig. 1 for lithium, whose absorption cross-section is well known. A value of J, was TABLE 1. -VALUES

FOR NEUTRON

SCATTERING RESONANCE INTEGRALS

Js

Element ! /

J,

Li B

where

J Be F CU 0 Mg N K Fe

Bi Pb Na V

Mn co Br Sb J IfJeW

70 50 64 59 65 80 31 78 179 200 51 190 425 435 9.2 36.3 53 1330

=

z’loBu dE 8E

f 0.49

25 63

ugJ.i= 1.4 barn uBB= 4.5 barn@)

Approximate calculation Appi-oximate calculation Approximate calculation Approximate calculation Approximate calculation Approximate calculation Approximate calculation Approximate calculation Approximate calculation Approximate calculation Reference w Reference (IX Reference (W Reference (Q Reference 16) Reference ~1 Reference M) Reference w

according according according according according according according according according according

to to to to to to to to to to

equation equation equation equation equation equation equation equation equation equation

(5) (5) (5) (5) (5) (5) (5) (5) (5) (5)

calculated for lithium on the basis of a thermal neutron absorption of oT =-; 71-O f 1-Obarns.“) Nine specimens containing different amounts of Li,CO, were used, and after correcting the observed effects for neutron slowing-down a least-squares fit to the straight line 2 in Fig. 1 gave Apa = (0.674 f 0*068)NVJ, x 10-j or J, = (1.48 & 0.15) FAPlZ x IO5barns. A number of measurements were taken with different amounts of the substance under investigation, where possible in different states of chemical combination, and a weighted average was taken for the final figure. The accuracy is determined by the errors in measuring Ap and in the lithium calibration, by the accuracy of the correction for neutron slowing-down and for the absorption of other nuclei present in the specimen. The reliability indext8) was 0.7.

V. B. KLWWTOV and V. M. GRIAZEV

24

Total number

of nuclei,

NVxlO-*’

FIG. 4.-The

reactivity

change induced by (1) indium and (2) hafnium concentration of these nuclei in the sample.

FIG. 5.-The

reactivity

change induced by (1) silver and (2) osmium concentration of these nuclei in the sample.

Total number of nuclei,

o-01

0.02

0.03

Total number of nuclei, FIG. 6.-The’rcactivity

as a function

of the

as a function

of the

NVxlO-*’

0.04

15

NV x10-24

change induced by (1) wolfram and (2) bromine concentration of these nuclei in the sample.

as a function

of the

Some neutron resonance-absorption TABLE

Z.-OBSERVED

NEUTRON

ABSORPTION

I

Li

i Li2C03 I

32.2 1 0.6

B

Na2B4G7

N

‘-Pwo&

F ~_. Cl K

4.8 & 2.4

Calculations, using(%, = 71 2: 1 barns

I

2.3 & 0.5 KC1

K&G,

12.8‘1 1.7

12

3.5 & 1.1

1.1

3.8 z 0.9

Ti

/

3.3 5 0.8

Cr

Reference for column 4

Calculation, using%, =I55 _i: 3 barns

NaF BaCl,;

r__

INTEGRALS

Resonance absorption integral according to other authors

Resonance absorption integral (barns)

Chemical compound

Element

RESONANCE

25

integrals

Cr,G,

1 Reference@)

3.0

Reference@)

2.2

2.6 :I: 1.1

1.9

ReferenoP

10.8 11.9

Referetw@ Referenc&) ReferenoP)

-

Mn 55Mn

Mn; MnO,

11.7 i 1.5

Fe

Fe; FeaOs

2.3 f 0.4

2.3 f 0.25

co

co203

38.3 i 4.0 -

48 49.3

3.2 + 0.5

4.0

-

s9co

/

Reference@) Reference(*) ,--

Ni

j Ni

cu

’ cue;

C&O

3.7 :r: 0.8

9Yzu 59cu Zn

; ZnO

Ga

! Ga

59Ga 71Ga

/

Ge

/ Ge

, I

Reference”)

’ I

4.4 2.2

3.4 f 0.8

1

2.0

11.7 rt 2.7

/

Referencet2) Referenceo) I

/

Reference(a1

I---9.2 1.50

Reference’z) Referencer2’

3.5 f 2.9

I

Se

,Se

9.6 _c 1.2

I

Br

I ,

118 f 14

I I

‘OBr

NaBr

I 147

Referem@)

V. B. KLIMENTOVand V. M. GRIAZN

26

TABLE 2.-continued

I Element

Resonance absorption integral (barns)

Chemical compound I

I

Rb

i RbCl;

Sr

i SrCO,;.Sr(NO,),

RbNOs

Zr

Zr .

