Average cross section of the 32S(n, p)32P and 27AI(n, α)24Na reactions for fission neutrons

Reactor Science and Technology (Journal of Nuclear EnergyParts A/B)1962. Vol.16.pp.447to453.PergamoaPress Ltd. printed in Northern Ireland

AVERAGE

CROSS SECTION OF THE 32S(n,p)32P AND 27Al(n, %)24Na REACTIONS FOR FISSION NEUTRONS H. DEPUYDTand M. NEVEDE MEVERGNIES Studiecentrum

voor Kernenergie,

Mol, Belgium

(Received 9 April 1962) Abstract-The main purpose of this work was to improve the experimental value 5 of the QS(n, P)~~Preaction cross section for a fission neutron spectrum. The sample in a cadmium box was centred on the axis of an enriched uranium disk irradiated by a thermal neutron beam. The absolute value of the thermal flux was determined by activation of a gold detector. The absolute value of the fast flux at the sample was calculated taking into account thedetector-uraniumgeometry. The average cross section 8 was deduced from an absolute measurement of thesampleactivity. Theresultsare: for ?S(n, P)~~P: (? = 65 & 3 mb, for 2’Al(n, cOz4Na: ii = 0.63 rt 0.03 mb.

1. INTRODUCTION

reactions are widely used for fast neutron flux measurements and standardization. In this respect the reaction 32S(n, P)~~P is important because the cross section is relatively large, the influence of secondary reactions is small and 32P has a convenient halflife. However, its cross section is not well known (Table 2 shows the various results found in the literature) and disagreements up to a factor 7 are apparent in the experimental values. In most of the measurements made until now, (HUGHES, 1953; STAFFORDet al., 1953; &ELAND et al., 1954), the sulphur samples were irradiated in the core of a reactor, where the fission neutron flux is large as well as the epithermal flux. Moreover, the fission spectrum was distorted by inelastic scattering. As it was impossible to calculate directly the fission neutron flux, the latter was standardized against a fission flux in a simpler geometry (HUGHES, 1953) or against a cross section of a reference threshold reaction (HUGHES, 1953; STAFFORDet al., 1953; &ELAND et al., 1954). In the present experiment, the irradiations are performedusing the‘convertor technique’developed by HUGHES et al. (1949) (Fig. 1). A thermal neutron beam falls on an enriched uranium disk ‘convertor’. The sample to be activated is put in a cadmium box and placed on the axis of the uranium disk, facing the side opposite to the incident thermal beam. A gold foil of 10 mm diameter by 0.05 mm thickness, located on an off-axis position, is irradiated simultaneously. The gold activity M is used to monitor the thermal neutron flux. The average cross section ii is then deduced from :

THRESHOLD

where I, is the absolute activity of the sample (Section 2B), N is the number of nuclei in the target sample and (nv), is the average fission neutron flux at the sample location. This flux is deduced from the incident thermal flux (I~u)~~by means of the relation:

Cs(cm-i) is the macroscopic fission cross section of the U-convertor, v is the number of neutrons per thermal fission.

(It&h

M

is determined

by a ,6-y coincidence

measurement of the activity of a gold sample irradiated in the thermal beam close to the U-disk (Section 3). G (cm) is a geometrical factor (Section 4), and f,, (Section 4) takes into account the secondary processes (scattering, absorption etc.) in the convertor, the cadmium box and the sample. As the U-disk is thin (1 mm), the inelastic scattering is found to benegligible. The main purpose of the present work was an attempt to improve the experimental value of the 32S(n, p) 32P reaction cross section. The absolute cross section for the 27Al(n, o()24Nareaction was also measured. 2. DESCRIPTION OF THE CONVERTOR AND THE TARGET-SAMPLES A. Description of the convertor* The main specifications of the convertor (U-metal, disk shape) are: radius: R = 3 cm thickness: t = O-0983 cm distance target-convertor: h = 0.55 cm. * The enriched uranium used was supplied by the U.S. Atomic Energy Commission. 441

H. DEPIJYDTand M. NEVEDE MEVERGNIES

448

Reactor shielding

L

1440

/60/;

