Precise measurement of the integral cross section for the reaction 24Mg(n,p)24Na between 13.5 and 18.0 MeV

Ann. nucl. Energy, Vol. 15, No. 3, pp. 155 159, 1988 Printed in Great Britain. All rights reserved

0306-4549/88 $3.00+0.00 Copyright © 1988 Pergamon Press plc

PRECISE MEASUREMENT OF THE INTEGRAL CROSS SECTION FOR THE REACTION 24Mg(n,p)24Na BETWEEN 13.5 AND 18.0 MeV J. JANCZYSZYN, G. DOMANSKA,W. POHORECKI, L. LOSKA and F. PACH Institute of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, 30-059 Krakow, Poland

(Received 26 July 1987) A~tract--Activation technique has been used to measure the cross-section ratio for 24Mg(n,p)24Na and 27Al(n, a)24Na reactions, the last being a reference one. The reaction T(d, n)4He was used to produce the neutrons. Countings of y-spectra were performed with a 75 x 75-mm Nal (T1) detector. The new crosssection values for 24Mg were calculated based on the best values of the 27Al-reaction cross-sections for respective neutron energies. In general, the obtained total error is 1.5 2 times smaller than previously.

INTRODUCTION

25o o At--27(n,a)

Despite the abundance of work devoted to the deterruination of neutron-induced threshold reaction crosssections the accuracy of the available data is still not satisfactory. The error is on the level of 1-2% for only a few reactions and in the neutron energy region between 14 and 15 MeV. F o r the rest, it ranges from 5 to 50% and in many cases is not even determined. The reaction for which cross-section values are most accurate is 27Al(n,a)24Na. According to Vonach (1983) the relative error of its cross section varies from 0.3% for neutron energies around 14.4 MeV to 3.0% for energies in the region of 13 and 19 MeV. The reaction investigated in this study: 24Mg(n,p)24Na leads also to the generation of the 24Na and is not as well-known as the first one. Based on those two facts and using the activation method of the cross-section ratio determination, proposed earlier by Janczyszyn (1983), one can precisely determine the cross section for the investigated reaction. Excitation functions of both reactions, drawn on the basis of the values given by Tagesen et al. (1979) and Vonach (1983), are shown in Fig. 1. In Fig. 4 the ratio o f their cross sections is depicted for the neutron energy range o f interest. Monoenergetic neutrons with energies between 13 and 18 MeV, produced in the T(d,n)4He-reaetion using a Van de Graaff accelerator in the Institute of Nuclear Problems in Warsaw, were applied.

- 2o0 E oE - ~so ~00

so

o 8

11

1/-~

17

20

E (MeV)

Fig.

1.

Excitation functions of 27Al(n,a)24Na and 24Mg(n, p)Z4Na reactions.

known equation for the number of counts registered during a measurement of an activated sample has the form: N N = ~_2"m'O'c'tr.$.

[1-exp(-2ti)].e.G

• exp ( - 2 t d ) • [1 - e x p ( - 2to)], where : N M m c

EXPERIMENTAL P R O C E D U R E

The cross-section measurements were performed with the use of the activation technique. The well155

= = = =

Avogadro's number, atomic mass, mass of the sample, element concentration in the sample,

(1)

156

J. JANCZYSZYNet al.

0 = isotopic abundance, a = reaction cross-section, q~ = neutron flux density, 2 = decay constant, ti, td, tc = irradiation, decay and counting times, respectively, ~, = counting efficiency, G = n u m b e r of 7-quantas emitted in a nuclear decay. The ratio of the n u m b e r of counts, of 24Na, measured for two samples, one made of Mg and the other of AI, irradiated simultaneously and counted in identical conditions is given by : N'

M

N

M'

/

.

2

.

.

.

.

