Angular distribution for the T(d, n)He4 reaction at 1 and 3 MeV deuteron energy

2.B

Nuclear Physics 56 (1964) 394--400; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or mlerofilm without written permission from the publisher

A N G U L A R D I S T R I B U T I O N F O R T H E T(d, n)He 4 R E A C T I O N

AT 1 AND 3 MeV D E U T E R O N E N E R G Y A. PAULSEN and H. LISKIEN Central Bureau for Nuclear Measurements, EURA TOM, Geel, Belgium

Received 3 March 1964

Abstract: The angular distribution for the T(d, n)He4 reaction was remeasured at 10° intervals from 0° to 130° for deuteron energies of 1 and 3 MeV. The calculated uncertainties are within ±2.0 ~o and 4-3.0 ~o. The experimental results were fitted to Legendre polynomials and comparisons with earlier measurements are presented. E[

NUCLEAR REACTION Ha(d, n), E a = 1 and 3 MeV; measured tr(0).

[

1. Introduction Angular distributions for the T(d, n)He 4 reaction at 1 MeV have been published by Hemmendinger and Argo 1) and Bame and Perry 2), while data for 3 MeV are reported by Bame and Perry 2) and Galonsky and Johnson 3). This reaction is widely used as a source o f fast mono-energetic neutrons for neutron cross-section determinations. The two independent measurements for each deuteron energy are considered inadequate for the practical importance of this reaction, and therefore a remeasurement was carried out in this laboratory.

2. Experimental Arrangement Fig. 1 shows the general arrangement of the experimental apparatus. An analysed deuteron beam of about 7 pA provided by a 3 MeV electrostatic accelerator was focussed on the target, the focus being a vertical line. In addition, the beam had to pass through a tantalum aperture about 100 cm from the target. This aperture restricted the beam cross-section to a width of 0.3 cm and a height of 0.8 cm. In this way the influence of geometrical uncertainties was minimized. The target was a tritium loaded titanium layer 200/~g/cm 2 thick evaporated on a copper backing. This thickness corresponds to a deuteron energy loss of about 60 keV at 1 MeV or 30 keV at 3 MeV. The deuteron energy was determined by a recently calibrated nuclear resonance system. The neutron angular distribution was measured with a proton-recoil telescope counter of the Los Alamos type 4). In this counter protons are knocked out of a thin polyethylene foil and are detected by a CsI crystal. Two proportional counters are 394

395

THE T(d, n)He 4 REACTION

inserted between foil and crystal. To suppress effectively spurious pulses, the pulseheight spectrum of the CsI crystal is gated by the triple coincidences between all three counters. In all our runs a well-resolved proton peak was observed. A typical one is shown in fig. 2. The telescope counter was placed with its foil 10.8 cm from the neutron-producing target. This distance corresponds to an acceptance angle of +_7 °.

sotids t ~ monitor

d

-tTo-aper ture 0.3cm w i d t h

10 cm |

\

i

\

~

telescope counter

Fig. 1. Experimental arrangement.

COUNTS

. . . . .

.I

I

J

t

CHA NNEL

Fig. 2. Typical recoil proton spectrum of the telescope counter. The figure shows the gated pulseheight spectrum of the CsI crystal.

During all the measurements at I MeV the neutron flux was monitored with a long counter, which was positioned at 90 ° to the deuteron beam at a distance of about 150 cm from the target. At 3 MeV deuteron energy the background caused by spurious neutrons increased considerably; consequently the foreground-to-background ratio

396

A. P A U L S E N A N D

H. LISKIEN

for the long c o u n t e r d i d not allow reliable m o n i t o r i n g at this d e u t e r o n energy. H o w ever, a solid-state d e t e c t o r o f the surface-barrier t y p e gave excellent results as a n e u t r o n m o n i t o r . This d e t e c t o r was m o u n t e d 10 c m f r o m the target at a n angle o f 150 °. T h e pulse-height s p e c t r u m due to the r e a c t i o n SiZS(n, a ) M g a5 was o b s e r v e d in a 256-channel analyser. T r a n s i t i o n s to the g r o u n d state a n d the first 12 excited states in M g 25 were used for m o n i t o r i n g , so t h a t o n l y n e u t r o n s with an energy higher t h a n 8.7 M e V could c o n t r i b u t e to the m o n i t o r counts. I

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90 °

120 °

i

1.0

:

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0°

30 °

60 °

90 °

120 °

P 150 °

180 °

Fig. 3. Experimental results and Legendre polynomial fit for 1 MeV deuteron energy. T e r m s up to P~ were used for the fit. The indicated errors are total uncertainties.

0°

30 °

60 °

150 °

180 °

Fig. 4. Experimental results and Legendre polynomial fit for 3 MeV deuteron energy. Terms up to P, were used for the fit. The indicated errors are total uncertainties.