Detail of the irradiation Mixture

of resin

spacehot

to scale)

and lead pellet5

Mixture of resin and

borax

Mixiure of resin and EQ,C Pile collimator and water shutter g

2

&I window

SIOW

Seam shutter(lcm Irradiation

bow,

lcm

lead)

p

a Neutrons

space

Shielding block Starting from the irradiation

space:

resin and S4C l6cm paraffin and S4C 2cm boral ‘25cm lead

5cm

8

Target handing

FIG. l.-Schematic

equipment

cross section through the pile collimator and the convertor. (Dimensions in mm.)

The overall geometry of the experiment is indicated in Fig. 1. The pile collimator is made of a stainless steel tube of 130 cm length, placed in the DX-25 channel of the BR-1 reactor. This tube, with thin (1 mm) Al windows, can be used as a water shutter. As the filling and emptying of this shutter proceeds slowly, another beam shutter of lead and boral is placed between the collimator and the irradiation space. This shutter is used to time the irradiations. The U-convertor is placed in the middle of the irradiation space. The target samples are fixed to a sliding rod, which allows the operator to place and remove them, while the reactor is at a power-level of 4 MW. During an irradiation, the U-disk and the samples are centred on the axis of the thermal neutron beam. The thermal neutron data relevant to the U-disk are summarized in Table 1.

The macroscopic cross sections of the convertor are: & = 28.3 f O-1cm-l & = 0.499 * 0.002 cm-l zj = 23.8 -& 0.2 cm-l. The subscript T refers to total cross section, s to scattering and f to fission.

B. Description of the samples (i) Sulphur. About O-1 g ammonium sulphate powder is put in an aluminium cylinder of 1 cm dia., 0.1 cm depth, 0.02 cm wall thickness and having 6 ,u mylar film cover (total weight of the film: ~10~ g). The cylinder is enclosed in a cadmium box. After about 3 days’ irradiation, the dried and carefully weighed powder is dissolved in distilled water to which an identical amount of ammonium phosphate is added to act as carrier and a few ml of nitric acid (3 to 4 N) to convert phosphite ions to phosphate, thus preTABLE1.-CONVERTORDATAFORTHERMAL NEUTRONS venting deposition of the phosphorus on the walls of (O-0253 eV) the vessel (according to WEALE et al., 1959). The V Abundance (%) solution (10 to 20 ml) is made up to 50 ml with dis0,” tilled water. Samples of 32P solution are counted in a zsau 9.02 ~0.5 mbt G.M. liquid counter, Mullard type MX-124. The 23qJ 060 ZSqJ 89.43 ‘8:$6;“,; 2.43 f 0.0211 counter is calibrated to 1 per cent with a reference 32P 234u 0.95 solution, measured in a 4r-proportional counter. The correction for absorption of the @-particles by the 7 HUGHESet al. (1958). ammonium sulphate and ammonium phosphate (about $ DERIJYTTER (1961). O-2 per cent) is deduced from an absorption curve, 11HUGHESet al. (1958).

Averagecross section of the 32S(n,p)““Pand 27Al(n,cOz4Na reactions for fissionneutrons giving the counting rate due to 32P as a function of various amounts of inactive ammonium sulphate. One day after the end of the irradiation, the activity of the secondary reaction products, except for 35Sand 33P, has decayed to a negligible amount, because of the short half-lives. The 35Sactivity due to resonance and fast neutrons is less than 0.01 per cent of the 32P activity. The half-life, T+, of 32P is deduced from 28 mealurements extending over 33 days. The value obtained [T& = 14.32 & 0.02 d] agrees with the published values given by WAY et al. This also shows the purity of the 32P source and the negligible amount of %P activity. (ii) Al uminium. A carefully weighed sample of spec-pure aluminium metal, 1 cm dia. and 0.07 mm thickness, is irradiated (~2.5 d) in a 1 mm thick cadmium box. After irradiation the foil is first counted in a Philips 18505 G.M. end-window counter and then dissolved in about 3 ml hydrochloric acid (37.38 per cent HCl) to which is added copper nitrate and l-2 mg sodium chloride to act as carrier. The solution is then made up to 25 ml with distilled water. Sources of 2.5 ~1, dried on mylar film, are counted in an anticoincidence counter with 1.6 c/set background. The two counters are calibrated to 1.5 per cent with a reference 24Na solution measured previously with a 47rThe secondary reactions proportional counter. 27Al(n, Y)~*AI and 27Al(n, p)27Mg can be neglected because of the short half-lifes, respectively 2.3 min and 9 min. The activity due to lz2Sb (produced by 2*1O-Gper cent in weight 12%b) is determined from the decay curve and the gamma spectrum of an aluminium foil irradiated in the core of the reactor, where the ratio of thermal to epithermal flux per In e energy interval is R c 23. In the thermal beam incident on the convertor R = 743, so that the lz2Sb activity is less than lop3 per cent of that due to 24Na and is consequently negligible. 3. NEUTRON THE

