Cadmium correction factors of several thermal neutron foil detectors

Journal of Nuclear Energy, Vol. 27, pp. 677 to 688. Fxreamon Press 1973. Printed in Northern Inland

CADMIUM CORRECTION FACTORS OF SEVERAL THERMAL NEUTRON FOIL DETECTORS Atominstitut

K. MUECK and F. BENSCH der Oesterreichischen Hochschulen, Vienna, Austria

(First received 19 September 1972; in revisedform 26 April 1973) Abstract-If theepithermal activation CeP of a foil detector is derived from its epicadmium activation Cc& the knowledge of the cadmium correction factor FCd = CeP/CCd is usually required. The cadmium correction factors of V, B, rOB, In, Au, Mn, Co, and Dy foil detectors of thickness O0.25 mm and cadmium cover thicknesses of 0+,0.8,1.0, and 1.2 mm have been numerically evaluated according to the most recent cross-section values and resonance parameters. FCdvalues are listed for both monodirectional and isotropic neutron incidence. While for most of these materials no results have been published so far, for gold and indium the results could be compared with previous calculations and measurements and a discussion of the results is given. Sincethe Fca values, particularly for Mn, Co, and Dy, exceed unity considerably, neglecting this correction is not tolerable with precise measurements of the thermal neutron flux density. Comments on the use of Fad values in the Westcott convention are added. INTRODUCTION THE absolute measurement of a thermal neutron flux density vtm is reduced to the determination of the proportional neutron absorption rate C,, of a suitable material. The usual method consists of subtracting the absorption rate Cc, of a detector foil covered with a cadmium sheet (thickness d cd > 0.5 mm) from the absorption rate C of an equivalent foil without Cd sheet. A sufficient thick Cd filter absorbs all thermal neutrons and-inevitably-a small part of the epithermal neutrons in the range Therefore, a correction factor Fed = between O-1 eV and 0.6 eV (approx.). Ce,/Ccd > 1 is introduced to take this effect into account: C,, = C- FCdCCd. C,, is the contribution of epithermal neutrons to the absorption rate of the uncovered foil. This procedure is valuable in cases where the use of very thin foils is difficult or impossible (e.g., extremely low neutron intensities). In other cases where extremely thin foils may be used, the Westcott convention is applicable, but in this formalism the quantity desired-the thermal neutron flux density-is determined in another way without explicit knowledge of Fed factors. In the following, we confine ourselves to plane foil arrangements. Absorptions in the detector material may cause activation (with the exception of boron). The value of Fc, depends upon

1. the thickness dcd of the Cd filter [this material being characterized by the macroscopic absorption cross-section &d(E)], 2. the thickness d of the detector foil [the material characterized by the macroscopic cross-sections X,(E) and E;,,,(E)] concerning absorption and activation, respectively, and 3. the directional distribution of the neutrons, e.g. monodirectional neutron incidence or isotropic neutron incidence. We assume the following energy distribution y(E) of the neutron flux density:

dE) =

E 9th

(kT)2

According to the usual nomenclature,

exp

(1)

prp is the epithermal neutron flux density per 611

K. MUECKand F. BEN~CH

678

logarithmic energy unit. A@/kT) is the joining function of COATES(1961), represented analytically by (BENSCH,1968) A(E/kT) = 0

0 I E/kT I 3.19

A(E/kT) = 1 + 1*6(E/kT - 5) exp (-E/3kT)

(2)

ElkT > 3.19

The values Fed depend strongly on the form of the joining function assumed. The values Fed as given in the literature are often inconsistent or known only for special cases. With some investigations reported the correction factor was incorrectly assumed to be unity. A direct measurement of FCd for foils of arbitrary thickness poses substantial experimental difficulties. Therefore, it is attempted to calculate FCd values for several important neutron detector materials according to recent data. MONODIRECTIONAL The epithermal activation given by (BENSCH,1968)

NEUTRON INCIDENCE

of a foil for monodirectional

neutron incidence is

(3) and the activation of a cadmium covered detector foil by &d

=

%p

m(Ca,t/~3[i,tC~d(E)d~d s0

+

&@)dl

-

&n(&d(@&d)lA

fi (1

(4)

$

where c,(X) is the neutron absorption probability 5,(X) = 1 - exp (-X).