/ /

/

Fig. 2. Standard sample positions in the sample holder around the T/Ti target. 1 = neutron source, 2 = samples. The arrow shows the deuteron beam direction.

m' 0' c' a' exp(--2t~) m 0 c a exp(-2ta) [1 --exp (-- 2t~,)] [1 --exp (-- 2to)] '

/-

1

, ~ct~4-, _ L5

Mg

At

/ - T- / T i

(2)

where the prime denotes the Mg sample. From this formula the cross-section ratio can be directly determined. The atomic masses and isotopic abundances are known with high accuracy. Application of pure elemental samples (with element content higher than 99.7%) eliminates other errors. Precise weighing and counting of the sample activity in identical times may be done easily. When both samples are counted directly, one after the other, the correction factor accounting for different decay times is very accurate. Thus the total uncertainty will depend on the statistical counting error of the n u m b e r of counts N and N ' and on the difference in irradiation and counting conditions. The 3 MV Van de Graaff used for producing neutrons gives a 50 #A deuteron beam. The applied Ttarget in the form of titanium tritide was a b o u n t 0.5 mg cm ] thick. The diameter of the beam hot-spot on the target was 6 mm. Samples were irradiated in a five-position standard holder. Angular positions of irradiated samples relative to the incoming deuteron beam were 0 °, 30 °, 60 °, 90 ° and 120 ° (Fig. 2). Neutron energies respective to those positions for several deuteron energies are given in Table 1, as calculated by E1-Konsol (1972). For irradiation 99.99% A1 and 99.7% Mg pure metallic samples were prepared. Both materials were activated simultaneously in the same position. Thus equal irradiation times and almost identical neutronflux densities were ensured. Sample shapes and dimensions and activation geometry are shown in Fig. 3. Sample weight of about 120 mg for Mg and 170 mg for A1 was chosen to achieve approximately equal dead-time and pile-up effects, during counting.

//

/

r

9

°"

I. Fig. 3. Activation geometry. Al--aluminium foil surrounding the magnesium rod--Mg. Table 1. Neutron energies and their resolution for different holder positions and deuteron energies Deuteron energy (MeV)

Angle (degrees)

Neutron energy (resolution)" (MeV)

0.44

0 30 60 90 120

15.40 (0.24) 15.23 (0.20) 14.78 (0.28) 14.17 (0.33) 13.59 (0.27)

0.60

0 30

15.80 (0.21) 15.54 (0.22)

0.80

0 30

16.23 (0.18) 15.93 (0.25)

0.99

0 30

16.59 (0.15) 16.29 (0.28)

1.30

0 30

17.09 (0.12) 16.77 (0.34)

1.80

0 30

17.86 (0.08) 17.42 (0.44)

~'Half width of the neutron peak at half of its height.

Applied irradiation times range from 2 to 15 h for deuteron energies from 0.44 to 1.8 MeV (depending on the neutron yield from the D - T reaction). /4Na, the radionuclide resulting from both reactions, decays with the 14.960+0.006h half-life

Precise measurement of the integral cross-section Table 2. Results of cross-section ratio measurements E (MeV) 13.59 14.17 14.78 15.23 15.40 15.54 15.93 16.23 16.29 16.59 16.77 17.09 17.86

157

(S'-B)m M O' a' ( S - B)m" exp [2(t~ - td)] = ~M" ~ " a "

(3)

Cross-section ratio (random error of the ratio) 1.6073 (0.0033) 1.6730 (0.0059) 1.6107 (0.0183) 1.5649 (0.0056) -1.5640 (0.0190) 1.5240 (0.0300) 1.5700 (0.0310) 1.5580 (0.0310) 1.6413 (0.0124) 1.6320 (0.0410) 1.6500 (0.0120) 1.6240 (0.0170) --

1.6025 1.6062 1.6359 1.5780 1.6134 1.6323 1.5930 1.5660 1.6107 1.7036

(0.0072) (0.0104) (0.0289) (0.0114) (0.0098) (0.0053) (0.0380) (0.0320) (0.0323) (0.0218)

-1.5719 (0.0071) 1.5562 (0.0073) -1.5831 (0.0078) 1.5356 (0.0078) 1.5588(0.0050) 1.6254 (0.0045) 1.6320 (0.0042) 1.6448 (0.0079)

--1.8045 (0.0098)

1.6352 (0.0105) 1.6159 (0.0114) 1.7826 (0.0079)