FLUX INCIDENT CONVERTOR

ON

A. Thermal neutron jkx The distributionf(r) of the neutron beam striking the uranium disk was measured with small gold detectors of 3 mm dia. (Fig. 2). The results have shown that it is constant up to a radius r = 2 cm, then decreases to 92 per cent of the central value at r = 3 cm. This lowers the average fission flux at the sample by 0.4 per cent. The absolute value of the incident thermal flux is derived from the average activity of 13 gold detectors irradiated successively in the thermal neutron beam at

449

a distance of 0.5 cm from the U-disk and counted in a G.M. Philips 18505 end-window counter. This counter was previously calibrated with two gold detectors whose absolute activities were determined by DE TROYER (1960) by a b-y coincidence method with Activity

t (arbitrary

units)

+Ce”tre

a

of target

and

cwertor

I

FIG. 2.-Distribution of the incident thermal flux as a fnnction of the radial distance to the centre of the convertor.

an error of 0.5 per cent. The thermal flux per monitor value, taking ~(~~sAu) = 98.8 & 0.3 b (HUGHES et al., 1958) is equal to 2.37 & 0.04 x 10s n/cm2 sec. The absolute value of (YEZ~)~~ is of the order of 1.28 x lo8 n/cm2 sec. Corrections are to be applied to this average gold activity. First, one has to take into account the epithermal activation (I.1 per cent) as deduced from measurements with and without cadmium. Secondly, the activity has to be increased by 1.1 per cent for neutron absorption and scattering in the gold detector and decreased by 0.3 per cent because the Au-detectors irradiated in a beam are compared to reference Audetectors irradiated in an isotropic flux. Thirdly, the thermal flux (nv),,/M, determined by gold samples, must be multiplied by a correction factor of 1.036 to refer the flux to the irradiation of a sulphur sample. This factor is the ratio of the monitor activity M(Au) for irradiation of a Au-detector to the monitor value M(S) for irradiation of a sulphur detector:

WA@ = 1.036 &- 0.006. M(S) B. Epithermal neutron,@ux R, the ratio of the thermal and the epithermal flux per In e energy interval, is determined from experimental cadmium ratios of lg8Au, 6oCo, 56Mn and lleIn detectors. One obtains: R = 743 & 15.

450

H. 4. CALCULATION FISSION

DEPUYDT and

M. NEVEDE MEVERGNIES

OF THE FLUX

NEUTRON

A numerical evaluation of (5) with a Ferranti-Mercury digital computer gives :

The fission neutron flux proportional to the thermal neutron flux is given by equation (2) in which G(cm) is given by: G=

G = 2.78 x 1O-2cm. This value is about 5 per cent smaller than the value corresponding to a ‘point’ detector located in C. The fission flux represented by (2) is then equal to:

w, = M

du 2~y dy ._.D

(4)

TR’2

where h’ = h + u. The meaning of the symbols is given in Fig. 3. The ranges of the variables are: (0 Q z < t), (0 < r < R), (0 < 8 < 27& (0 < u < D)(O < y < R’). -Uranium

II I II I 2 ,I I _ t

“I I ! I 1 _

, I ,

h h’