F o r the a d j u s t m e n t o f distance a n d angle o f the telescope c o u n t e r relative to the t a r g e t centre a n d b e a m direction a g r a d u a t e d circle was used. This circle was a d j u s t e d with its centre a b o v e the g e o m e t r i c a l centre o f the b e a m spot. W i t h the aid o f a m i r r o r system this a d j u s t m e n t was effected with a n a c c u r a c y o f ___0.2 m m in each direction. But the 3 m m width o f the b e a m spot, t o g e t h e r with the u n k n o w n intensity distribution o f the b e a m , resulted in a left-right a s y m m e t r y . As a check on the r e p r o d u c e a bility, s o m e m e a s u r e m e n t s were r e p e a t e d a n d d a t a for a d j a c e n t angles were t a k e n at different times. T h e m e a s u r i n g time for each angle was a b o u t 90 rain. S o m e b a c k g r o u n d runs were c a r r i e d o u t with the p o l y e t h y l e n e foil r e m o v e d f r o m the telescope counter, a n d others w i t h the c o p p e r - b a c k e d T-Ti t a r g e t r e p l a c e d b y a sheet o f copper.

THE T(d, n)He * REACTION

397

3. Results

Background corrections for the telescope counter were only necessary at 3 MeV deuteron energy and did not exceed 1 ~ . Background corrections for the monitors were only necessary for the long counter in the measurement at 1 MeV deuteron energy. This correction was approximately 5 ~ and was observed when the target was replaced by a dummy target. At 3 MeV the solid-state monitor showed a negligible background. TABLE 1

Experimental results of this work Lab. angle 0 (deg) 4.3 9.2 19.8 29.9 40.0 50 60 70 80 90 100 110 120 130

Relative flux Ed = 1 MeV Ed = 3 MeV 0.988- - 0.026 1.019- - 0 . 0 2 0 0.988- -0.020 0.979- = 0 . 0 2 9 0.959- - 0 . 0 1 9 0.947- -0.019 0.945 - 0 . 0 2 5 0.910- - 0 . 0 1 8 0.845- - 0 . 0 2 1 0.837- -0.025 0.822- - 0 . 0 1 6 0.755- - 0 . 0 1 5 0.749- - 0 . 0 1 5 0.707- - 0 . 0 1 4

1.0084-0.020 0.942-t-0.019 0.851 ±0.017 0.739±0.015 0.632_4-0.013 0.571 ::ko.o12 0.502:k::0.011 0.449q-0.010 0.4024,0.010 0.3534,0.01 l 0.3554-0.008 0.3594-0.008 0.3594-0.008 0.3634-0.008

In the evaluation of the telescope counter data, the semi-empirical formula of Gammel 5) was used for the total n - p scattering cross-section. In addition, corrections were applied for the neutron flux attenuation caused b y t h e target holder. These corrections are only important at 80 ° and 90 °, where they are of the order of 5 to 6 ~ . The results were transformed to the centre-of-mass system and least-squares fits to Legendre polynomials were carried out. Data for 1 MeV deuteron energy were fitted with terms up to P2, while for the 3 MeV data terms up to P5 seemed necessary. However, to enable a better comparison with the results of Bame and Perry 2) terms up to P6 were used for the fit of the 3 MeV data. Experimental results and fits were normalized to unity for the fits at 0 ° and are shown in figs. 3 and 4. In addition, these normalized results are summarized in table 1. 4. Accuracy of the Measurement

Typical uncertainties are listed in table 2. Due to the lower differential cross-section of the T(d, n)He 4 reaction at 3 MeV and backward angles, the statistical uncertainty here reached its maximum of ___1.2 ~/. The estimated uncertainty of the neutron flux attenuation in the target holder was 30 ~ . This leads to a maximum uncertainty

398

A. PAULSEN AND H. LISKIEN

contribution of + 2 ~ for the 90 ° results. The uncertainty due to the anisotropy of the n - p scattering, as quoted in table 2, is in fact an upper limit at the highest neutron TABLE 2 Sources and typical values o f errors Source o f uncertainty

Typical error (%) 0.9 1.0 1.0 0.3 0.3 0.7 0.8

Statistics o f telescope c o u n t s Geometry T o t a l m o n i t o r accuracy a) F l u x a t t e n u a t i o n in the target holder b) Choice o f limits for p r o t o n p e a k T o t a l n-p scattering cross-section e) A n i s o t r o p y o f n-p scatttering d)

a) C o m p r i s i n g statistical error, u n c e r t a i n t y o f b a c k g r o u n d correction a n d instability o f electronic thresholds. b) M a i n l y due to inaccurate knowledge o f cross-sections. e) T h i s absolute u n c e r t a i n t y is discussed in ref. 5). F o r the evaluation o f the data f r o m this exp e r i m e n t only relative cross-sections are involved. d) E s t i m a t e d u p p e r limit o f uncertainty.

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1.0

l

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30 °

60 °

90 °

I 120 °

I 150 °

O

LAB.ANGLE O 180 °

Fig. 5. C o m p a r i s o n o f the Legendre polynomial fits between existing Eo = 1 M e V data. T h e d a s h e d line is the fit given by Bame a n d Perry ~), the d o t - a n d - d a s h line is based on the d a t a o f H e m m e n d i n g e r a n d A r g o t), the fit h a v i n g been carried o u t by us, a n d the solid line is the fit f r o m this work. All fits include t e r m s up to P~.