[according to Lorenz's compilation (1983)] and emits two y-rays with energies of 1.368 and 2.754 MeV. Activities of Mg and AI samples were measured with a 7.5x7.5-cm NaI (T1) detector at least 2h after the end of irradiation. Since the 24Na-lines only were observed, the integral counting was performed within the energy range 0.4 to 3.0 MeV. Both samples Mg and AI, activated in the same holder position, were counted directly one after another for equal counting times to minimize instrumental errors. Usually 2000 or 4000 s counting times were used. The stability of the number of counts due to natural background was frequently checked between measurements. DATA REDUCTION AND RESULTS

The numbers of counts S' and S obtained for simultaneously irradiated Mg and A1 samples, respectively, after the background subtraction, normalization to the unit sample mass, correction for the different decay times and division one by the other, give the ratio :

Then the cross-section ratio can easily be calculated : O"

M'OS'-Bm

0"

M 0' S - B

m' exp(2"Atd).

The following values for atomic masses and abundances were adopted in computations: M ' = 23.985 g, M = 26.982g, 0' = 0.787, 0 = 1.000. The results of cross-section ratios obtained in four runs of measurements are presented in Table 2. The values of random error given in Table 2 were calculated from the results of two subsequent measurements made for each pair of samples after their activation. Starting from the results in Table 2 the average ratios and their standard deviations were evaluated. The apparatus error, thought of as the excess of the random error over the counting statistics, was also deduced. It amounts to 1.6+0.6%. The final results of the determined cross-section ratios and values of their uncertainty are given in Table 3 and Fig. 4. Table 3 contains also the literature values of cross sections of both considered reactions, recalculated for those neutron energies for which the measurements were performed. Recalculations were made under assumption that the activating neutron flux had a truncated Gaussian distribution. It was assumed also that the FWHM (full width at half maximum) of the distribution is equal to double the value of the energy resolution for the given neutron energy (see Table 1). Values of cross section were then calculated by numerical integration of the ~(E) function over the energy interval of one FWHM on both sides of the given experimental neutron energy. The values ofa(E) for both reactions were obtained by a polynomial

Table 3. Measured and recalculated values of cross sections Neutron energy (resolution) (MeV)

Cross-section ratio (uncertainty) Mg/AI

13.59 (0.27) 14.17 (0.33) 14.78 (0.28) 15.23 (0.20) 15.40 (0.24) 15.54 (0.22) 15.93 (0.25) 16.23 (0.18) 16.29 (0.28) 16.59 (0.15) 16.77 (0.34) 17.09 (0.12) 17.86 (0.08)

1.607 (0.014) 1.628 (0.015) 1.567 (0.013) 1.567 (0.017) 1.595 (0.018) 1.600 (0.015) 1.558 (0.014) 1.623 (0.015) 1.630 (0,015) 1.646 (0.014) 1.642 (0.019) 1.618 (0.020) 1.791 (0.020)

(4)

Cross section (uncertainty) (mbarn) 27Al(n, a) ~ Z4Mg(n,p) Vonach (1983) This work Tagesen et aL (I 979) 125.2 (0.6) 120.6 (0.6) 112.6 (0.7) 108.0 (1.5) 105,7 (I .8) 103.5 (1.9) 95,8 (1.8) 89,3 (1.8) 88.1 (1.7) 81.8 (1.7) 78.9 (1.8) 73,6 (1.9) 62.9 (2.1)

201.2 (2.0) 196.2 (2.0) 176.5 (2.0) 169.2 (3.0) 168.5 (3.4) 169.0 (3.5) 149.2 (3.2) 144.9 (3.2) 143.6 (3.1) 134.6 (3.1) 129.5 (3.3) 119.2 (3.4) 112.7 (4.0)

a Values obtained by recalculation of Vonach (1983) and Tagesen et al. (1979) data.