J

To evaluate the correction factorf,,, it is assumed that the neutrons from primary and secondary fissions as well as scattered neutrons, are isotropic and that the fission spectrum is undisturbed, since a neutron loses practically no energy in an elastic collision with a heavy nucleus such as U or Cd. Fast neutrons directed towards C (Fig. 3) are partially removed by scattering, absorption or secondary fission in the convertor; numerical calculations show that only 94.7 per cent of them reach C. On the other hand, primary fission neutrons not originally directed towards C may be scattered in this direction by the convertor; this increases the fast flux by 4.7 per cent. The fission neutrons may also produce secondary fissions, from which results an increase of the fast flux by 4-l per cent. Thermal neutrons can be scattered and produce fissions; this increases the fast flux by 1.5 per cent. In total, one gets an increase of 10.3 per cent. Finally, only 96.2 per cent of the fast neutrons incident on the sample holder contribute to the (n, p) or the (n, IX)reaction, due to absorption and scattering by the cadmium box and the sample. One gets for the total correction factor: f,,, = 0.947 x 1.103 x 0.962 = 1.005.

FIG. 3.-Relative

geometry of the convertor and the target.

The 32P activity due to inelastically scattered neutrons is less than O-1 per cent of the total activity.

The expression:

5. RESULTS

A. 32S(n, P)~~P

1

1

4rr APs

47r[y2 + y2 - 2yr cos 8 + (h’ - z)~

-=

gives the probability (in cm-q that a fission neutron formed in A arrives in P. After integration over f3and Y, one gets:

R2 + (A’ 1%

3.83 x lo8 x f,,,.

zj2 -

y2 + 2/‘[R2 + (h’ -

2(h’ - 2)”

z)” -

Following the procedure outlined above, one obtains as average cross section 5 for a fission neutron spectrum the following value : 3 = 645 f 2.8 mb.

This value is consistent with IJ?O(~~~U) = 587 f 6 (DERUYTTER, 1961). Any other value of o,“(~““IJ) would give an inversely proportional change in crr?S(n, P)~~P]. The standard deviation quoted for u is

1

y212 + 4y2(h’ - z)” dz duy dye

(5)

Average cross section of the ?‘S(n, P)~~Pand 27Al(n,Cr)24Nareactions for fission neutrons

calculated from the errors on the various factors. The error due to the inaccuracy of the thermal neutron data is assumed to be I.1 per cent. The error on the absolute value of the thermal flux is approximately 1.6 per cent. The inaccurate data for fission neutrons gives I.4 per cent error on f,,,. The assumed error [f0*03 cm] on the 0.55 cm distance between target and uranium convertor causes an error of 3 per cent on the flux (nz;),. The irradiation, calibration and counting of the four sulphur samples produce on the average activity a standard deviation of 2 per cent. This all together gives a standard deviation of 4.3 per cent on I?. B. 27Al(n, x)24Na For the 27Al(n, or)24Na reaction, our experimental result is: 5 = O-628 i_ 0.031 mb. This value is consistent with u~‘(~~~U)= 587 i_ 6 b (DERUYTTER,1961). A standard deviation of 5 per cent is assumed on 5:. 6. COMPARISON WITH PREVIOUS RESULTS A. 32S(n, P)~~P (i) ‘Calculated’ values. The average value obtained in the present work can be compared with that deduced from a known fission spectrum and from the available differential cross-section data. The average cross section 3 for a given neutron spectrumf(E) is given by the following equation:

z=

mo(E)f(E) dE c *o s0

mfOdE

(6)