(5)

At least in the narrow energy interval where epithermal neutrons are absorbed in the cadmium cover, Zact/Ca may be taken as constant. In this interval, which is of prime interest to us, the neutrons give approximately the same contribution to C,, and to C cd. &&Z. may therefore with good approximation be left out of the evaluation of Fed and we obtain in the case of collimated neutron incidence

s

m[1 - exp (-X,(E)d)]A

0

Fed=

oD

o [exP (-&@)dcd)

k

$

(1

*

- exP (--I;,(E)d

(6)

- &,(E)dc,)]A

s

ISOTROPIC

NEUTRON

INCIDENCE

The epithermal activation of a foil for isotropic neutron incidence is given by (7) and the activation of a cadmium covered detector foil by 'Cd

=

(V,p/')

m(',/',){l~(~Cd(E)dCd s0

+&z(E)

-

5iPCd(E)dcd]}A

6 (1

y

-

(8)

Cadmium correction factors of several thermal neutron foil detectors

The absorption

probability

[,(x) is related to the third-order

679

exponential integral

Es(x) by &(X)=1--2&(X)=1--2lpexp(--:)dp Using the same approximations we obtain

(9)

as in the case of monodirectional

s

m{l - 2E,[Z,(E)d]}A

0

Fed = 2

a{E,&d(E)dCdl s0

5

neutron incidence,

y

(1 (10) -

&K&W

WESTCOTT’S

+&d(~%&dl)A

NOTATION

In Westcott’s notation a different procedure is used to determine the thermal neutron flux density (‘true Maxwellian flux density’, cf. ICRU-Report 13, p. 3). As in the more general method as described before, the activities of a bare (C) and of a cadmium covered foil (Cc,) have to be measured for this purpose. The foils used must be equivalent and ideally thin. If the activity C,, induced by thermal neutrons is determined with the formula C,, = C - FcdCcd but using the Westcott parameters ,u and s, Fed is given by

&Ii + (Jab Fed =2&T)/&] + (472)s

(104

as can be easily verified. If equation (2) is used, ,Q=3-30. Of course, the values obtained by equation (lOa) correspond to the values obtained by equation (6) and (10) as given in Tables 1-6 (d-+ 0). EVALUATION

The evaluation was carried out by numerical integration of the above formulae (6) and (10) using Simpson’s rule. For this purpose the energy interval from 0.0807 eV (below this energy the joining function is assumed to be zero) to 3 keV was divided into subintervals with different step widths AE:

O-0807IE I O-6 IEI 3 32 100 600


0.6eV 3 eV 32 eV 100 eV


AE =

O-01 eV

AE=

O-05eV

AE =

0.5 eV

AE=

2

eV

eV

AE =

10

eV

eV

AE = 200

eV

By the use of these small energy steps the error was kept reasonably small (less than 10 per cent of the uncertainty of the measured cross-section values), and the effects of the cadmium resonance absorption could also be taken into account. Due to the l/Eneutron spectrum, energies above 3 keV contribute minimally. Nevertheless an approximation was used to take into account this small contribution. As most nuclides, particularly the detector materials here, have an absorption cross-section with an approximate l/v distribution in this energy range, the following formulae

680

K. MUECKand F. BEN~CH

were used to calculate this contribution Monodirectional

(BENSCH, 1968):

neutron incidence :

numerator + 2(&(X3

+ In X, + 7)

+ 2 E,(X, + Xd + In X1 - + X, - &(X1) [ X1 Isotropic neutron incidence : denominator

numerator $ E,(X,) denominator

1

- E,(X1) + In X, + y + 3

+ E,(X, + X2) - l&(X,) + E3(X1) - EdX,

(11)

+ X2) + In

(12)

