Resonance absorption in the power station reactor

J.

Nuclear

Energy

II, 1958. Vol. 6, pp. 345 to 350.

Pergamon

Press Ltd., London

RESONANCE ABSORPTION IN THE POWER STATION REACTOR* Z. I. GROMOVA, B. G. DUBOVSICY, A. V. KAMAEV

and V. V. ORLOV

(Received 2 November 1956) Abstract-One of the important quantities governing the conditions of a chain reaction in a uraniummoderator system is the probability (1 -p) that the fission neutrons will undergo resonance absorption during the process of slowing down. At the present day (1 -p) cannot reliably be calculated for heterogeneous reactors, so that it has to be determined experimentally. Methods of measuring it are discussed, and the corrections which must be applied for neutron leakage, uranium fission and resonance capture are considered. These corrections are substantial in the case of the power station reactor, which operates with uranium containing 5 per cent 235U. The resonance escape probability p for this reactor is calculated by three methods and found to be 0.900 rt 0.015. METHOD THE

basic experimental datum for a measurement of the resonance escape probability

FIG. 1. The neutron

balance in a reactor. U, is the leakage probability the other quantities are defined in the text.

for thermal

neutrons;

in a given reactor is the ratio R/T, where R is the number of resonance neutrons and T the number of thermal neutrons captured by 238Uper second.(i) In combination with certain other data this ratio allows p to be calculated in the following three ways. (1) Suppose that the number of fission neutrons created per cm3 set in a lattice cell be Q. Then the slowing-down density at the energy E is the product Qp(E)@(E), where O(E) is the probability that the neutron has also escaped capture in 235U, in the constructional materials, and has not leaked from the reactor. If it be assumed that O(E) varies only slowly with E, and that the absorption in 238Uessentially occurs only in the narrow interval between 6 and 200 eV, then

p

R i

Q@(g)

. (1 - p),

(1)

@(E)

being that fraction of the fast neutrons Q which is slowed down to the energy at which resonance absorption in 238Ubecomes effective (Fig. 1). The thermal-neutron-induced activation of 238Ucan be written in the form 0.4 eV

TS *

s0

(nv)U%23,(E)

dK

Translated by R. D. LOWDE from Atomnaya Energiya 2, 411 (1957). [Reprint No. AE109.1 345

346

Z. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEVand V. V. ORL~V

in which (nv), is the thermal neutron flux in the uranium and &233 is the macroscopic absorption

cross-section

of 233U. Thus

R T

Q@(E)

s

-z

@4

(N u &233(E)

0

Q is related to the thermal

-(1 - p)

neutron

(3)

dE

flux by

Q = bdS(hA~~(E) -dE}[l+ WTM where ,u is the fast neutron multiplication per fission, Xf235 the macroscopic

uranium reactors

Y the number of neutrons created

fission cross-section

of the 235U fissions that is induced the fact that a substantial

coefficient,

by epicadmium

part-between

(4)

of 235U, and

neutrons.

10 and 20 per cent-of

takes place at energies above O-4 eV.

(R/T), is that part

Equation

(4) allows for

the fission in enriched

It follows that

%a238 y$%235[1

(3

+ (W)$‘(~)

*

cross-sections for absorption in 233U and %233 and %235 here are the macroscopic fission in 235U averaged over the spectrum of sub-cadmium neutrons at the appropriate temperature (2) A

and with allowance somewhat

RADKOVSKY.‘~)

for departures

different

The number

expression of neutrons

from the l/u law.

for p has

been

ECd = 0.4 eV, the absorption limit of cadmium, is Qp@(&,). neutrons

absorbed

used

by KRASIK and

per second slowed down to energies below

in 238U is related to this quantity

The number of thermal

by

0.4 ev

Here

PCd is the probability

region

that a neutron

of energies, f is the thermal

thermal

neutron

. dE = QPWC&‘,,P

W,&233(E)

s0

absorption

coefficient,

F is that part of the Fare defined by

f and

.dE

(n%F&)

s

and

which is due to 233U.

0.4 ev

.