451

KLEMAand HANSON(1948) measured o(E) in the range 1.6-5~8 MeV; their estimation of the error with respect to the absolute value of o(E) is about 15 per cent. A statistical error of 2 per cent, with no estimaet al. tion of the systematic errors, is given by L~~SCHER (1950) for the measured values in the range l-6-4 MeV. The average error of the cross sections measured by H~~RLIMANN and HUBER(1955) in the range 2-4 MeV is 12 per cent. ALLEN et al. (1957) measured b(E) in the range 2-10 MeV and 13-15 MeV; the error on the absolute values of o(E) varies between 6 and 9 per cent. All the calculations with equation (6) given in Table 2 are not independent from each other and the error on the results is at least 9 per cent (5 per cent onf(E) and 6-9 per cent on o(E)). (ii) E.yperimentaI values. The experimental values quoted in Table 2 are taken over from the review article by ROCHLIN (1959). The irradiations of et al. (1953) were performed in the Harwell STAFFORD pile, and the 32S(n, p) cross section was derived from the cross section of the 54Fe(n, p)54Mn reaction. The quoted error on the fast flux is 10 per cent but is probably underestimated. HUGHES(1953) performed their irradiations inside a uranium fuel lump of the heavy water pile at Argonne, and the fission flux was standardized against a fission flux in a simple geometry. SAELANDet al. (1954) performed their irradiations near the centre of the Kjeller Reactor; the fission flux was based on the assumed 19 mb cross section of the 31P(n, p)“lSi reaction. For this reaction RICHMOND obtained 31.2 mb, using as reference the experimental fast fission section of 23sU(304 mb). The large discrepancies between the results are probably due to a distortion of the virgin fission neutron spectrum used in the experiments or to an error on the value of the fast flux. The good agreement between our result and the ‘calculated’ average value is gratifying.

is the experimental cross section measured as a function of the energy E. Experimental values are given by BLEULER(1947), KLEMAand HANSON(1948), L~~SCHERet al. (1950), PAUL and CLARK (1953), H~~RLIMANN and HUBER (1955), ALLEN et al. (1957), for 32S(n, p) and by GRUNDLet al. (1958) and HOWER- B. z7Al(n, a)24Na TON (1956) for 27Al(n, a). f(E), the fission neutron Table 3, partly taken over from MELLISH(1961), gives spectrum, is given by CRANBERGet al. (1956) as: a summary of the calculated and measured values of the average cross section for 27Al(n, or)2”Na. The errors f(E) = const. exp (-E/0*965) sinh d2*29E. on the measured values o(E) of GRUNDLet al. (1958) vary from 7-15 per cent. This expression fits the experimental fission spectrum; The experimental cross sections are measured the overall accuracy of the data above 1 MeV is relative to a reference cross section given in column 5. approximately 5 per cent. Column 3 gives the value of 5, when assuming a The data of L~~SCHER et al. (1950) are systematically low and the only value given by PAUL and CLARK value of 64.5 mb for the 32S(n, p) reaction. It is seen (1953) (at 14.5 MeV) strongly deviates from that given that in this case the three last values are in agreement. by ALLEN et al. (1957).

o(E)

3

H. DEPIJYDT and M. NEVE DE MEVERGNIES

452

TABLE2.-PUBLISHED VALUESOF THEAVERAGECROSSSECTIONFOR %(n, P)~~P References for 0 (E)

3 (mb)

Reference cross section

(1) ‘Calculated’ cross section obtained by averaging differential data with a fission spectra. MELLISH(1961) 61 Sf PA~SELLand HEATH(1961) 65 *, t, 1, **, tt, $1 66.2 GLOVERand MADDOCKS(1958) $9 tt, $1 64 & 3 WEALEef al. (1959) tt, $3 PARKER(1960) 65 f 3 GAGE (1957) 63.8 rt 5.7 :;“* tt7 St (2) Experimental cross section obtained by irradiation STAFFORDet al. (1953) 154 RICHMOND 60.3

HUGHES(1953) SAELANDet al. (1954)

30 21

This work

64.5 f 2.8 * BLEULER(1947). t KLEMAand HANSON(1948). $ L~~SCHER et al. (1950).

in a fission spectrum. 23aU(n, f) : 304 mb (measured) 32P(n, p) : 31 mb (assumed)

** PAUL and CLARK (1953). tf H~~RLIMANN and HUBER (1955). $$ ALLEN et al. (1957).

TABLE3.-PUBLISHED VALUESOF THE AVERAGECROSSSECTIONFOR a7Al(n, cz)24Na

a(mb)

a(mb) for %(n, p) = 64.5 mb

References 0 (E)

for

Reference cross section

-

(1) ‘Calculated’ cross section obtained by averaging differential data with a fission spectrum. PASSELLand HEATH (1961) 0.60 MELLI~H(1961) 0.5 - 0.8 ; WEALEet al. (1959) 0.54 f 0.05 t (2) Experimental HUGHES(1953)

cross section obtained by irradiation in a fission spectrum. 0.60 1.29

SAELANLI et al.