X1 + X2 Xl

’

where E,(X) and E,(X) are the exponential integrals of 1st and of 3rd order, y = O-5772 . . . Euler-Mascheroni-constant,

and

x, = C,d X2.= &+&,. The evaluation was carried out by an IBM 360/44. The values of the absorption and activation cross-section were obtained by a combination of the best available data from HUGHES (1958), TRALLI (1958), NEILER (1961), BECKURTS(1964), VERTEBNY (1968), and from the Neutron Data Compilation Centre, Saclay. An optimal fitting between the (n, y)- or absorption cross-section and the difference between total cross-section Zt and scattering cross-section Zg was realized. For some energy intervals, the absorption cross-section was inferred from the difference between Et and Z8. The resonance integral was calculated numerically for each element from the cross-section data and compared with the measured resonance integral. The chosen values of the cross-sections used for the calculations will be discussed with some elements separately. The cadmium cross-section data including resonance structure up to 3 MeV were taken from BACHMANN (1969) and HUGHES(1958). TESTING OF THE CALCULATED CADMIUM CORRECTION FACTORS For ideally thin foils (C,d Q 1) having a l/v cross-section in the energy range E < 20kT, an approximation can be used to calculate Fed in a rather simple way. If the above assumptions are valid, according to BENSCH(1968) the following formula holds : (13) bT is the cross-section at the energy E, = kT corresponding to the most probable velocity of thermal neutrons, a,, is the absorption resonance integral, the lower energy limit being ECd, EICT= pkT is the thermal cut-off energy (effective joining energy) p = 3.30 assumed, and ECd is the given cadmium cut-off energy. This formula may be used for each of the elements listed below except In and Dy.

Cadmium correction

factors of several thermal neutron foil detectors

681

The energy of the first indium resonance is too low, and dysprosium does not possess a genuine l/u cross-section. Calculations by use of this formula have been carried out for each of the other foil materials and the values thus obtained are listed in the tables and plots for d---t 0. In most cases there is good agreement with the curve obtained by the general formula (10) when extrapolated to zero. For uT and uaaothe values of HUGHES(1958) and BECICURTS (1964) were used and the cadmium cut-off energies were taken from YAWNO (1965). RESULTS AND DISCUSSION Calculations for monodirectional (‘collimated flux’) and isotropic neutron incidence (‘isotropic flux’) were made for three different l/v absorbers commonly used: vanadium, natural boron, and boron-lo. In the case of a pure l/v absorber, the influence of the material enters into the Fca values only as the product J&d. Therefore, the values of FCd are given in dependence on this product. For practical purposes the thickness is also given in mm and in mg/cm2. Errors of the Cd correction factors are not separately listed in the tables as they are of the same order as the last decimal of each value. 1

3oL 2.9

Collimated

21)

I k0tpa q ho,

pw

llux

I

I

I

I

I

02

03

a4

0.5

0.6

cl7

aa

a9

1.0

QOZ

U/73

Op

a05

0,06

o.p7

00.9

ap9

0.1

I

I

=0 I

LWOS 1.0

I , 100

0.M 2b

110

I

0. ol5 3.0

fw6m

’ 250a02mm

200 COI

mm

I

mg/cm’ mm mg/cm’ mg/cm’

thickness

V B 8”

of toil

FIG. l.-The cadmium correction factor &d for l/o absorber foils. The results obtained for indium were found to be very similar to those published by BECKURTS(1964), but did not resemble the measured values of POWELL and BECK (1964) or POWELLand WALKER (1964). The calculated values of WALKER et al. (1966) are probably too low and seem to coincide with the values obtained with our calculations for monodirectional neutron incidence (see Table 2). The cadmium correction factors for gold foils were found to be very close to those given by BECKIJRTS(1964), and a rather large discrepancy, particularly for thicker foils, was found to POWELLet al. (1964). It may be noticed that the correction factor depends more strongly upon the foil thickness than mentioned by POWELL. The discrepancy may be due to unavoidable errors in experimental methods (uncertainties

K. MUECK and F. BEN~CH

682

l/v ABSORBER FOILS

TABLE l.-THECADMIUMCORRECTIONFACTORPOR Collimated tlux thickness of Cd (mm) Foil material

Thickness (mm) (m&m’)