207.4 (3. I) 193.9 (1.3) 180.0 (4.0) 175.4 (6.8) 171.7 (6.3) 167.5 (6.0) 153.0 (5.3) 145.3 (5.5) 144.2 (5.5) 137.4 (5.3) 133.6 (5.0) 128.2 (4.8) 119.5 (4.3)

158

J. JANCZYSZYNet al.

,9

Iva.....*coLaold from

this

Vonach's ( t 9 8 3 ) and Tagesen et al (1979) d a t a

/

work

18

.o p,

8

15

I/*

i

12

13

II5

11/~

I~eutron energy

1 16

117

l t8

(MeV)

Fig. 4. Cross-section ratio of the 24Mg(n,p)24Na and 27Al(rt, a)24Na reactions in the energy range of interest. The line is drawn just to guide the eye.

220

F

interpolation between the values of Tagesen e t al. (1979) and Vonach (1983). Values for the 27Al(n, a)ZgNa-reaction obtained in such a way were then multiplied by the determined cross-section ratios producing new cross-section values for the 24Mg(n, p)24Na-reaction. They are shown in Table 3 and Fig. 5 together with the recalculated literature values.

this work

N

200

180

Tagesen et at. 11979)

Y/////-

16o

DISCUSSION AND C O N C L U S I O N S

~

1/*0

N4

120

I

13

I ~//////////~,

I

L

I

L

I

I

14

15

16

1"7

18

19

Neutron energy ( M e V )

Fig. 5. Results of the 24Mg(n,p)24Na reaction cross-section determination compared with results of Tagesen et al. (1979).

As can be seen from Table 3, the differences between the new values of the 24Mg(n,p)24Na-reaction crosssection and those of Tagesen e t al. (1979) are rather small and only for the highest neutron energies, 17.09 and 17.86 MeV, are remarkable. Uncertainties of the obtained cross-section values range from 2 to 4 mbarn, and are lower than the values of Tagesen e t al. (1979) for most neutron energies. The best improvement is reached for 14.78 and 15.23 MeV neutron energies, for which the ratio of cross-section uncertainty for the investigated and reference reaction is the highest. Most of the systematic errors were eliminated in the applied procedure. Some of them were shifted to the random uncertainty due to unavoidable changes in experimental conditions in different series of measurements. Only two sources of error were not taken into consideration : chemical purity and isotopic

Precise measurement of the integral cross-section composition of materials used. They are estimated to 0.3 and 0.2%, respectively. There is, however, one physical reason, which may cause an over-estimation of the determined cross-section values. Since Mg is not a monoisotopic metal the 24Na may also be produced in such reactions as : 25Mg(n, np + n, d + n, pn)24Na and 26Mg(n, 2np + n, n d + n, t + n, d n + n, p2n)24Na. Most of these reactions should have small values of cross section, but for some of those for 25Mg, crosssections can be significant and therefore the authors plan to perform appropriate measurements with a pure isotopic sample of 25Mg. It can be concluded, the applied procedure is precise and could be useful for improving cross-section determination for some reactions, under the condition however, that a reference reaction with a well-known cross section is available. For neutron energies from 13 to 20 MeV its usefulness seems to be rather limited since there are only about 20 such pairs of reactions leading to the same radionuclide. A more promising

159

area of application lies in the higher energy region, where the variety of possible reactions is much larger. Acknowled#ement--Thanks are due to Dr A. Marcinkowski

from the Institute of Nuclear Problems in Warsaw for making possible the use of a Van de Graaff accelerator and accompanying facilities and for his kind attention to problems that arose during measuring sessions. This work was done under Polish Government Program No. CPBP 01.09, REFERENCES

E1-Konsol S. (1972) The investigation of the reactions induced by fast neutrons in the medium nuclei. Ph.D. Dissertation, University of Warsaw. Janczyszyn J. (1983) Nuclear Data for Science and Technolo#), (K. H. Bockhoff, Ed.), p. 869. ECSC, EEC, EAEC, Brussels and Luxembourg. Lorenz A. (1983) Nuclear Data Standards for Nuclear Measurements, p. 89. IAEA Technical Report Series No. 227, Vienna. Tagesen S., Vonach H. and Strohmaier B. (1979) Physics Data. Compilation Series, Fachinformationszentrum Energie, Physik, Matematik, Karlsruhe, 13-1. Vonach H. (1983) Nuclear Data Standards for Nuclear Measurements, p. 59. IAEA Technical Report Series No. 227, Vienna.