0.44

1.43

MELLI~H(1961)

0.24

0.52

RICHMOND

0.60

0.65

ROY (1959)

0.29

0.62

This work

0.628 rt 0.031

0.628

?3(n, p) : 30 mb (measured) 31P(n, p) : 19 mb (assumed) Y3(n, p) : 30 mb (assumed) 3z*U(n, f): 304 mb (measured) 32S(n, p) : 30 mb (assumed)

* HOWERTON(1956) t GRIJNDLet al. (1958). Acknowledgments-The authors wish to thank MR. E. JONCKHEERE,head of the Metallurgy Department, for the preparation of the U-disk, MR. L. VANSTEELANDT for the mechanical construction and the BR-1 reactor operation group. REFERENCES ALLEN L., BIGGERSW. A., PRES~VOODR. 5. and SMITHR. K. (1957) Phys. Reu. 107, 1363. BLEULERE. (1947) Helu. Phys. Acta 20, 519. CRANBERGL., FRYE G., NERESONN. and ROSENL. (1956) Phys. Rev. 103, 662. DERIJYI-~ERA. (1961) Reactor Sci. Technol. (J. Nucl. Energy Parts A/B) 15, 165. GAGE A. M. (1957) LA-2155.

Unpublished.

GLOVER R. N. and MADDOCKSK. (1958) AERE-R/R-2687. Unpublished. GRIINDL J. A., HENKEL R. L. and PERKINSB. L. (1958) Phys. Rev. 109, 425. HOWERTONR. J. (1956) UCRL 5226. Unpublished. HUGHESD. J., SPATZ W.D.B. and GOLDSTEINN. (1949) Phys. Rev. 75, 1781. HUGHES D. J. (1953) Pile Neutron Research, Addison-Wesley, Cambridge, Mass. p. 93. HUGHES D. J. and SCHWARTZ R. B. (1958) BNL325,2nd Edn. HUGHES D. J., MAGLJERNOB. A. and BRUSSELM. K. (1960) Suppl. No. 1, BNL-325.

H~LIMANN T. and HLI~ERP. (1955) Helv. Phys. Acta 28, 33. KLEMA E. D. and HANSONA. 0. (1948) Phys. Rev. 73, 106. L&CHER E., RICAMO R., SCHERRERP. and ZIJNTI W. (1950)

Helv. Phys. Acta 23, 561.

Average cross section of the ?S(n, P)~*P and 27Al(n, #*Na MELLISHC. E. (1961) Nucleonics 19, (3) 114. PARKERB. M. (1960) AERE-R. 3443. Unpublished. PASSELLT. 0. and HEATH R. L. (1961) Nucl. Sci. Engng. 10, 308. PAUL E. B. and CLARK R. L. (1953) Canad. J. Phys. 31, 267. RICHMONDR. Unpublished. Quoted in ROCHLIN R. S. (1959). ROCHLINR. S. (1959) Nucleonics 17, (1) 54. ROY J. C. (1959) Atomic Energy of Canada Ltd., Report C.R.C.852. Unpublished.

reactions for fission neutrons

453

S&LAND E., LYKAASM. and SAMSAHLK. (1954) JENER Report No. 23. Unpublished. STAFFORDG. M. and STEIN L. M. (1953) Nature, Lord. 172, 1103. TROYERA. DE (1960) Union Mini&e du Haut-Katanga, Brussels. Private communication. WEALE W. J., HYDER H. R. MC K., GREEN A., JONES E. D., KENWARDP. J. and ORAMP. J. (1959) Nucl. Power 4, 123.