0.0

0.0

Ndo,

0.5

0.8

1.0

1.2

0.0

Isotropic flux thickness of Cd (mm) 0.5

0.8

1.0

2.60 10.08

2.82 1tO.08

2.92 rtO.08

1.2

V

0.005

2.98

0.00018

2.28

2.46

2.52

2.59

2.60

2.82

2.92

3.01

V

0.01

5.96

0.00035

2.21

2.44

2.51

2.58

2.60

2.82

2.92

3.01 3.00

V

0.02

11.92

0.00070

2.21

2.43

2.50

2.57

2.60

2.81

2.91

V

0.05

29.80

0.00175

2.26

2.41

2.49

2.56

2.60

2.80

2.91

3.00

V

0.10

5960

0.00351

2.25

2.41

2.49

2.56

2.60

2.80

2.90

2.99

V

0.15

89.40

0.00526

2.25

2.41

2.49

2.56

2.60

2.80

2.90

2.99

V

0.20

119.20

0.00702

2.25

2.41

2.49

2.56

2.59

2.79

2.90

2.99

V

0.25

149.00

0.00877

2.25

2-41

2.49

2.56

2.59

2.79

2.89

2.98

nat. B

0.005

1.18

0.04984

2.24

2.40

2.48

2.55

2.55

2.74

2.84

2.92

nat. B

0.01

2.31

0.09968

2.24

2.39

2.47

2.54

2.50

2.69

2.79

2.88

nat. B

0.02

4.74

0.1994

2.22

2.37

2.45

2.52

2.44

2.62

2.12

2.80

1°B

0.005

1.18

0.2726

2.21

2.36

2.44

2.51

240

2.58

2.67

2.75 2.63

nat. B

0.05

11.85

0.4984

2.18

2,33

2.40

2.47

2.31

2.47

2.56

1°B

0.01

2.37

0.5452

2.11

2.32

2.39

2.46

2.29

2.45

2.54

2.61

nat. B

0.1

0.9968

2.11

2.25

2.33

2.39

2.16

2,30

2.38

2.44

‘OB

0.02

1.090

2.10

2.24

2.31

2.37

2.13

2.28

2,35

2.42

23.1 4.14

FIG. 2.-The

cadmium correction

factor Fed for indium foils.

Cadmium correction factors of several thermal neutron foil detectors

TABLE Z.-THE

CADMIUM

CORRECTION

FACTOR

FOR INDIUM

FOILS

Isotropic flux thickness of Cd (mm)

Collimated flux thickness of Cd (mm)

In thickness

683

(mm)