MO

MO; MoOI

/

I

9.0 5: 2.8

’

10.0 ::- 2.6

16

I I II

3.7 5 0.5

3

13.8 :k 1.7

Ag lO’Ag lOQA g

( AgCl

466 f 70

In

, In@, !

2220 & 300

Sn

Sn

5.7 & 0.7

Sb %b l”Sb

Sb,G,

106 f 13

Te

Te

llaIn

Resonance absorption integral according to other authors __-.__ ~

/

I

/ I;KI I

1

106 f 12

‘B?I

I

cs

cs,co,

Ba

BaCO,

Ce

CeO,

3.7 i 1.7

Sm&

1790 f 270

Sm ls*Sm

j

Gd

i Gd

Hf

169 f 28

/

_-_

Referenc# ReferenoPi Referencecar

650 74 1160

Referen& Referenceor Referemx+

1050 2640

ReferenoP Reference@’

4.3

Reference(a’

162 138

RefererxxP Reference(*)

36

Reference(2)

90 130 140

Reference’2) Reference’9’ Reference’*’

j I

7.5

Reference(z)

1750

Reference(~)

1750 1300 21.8

Reference@’ Referenc&) Reference@’

590

Reference@’

170 355

’ Reference@’ i Reference@’

67.0 f 8.0

HfF,

1470 f 200

1 I

474 f 62

Tag%

HeWOh;

I

13.0

j

12.6 f 1.7

lsOHf Ta lBITa

column 4

I ._

/

l141n

50.0 f 6.0

I 1 Referencefor j

WO,

/

290535

I

Some neutron resonance-absorption

21

integrals

TABLE2.-continued I

Element

Chemical compound

Resonance absorption Resonance absorp1 integral according to tion integral (barns) : other authors

Reference for column 4 I /

OS

180 i: 20

OS

Ir 1911r lo3Tr

._~_

I

I

!

Th

i ThOZ

U

/ u,os;

._ -

-.._--

2000 -4 490

Ir

Hi?

238~

-

_--

- . ._ _._.__-

I

HgO

uo,

I

3500 1370

Referencef2’ Reference’2) Referenceol Reference”‘)

72.4 1- 8

: ! I

31 73

61.8 -c 12

j

69.8

224 _!- 40

’ 282

I

:

Reference12)

/ 1 Referencet2’

RESULTS Our results appear in Table 2, together with those of other workers where appropriate. In general, there is good agreement between our measurements and the values in the literature. Our results for cobalt, strontium and silver are somwhat smaller than those of MACKLIN and POMERANCE, t21although in agreement with SPIVAK et uZ.(~) the figure for mercury is considerably higher. On the other hand, our values for hafnium and iodine differ from what was found by SPIVAK(‘)and agree with those which MACKLIN and POMERANCEf2) obtained integral for zirconium

is corrected

using a pile oscillator.

for a hafnium

impurity

The absorption

of O-04 per cent by weight.

Acknowledgements-We are greatly indebted to E. D. BOROBEV for his continued interest in the work, to V. B. MUZRUKOVfor making it possible to carry out the experiments at the reactor, and to E. A. SAVELEVAYA for assistance with the calculations.

REFERENCES 1. HUGHESD. J., Pile Neutron Research. Addison Wesley (1953). H. S., Proceedings of the International Conference on the Peaceful 2. MACKUN R. L. and POMERANCE Uses of Atomic Energy, Geneva 1955, Vol 5 p. 96. United Nations (1956). H. C., Phys. Rev. 74,851 (1948). 3. WEINBERGA. M. and SCHWEINLER 4. Ross M. and STORYJ., Rep. Progr. Phys. 12,291 (1949). 5. ADAIR R., Rev. Mod. Phys. 22,249 (1950). C. 0. and THOMMAS G. E., Phys Rev. 79, 11, (1950). 6. HARRISS. P., MUEHLHAUSE 7. HUGHESD. J. and HARVEYJ. A., Neutron Cross-sections. McGraw Hill (1955). 8. ROMANOVSK~I V. I., Fundamentals of the Theory of Errors. Gostekhizdat, Moscow (1947). B. G., DOROFEEV G. A. and LAVRENC~IKV. N., Proceedings of the 9. SPIVAKP. E., EROZOLIMSKII International Conference on the Peaceful Uses of Atomic Energy, Geneva 1955, Vol. 5 p. 91. United Nations (1956).