(6)

will not leak out of the cell in the thermal

utilization

in uranium

.

f= 00.4eV 1 W,&dE) ,O

.dE '

0.4 ev (nZ))&a238(E)

s

F=

O cl.4ev (%,&z,(E)

s0 EC,,

is the macroscopic

scopic

cross-section

materials.

absorption for neutron

Substituting

. dE dE

cross-section absorption

'

of uranium, in uranium

and Xatot is the macro-

and in the constructional

(6) in (3),

TIR

’=T/R + fWE,,Pc#W) W%3f’cdW) gives

the reduction

in the number

(7)

* of neutrons

at thermal

energy,

Resonance absorption

in the power station reactor

347

compared with the number at the energy E where the preponderant part of the resonance absorption occurs. Capture and leakage are responsible for this reduction. a(,!?) may be written in the form P(&@), in which P and x are respectively the probabilities of escaping leakage and of escaping capture by 235U and the constructional materials while slowing down to the resonance energy of 238U. x can be estimated from the known nuclear cross-sections and resonance integrals. (3) p may also be determined by comparing R/T for uranium with the value obtained for a resonance detector having a known resonance absorption integral and a known cross-section in the thermal region. Writing E, for the resonance energy dE

E for its resonance absorption

of the detecting substance and

integral,

In (8), 6 is the mean logarithmic energy loss per collision and ES is the macroscopic scattering cross-section of the moderator; (nv) is the thermal neutron flux. For uranium R QW%1 - P) (9) T = 04eV 0 238

I

0

Wh,~,,,~a,,,W

dE

’

in which N238is the number of 238Unuclei cm-3 and a,,,, the absorption cross-section of =IJ. Thus

-=-.

0

PE)

;$3

1-P

s

@4 eV (nvhJN23,%23,(E)

0

0.4

j-

dE (10)

ev

nvo,,(E) dE 0

MEASUREMENTS

The number of neutrons absorbed in 238Uwas determined from the #?-activity of 23gU as follows: =sIJ + .--+239u- 23’5min 8. Y

239Np

2.3

days+

230pU.

BY

R/T was derived from measurements on bare and cadmium-wrapped uranium, a cadmium thickness of O-25 mm being chosen to fix the effective upper limit of the absorbed range of energies at 0.4 eV. As shown in Fig. 2, the specimen consisted of a length of uranium especially inserted into a fuel rod. The sample and holder were designed to be an exact copy of the uranium fuel element normally used in the reactor, and were exposed in a hole similar to a fuel-element hole; the results for p therefore apply to the actual lattice under working conditions. Determination of R The cadmium-encased specimen was loaded into the reactor together with iodine and indium detectors which served to monitor the integrated exposure. A ten-minute

348

2. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEV and V. V. ORLOV

irradiation was then made at 1 kW, after which the material was processed chemically to purify it from fission fragments and natural decay products. The specimen was dissolved in concentrated nitric acid and two successive ether extractions performed. (Uranyl nitrate, UO,(NO,), is very soluble in ether, a fact which is also the basis of a purification method in which the nitric acid salt of uranium is recovered from aqueous solution by the addition of ether.) The ,@activity of 239U in the purified

L (a) FIG. 2. Specimens,

(b)

1

of segments of. a. fuel rod; (a) uncovered, and (b) encased m cadmium. 2-the specimen; 3-water; 4-the cadmium cover.

consisting

l-uranium;

solution was measured by a cylindrical p-counter in standard geometry. Measurements were made throughout three to four decay periods as a check on the purification procedure. Since a half-life of 23.5 min was obtained, in agreement with the figure for 239U, the purification would appear to have been entirely satisfactory. Determination of R + T The procedure described above was carried through again with an uncovered specimen, yielding a uranium solution whose activity was proportional to R + T. R/T was derived from the above results after normalising to the same integrated exposure and applying a correction for the differing amounts of uranium in the two solutions. Ten series of measurements were made in the central fuel channel of the reactor, and gave a figure R/T = 1.67 + 0.03. The quoted error is the standard deviation. Control experiments Measurements were made with a view to detecting a possible effect of cadmium thickness on the figure for p. With the experimental arrangement employed this effect was in fact negligible. A measurement at the boundary between the core and the reflector gave the value R/T = 1.2. As might have been expected, this figure is smaller than in the centre of the reactor, because the presence of the reflector enhances the thermal component of the neutron spectrum. Another measurement made in a lattice cell between two of the boron compensating rods gave R/T = 1.9. These observations serve to underline the fact that a reliable measurement of p must be made in a region where the neutron spectrum has its equilibrium shape. The central cell of the reactor is sufficiently far from the absorbing rods to satisfy this condition.