(mg/cmY

0.5

0.8

1.0

1.2

0.5

0.8

1.0

1.2 -

0+05 0.01 0.02 0.05 0.1 0.2 0.25

3.65 7.31 14.62 36.55 73.10 146.20 182.75

I ,067 I.074 1.087 1.121 1.160 I.213 1.233

1.079 1.087 1.102 1.138 1.181 1.240 1.263

1.086 1.094 1,109 1.148 1,193 1,255 1.279

I.093 1.102 1.118 1.157 1.204 1.269 1.294

1.116 1.130 1.157 1.214 1.275 1.353 1.381

1.142 1.157 1.185 1.248 1.316 1.403 1.435

1.159 1.174 1.203 1.268 1.339 1.431 1.465

1.174 1.189 1.219 1.287 1.361 1.457 1.492

etc.), or possibly due to the use of obsolete cross-section values. Due to this, the calculation for the extrapolated value d--+ 0, according to equation (13), was carried out and compared with the extrapolation to zero of the curve of cadmium correction factors versus foil thickness. Good agreement was found with the theoretical values. Especially for the determination of the correct slope (increase of the cadmium correction factor versus increase of foil thickness) the theoretical method as applied here is superior to experimental methods since the calculations are straightforward and not dependent on statistical errors. Any errors in the cross-section values only influence the absolute values of the correction factors while the slope of the curve is minimally influenced. The activation cross-section for manganese was obtained by taking a I/o slope up to 100 eV. According to BOLLINGER et al. (1955) about 97 per cent of the peak in the total cross-section at 337 eV is due to scattering. In fact, by using 2.9 per cent of the total cross-section as value for the absorption cross-section, the numerical evaluation of the resonance integral gave the same value as published by BECKURTS(1964), p. 418 and LOUWRIERet al. (1965). The results of the calculation using these crosssection values are listed in Table 4. Up to 30 eV a l/a slope was used for the Co cross-section. If 9 per cent of the total cross-section are taken as absorption contribution to the resonance peak, then the measured value of the resonance integral (BECKURTS,1964) is precisely obtained. Using these absorption cross-section values the data of Table 5 were computed. As dysprosium consists of several isotopes with only one (Dyl”“) leading to activation, the cross-section of this isotope has to be used to calculate the cadmium correction factor for activation foils. Unfortunately, this cross-section is very little known. Therefore several approximations had to be made: The first block of correction factors in Table 6 were calculated by assuming a l/u slope up to 20 eV, then a constant value of 30 barn up to 200 eV, and the data from NEILER(1961) for the energy range 200 eV < E I 3000 eV. The second block was obtained by using the non-l/v activation cross-section of SHER et al. (1961) up to 2 eV and an extrapolation of this curve to 15 eV, a constant value of 5 barn in the range 15 eV < E 2 200 eV, and the values of NEILER in the range 200 eV < E I 3 keV. The constant values in the range 15 eV < E i 200 eV (20 eV < E I 200 eV for block 1, respectively) were fitted to give the resonance integral for absorption as given by Scovr~ru et al. (1966) (by BECKURTS, 1964, p. 420 for block 1, respectively).

in extrapolation,

684

130

K. MUECK and F. BENSCH

-

AU

1.2s 126 1.24 1.221.20 0.5

IL!

cotlknated

flux

t

am

LlOS

0.20

0.15

0.25 I

.600 FIG. 3.-The

cadmium correction

.

thickness

mgkIn’ of foil

factor FCdfor gold foils

It is obvious that rather large discrepancies in the correction factors result from different cross-section values used for the calculations. The Fca values obtained by using the non-l/v cross-section range from 3.28 to approximately 6 and seem to be a trifle too large. On the other hand, they should be definitely larger than those obtained by using a l/u cross-section which may be easily shown (see below). The calculations should be repeated if absorption cross-section values covering the full energy scale are obtainable. If we consider the correction factors for different elements but constant thickness of absorber and cadmium foil, we find values for gold and indium close to unity, TABLE 3.-THECADMIUMCORRECTIONFACTORFORGOLDFOILS Collimated flux thickness of Cd (mm)

Au thickness (mm)

0.0

(mg/cm*)

05

0.8

1.0

Isotropic flux thickness of Cd (mm) 1.2

0.0

0.5

0.8

1.0

1.043 ~0~001

1.045 *o~OOl

1.046 fO.OO1

1.2

0405

9.66

1.039

1.042

1 a043

1.044

1.064

1 a069

1.072

1.074

0.01

19.32

1.051

1.054

1.056

1.058

1.087

1.094

1.098

1~101

0.02

3864

1.072

1.077

1.080

1.082

1.123

1.133

1.137

1.142

0.05

96.6

1.114

1.123

1.127

1,130

1.179

1.193

1.200

1.206

0.10

193.2

1.148

1.159

1.165

1.169

1.223

1.240

1.249

1.257

0.15

289.8

1.169

1.181

1.187

1.193

1.250

1.271

1.281

1.290

0.20

386.4

1.184

1.198

1.205

1.210

1.272

1.294

1.305

1.315

0.25

483.0

l-196

1.211

1.219

1.225

1.286

1.309

1.321

1.332

Cadmium correction 1.75

factors of several thermal neutron foil detectors

I

I

685

I

I

Mn lsofmpic

171

flux

1.2 1.0

Lb!

2

a8

-

1.61

0.5 Cdlima 1

ted

I lux

L

1.55

1.2 1.0 0.8

i

l.sr

as 1.1!