0°

30 °

60 °

90 °

t 120 °

I 150 °

180 °

Fig. 6. C o m p a r i s o n o f the Legendre p o l y n o mial fits between existing E a = 3 M e V data. T h e d a s h e d line is a g a i n the fit with t e r m s u p to Pe as given by B a m e a n d Perry s), the dota n d - d a s h line is t a k e n f r o m the p a p e r o f G a l o n s k y a n d J o h n s o n 3) a n d is p r o b a b l y n o t a Legendre p o l y n o m i a l fit. T h e solid line is t h e fit f r o m this w o r k with t e r m s u p to P6-

399

THE T(d, n)He t REACTION

e n e r g y , b u t t h e q u o t e d n u m b e r was u s e d f o r all results. C o m p o u n d i n g q u a d r a t i c a l l y t h e e r r o r s listed in t a b l e 2 w e find a t y p i c a l t o t a l u n c e r t a i n t y o f _+ 2.0 ~o t h e i n d i v i d u a l e r r o r s are g i v e n in t a b l e 1. TABLE 3 Values of fitted curves for practical application • ,

Lab. angle 0 (deg)

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

(0)

~

(0 °) at E a = 1 MeV

Bame and Perry

Hemmendinger and Argo

1.000 0.998 0.992 0.982 0.967 0.946 0.922 0.894 0.860 0.825 0.788 0.751 0.717 0.685 0.658 0.635 0.618 0.608 0.606

1.0C0 0.998 0.991 0.982 0.964 0.942 0.914 0.884 0.846 0.806 0.768 0.728 0.687 0.651 0.619 0.592 0.573

da

This work 1.000 0.999 0.992 0.983 0.969 0.951 0.926 0.900 0.870 0.837 0.805 0.771 0.741 0.711

(0)

/ da ~(0 °)atEa=3MeV

Bame and Perry

This work

1.000 0.958 0.849 0.733 0.639 0.573 0.517 0.461 0.415 0.379 C.360 0.356 0.356 0.356 0.354 0.351 0.347 0.346 0.346

1.000 0.957 0.849 0.731 0.638 0.568 0.506 0.444 0.396 0.363 0.352 0.355 0.362 0.362

TABLE 4 Legendre coefficients E a = 1 MeV

Ed = 3MeV

0g~

Bame and Perry

Hemmendinger and Argo

This work

Bame and Perry

This work

~0 ~1 ~2 ~a ~4 ~ ~e

0.819 0.578 --0.031

0.798 0.108 --0.040

0.831 0.063 --0.028

0.455 0.102 0.130 0.032 0.022 0.034 0.014

0.448 0.117 0.126 0.054 --0.015 0.050 0.010

5. Comparison with Existing data I n figs. 5 a n d 6 all e x i s t i n g d a t a a r e p r e s e n t e d f o r c o m p a r i s o n . F o r p r a c t i c a l a p p l i c a t i o n s n u m e r i c a l v a l u e s f o r e a c h c u r v e are listed in t a b l e 3. I n t a b l e 4 the coefficients o f t h e fits a r e c o m p a r e d .

400

A. PAULSEN AND H. L1SKIE,N

The 1 MeV curves in fig. 5 are all Legendre polynomial fits with terms up to P2. The curve of Bame and Perry was taken directly from table 2 of ref. 2). If one takes into account the experimental uncertainty of _ 3.5 ~ which is quoted by these authors, one can state a satisfying agreement with our results. The experimental data from table 1 of ref, 1) were fitted by us to obtain the curve of Hemmendinger and Argo. Here +3.0 ~o is reported for the experimental uncertainties. At larger neutron emission angles the difference between this curve and our fit is outside the experimental uncertainties. The 3 MeV curve of Galonsky and Johnson in fig. 6 represents the normalized curve fig. 3 of ref. 3) and does not seem to be the result of a least-squares fit. The distribution of Bame and Perry is taken again from table 2 of ref. 2). Their experimental uncertainties are _ 8 ~o (ref. 3)) and + 3.5 ~ (ref. 2)). Taking into consideration these errors all three distributions show a satisfying agreement. We wish to express our special gratitude to Mrs. M. G. Cao for carrying out the above-mentioned Legendre polynomial fits. Our thanks are also due to Mr. T. Van der Veen for his assistance during the measurements and to Messrs. J. Leonard and R. Duchez, both from the VdG accelerator staff. References 1) 2) 3) 4) 5)

A. Hemmendinger and H. V. Argo, Phys. Rev. 98 (1955) 70 S. J. Bame, Jr. and J. E. Perry, Jr., Phys. Rev. 107 (1957) 1616 A. Galonsky and C. H. Johnson, Phys. Rev. 104 (1956) 421 S. J. Bame, Jr., Eugene Had.dad, J. E. Perry, Jr. and R. K. Smith, Rev. Sci. Instr. 28 (1957) 997 J. L. Gammel, in Fast neutron physics, Part 1I, ed. by J. B. Marion and J. L. Fowler (lnterscience Publishers, New York, 1963) p. 2209