Resonance absorption

in the

power station reactor

349

RESULTS

Results obtained by taking the three methods of calculation in turn are given below. (1) Into equation (5) were inserted the following constants:

Here the first factor on the right-hand side is the ratio of the appropriate crosssections after averaging over a Maxwell spectrum for a temperature* of 500”K, while the second is the ratio of the number of nuclei cm-3. (D(E) = P(E)x(E) = 0.8.

/L= 1;

v = 246;

P(E) was calculated from the formula P(E) = exp [-K%-(E)], and K(E) was estimated from the cadmium ratio for fission capture and from the resonance integrals of the absorbing substances present in the lattice cell. (R/T)f was obtained by measuring the cadmium ratio, which came to 12, of a 235U foil exposed in the central hole of the reactor. It is found thatp = 0.906. The error in this figure is principally due to inaccuracies in the above constants and in the estimate of neutron leakage; we estimate it to be l-5 per cent. (2) Using the values

@(Ed qiF)=.

PCd= 0.955;

go5.

0

f = 0.74;

’

F = 0.108

formula (7) gives p = O-90. The good agreement between this figure and that derived from equation (5) suggests that the estimates of neutron leakage and capture have been made correctly. (3) To apply method 3 we have used a resonance detector consisting of gold. The resonance energy of gold is 4.91 eV, which is below the first level of 23sU(6.7 eV); thusp(4.91 eV) may be considered to be identical withp(0.4 eV), and in formula (lo), p(E,) can be replaced by p. The measurement of (R/T)‘38 = I.67 was taken wirh an actual fuel element so as to reproduce the working conditions of the reactor. To ensure that the cadmium ratio observed with gold maintained these conditions a foil thickness of 10 mg cmW2 was employed, which is thin enough not to distort the neutron flux. A figure (R/T), = 2 was obtained for a position in the moderator. The mean neutron flux in the fuel element is 85 per cent of that in the moderator. Thus assuming that the cross-sections of both 238U and Au follow the (I/v) law in the thermal region, the second factor in (10) should be written

o*85aa238N238

. Since

OAU E,

+

17,

Q(E)

&

(D(E,) and (10) reduces to R

1 --p

P

=

0 F

0T

* The neutron 6

temperature

238

R

.

o-85%a238N238

~guG5 Au

was measured

by E. F.

MAKAROV.

m

(11)

Z. I. GROMOVA,B. G. DUBOVSKY,A. V. KAMAEVand V. V. ORLOV

350

These constants

were used:

s

dE (TaAll- = 1300; 0.4ev E 03

uA,~=95;

all values being in barns. per 23sU atom.

The agreement

us is the scattering

cross-section

between these three determinations

principles

are sound.

bility in the power station reactor

of factors

combine

enrichment

of the uranium, in the core.

and an unusual

POMERANCHUK,(~) taking -account Our methods We

are

amount

of absorption

The result agrees satisfactorily

by EGIAZAROV’~) and

of the elaborate

of dealing with the various complications

in other reactor continued

given

escape rather

high neutron leakage,

For these reasons p has not been deter-

better than I.5 per cent. formulae

of resonance

There is a comparatively

mined to an accuracy

from

escape proba-

REMARKS

materials

calculated

may be taken to indicate that

to make a measurement

due to constructional figure

expressed

is 0,900 & 0.015.

difficult in the power station reactor. a considerable

of the moderator

A mean figure for the resonance

CONCLUDING A number

F=&rs=216; 238

(1 l), p = 0.89 + O-02.

From

the underlying

~~s=2.8;

geometry

with a

by GUREVICH and of the fuel element.

may conceivably

be of interest

calculations.

greatly

indebted

to Dr.

A. K.

KRASIN for valuable

interest in the work and for assistance

also due to M. E. MINASHIN for helpful remarks,

in carrying

advice,

it through.

for

his

Thanks

are

and to the staff of the power station

for their co-operation. REFERENCES Conference of the U.S.S.R. Academy of 1. EGIAZAROV M. B., DIKAREVV. S. and MADYEEVV. G. Sciences on the Peaceful Uses of Atomic Energy, Moscow, 1955. Physical Sciences Division. English language edition p. 59. Consultants Bureau, New York (1955). 2. KRASIKS. and RADKOVSKY A. Proceedings of the International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1955. Vol. 5, p. 229. United Nations (1956). 3. GUREMCHI. I. and POMERANCHUK I. YA. Ibid. Vol. 5, p. 466.