I

I

I

005

[II

0.15 :

1:::::::

:

:

; nm

50

1

rn(

0.2 :

:

:

‘5 / I50

:

! w.

rhickness

FIG. 4.-The

cadmium correction

factor Fed for manganese

TABLET.-THECADMIUMCORRECTION

Mn thickness (mm) 0.0

0.5

0.8

1.0

foil

foils.

FACTORFORMANGANESEFOILS

Collimated flux thickness of Cd (mm)

(mglcm”)

n* d

1.2

0.0

Isotropic flux thickness of Cd (mm) 0.5

0.8

1.0

1.58 *to.04

1.62 10.04

1.64 kO.04

1.2

0.005

3.60

1.41

1.52

1.53

1.55

1.58

1.63

1.66

1.69

0.01

7.21

1.47

1.52

1.53

1.55

1.58

1.63

1.66

1.69

0.02

14.42

1.48

1.52

1.54

1.55

1.58

1.63

1.66

1.69

0.05

36.05

1.48

1.52

1.54

1.56

1.58

1.64

1.66

1.69

0.10

72.10

1.48

1.52

1.54

1.56

1.58

1.64

1.67

1.69

0.15

108.15

1.48

1.52

1.54

1.56

1.59

1.64

1.67

1.70

0.20

144.20

1.48

1.52

1.54

1.56

1.59

1.65

1.67

1.70

0.25

180.25

1.48

1.52

1.54

1.56

1.59

1.65

1.68

1.70

values for cobalt near 1.4, for manganese near 1.6, and for I/v absorbers near 2.6. The reason is obvious as elements with large epithermal resonance (as gold and indium) are activated to a greater extent by epithermal neutrons resulting in a smaller difference between the activation above cadmium cut-off energy and the activation above thermal cut-off energy which will give a correction factor closer to unity. This argument can also be understood if we change the value da0for the resonance integral in equation (13) leaving the other parameters constant. Thus, the correction factor of an element with a steeper cross-section slope than l/u and a resonance integral smaller than that of a perfect I/U absorber will be greater than that of a perfect l/v absorber.

686

K. MUECK

and F. BENSCH

1.60

f.55

2 IM T

f.45

l.LI

1.35

1.3

im FIG. 5.-The

cadmium correction factor Fadfor cobalt foils.

TABLE 5.-~HECADMIUMCORFWTIONPACTORPORCOBALTFOILS

co (mm)

Isotropic flux thickness of Cd (mm)

Collimated flux thickness of Cd (mm)

thickness (m&m”)

0.5

0.8

I.0

1.2

0.5

0.8

1.0

1.35 zto.04

1.38 kO.04

1.40 jro.04

1.2

0.0

0.0

0*005

4.45

1.31

1.33

1.34

1.35

1.37

1.40

1.42

1.43

0.01

8.9

1.31

1.33

1.34

1.35

I.38

1.41

1.43

144

0.02

17.8

1.31

1.34

1.35

1.36

1.39

1.43

1.44

1.46

0.05

44.5

1.32

1.35

1.36

1.37

1.42

1.46

1.48

1.49

0.10

89.0

1.34

1.37

1.38

1.39

1.47

1.51

1.53

1.54

0.15

133.5

1.36

1.39

1.40

1.42

1.50

1.54

1.57

1.59

0.20

178.0

1.38

1.41

1.42

1.44

1.53

1.58

1.60

1.62

0.25

222.5

1.39

1.43

1.44

1.46

1.55

1.60

1.63

1.65

Despite the obvious discrepancies in the values for ltiDy, the results are given in Table 6 for the following reasons : Approximate values may be obtained from Table 6

according to the best available cross-section data; since the data using the non-l/v cross-section for the calculation seem to be more reliable, only these data were listed

DY

213.4

85.36

0.10

0.25

42.68

0.05

128.0

17.07

0.02

170.7

8.54

0.01

0.20

4.27

0.005

0.15

(mGm”1

(mm)

thickness

2.01

2.03

2-05

2.06

2.08

2.09

2.09

2.10

0.5

2.13

2.15

2.17

2.19

2.21

2.22

2.22

2.23

0.8

2.19

2.21

2.23

2.25

2.27

2.28

2.29

2.29

1.0

Collimated flux thickness of Cd (mm)

2.25

2.27

2.29

2.31

2.33

2.34

2.35

2.35

1.2

2.09

2.13

2.17

2.23

2.29

2.34

2.37

2.38

0.5

2.22

2.26

2.31

2.37

2.45

2.50

2.53

2.54

0.8

2.29

2.33

2.39

2.45

2.53

2.35

2.39

2.45

2.51

2.59

2.66

2.68

2.59

2.70

2.63

1.2

2.61

1.0

Isotropic flux thickness of Cd (mm)

3.28

3.38

3.49

3.61

3.74

3.83

3.86

3.81

0.5

3.66

3.77

3.90

4.04

4.20

4.30

4.33

4.35

0.8

4.04

4.17 3.86

4.32 3.99

4.48

4.28 4.13

4.66

4.77

4.45

4.56

4.81

4.83

4.61 4.59

1.2

1.0

Collimated flux thickness of Cd (mm)

3.28

3.45

3.66

3.92

4.28

4.59

4.74

4.83

0.5

3.66

3.86

4.10

4.41

4.83

5.20

5.37

5.47

0.8

4.34

3.86

4.08

4.04

4.27

4.55

4.90

5.39 4.67

5.81

5.53

6.00

6.12

1.2

5.13

5.71

5.82

1.0

Isotropic flux thickness of Cd (mm)

non 1/v-cross-section

CADMIUM CORRECTION FACTOR FOR DYSPROSIUM FOILS

l/u-cross-section

TABLE &-THE

K. MUECK and F. B~NSCH

688

Collimated

flux

!S i0

Lb

FIG. 6.-The

&l

ii0

lie

cadmium correction

lh

NO

rko

do thickness

a00 mgkma of toil

factor Fca for dysprosium foils.

in Fig. 6; the error caused by using either one of the two given values for a particular detector arrangement or a mean value of the two is much less than assuming the correction factor to be unity as was usually done with dysprosium measurements up to now. REFERENCES BACHMANNH., HINKBLMANNB., KRIEG B., LANGNERI., SCHMIDTJ. J., SIEP I. and WOLL D. (1969) KFK 1080. EANDC (E)-125‘U: BECKURTSK.-H. and WI&Z K. (1964) Neufron Physics. Springer-Verlag, Berlin. BEN~CHF. and FLECK C. M. (1968) Neutronenphysikalisches Praktikum I. Bibliographisches Institut, Mannheim. BOLUNGER L. M., DAHLBER~ D. A., PALMERR. R. and THOMAS G. E. (1955) Phys. Rev. 100, 126. CoATr!s M. S. (1961) Neutron Time-of-Flight Methods, p. 233. Euratom, Brussels. HUGHESD. J. and SCHWARTZ R. B. (1958) Neutron cross-sections, BNL 325. L~UWRIER P. W. F. and ATEN A. H. W. Jr. (1965) J. nucl. Energy 19,267. NEILERJ. H. (1961) Symp. of Fast andbtermediate Reactors, Vienna, STI/PUB/49 Vol. 1, 95. POWELL J. E. and BECK C. L. (1964) Nucl. Sci. Engng 25,204. POWELL J. E. and WALKER J. V. (1964) Nucl. Sci. Engng 20,476. SCOVILLEJ. J., FAST E., ROGERSJ. W. (1966) Nucl. Sci. Engng 25,12. SHER R., TA~SAN S., WEINSTOCKE. V. and HELL~TENA. (1961) Nucl. Sci. Engng 11,369. TRALLI N. et al. (1958) Report APEX 467. VERTEBNYV. P., GNIDAK N. L., KOU)TY V. V. and PAVLENKOE. A. (1968) Ukr. Fiz. Zh. 13,605. WALKER J. V. and KOELLINGJ. (1966) Radn Meas. Nucl. Power, 87. WESTCOTTC. H. (1960) AECL 1101. YA~UNO T. (1965) J. nucl. Sci. Technol. 2,427.