The mechanism of the (n, 2n) reaction

Nuclear Physics 4 9 (1963) 4 8 9 - - 4 9 5 ; {~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

THE MECHANISM

O F T H E (n, 2n) R E A C T I O N

A. /~D/~M, P. HRASK6, GABRIELLA P/~LLA and P. QUITYNER Central Research Institute of Physics of the Hungarian Academy of Sciences, Budapest Received 17 June 1963

Abstract: An experimental investigation has been made on the extent of the angular correlations between the neutrons produced in the (n, 2n) reaction. The fast neutrons have been detected by means of scintillation counters and fast coincidence circuits. From measurements on bismuth and lead, the cross section of the (n, 2n) reaction was found to be 20-30 ~ lower than the values obtained by activation or any other method insensitive to the direction of the emerging neutrons thus suggesting a correlation between the neutrons.

1. Introduction A l t h o u g h at high energies the (n, 2n) reaction is k n o w n to be d o m i n a n t a m o n g the processes i n d u c e d b y fast neutrons, owing to e x p e r i m e n t a l difficulties involved in the detection a n d energy m e a s u r e m e n t o f neutrons, our knowledge o f these reactions is still restricted to cross section d a t a o b t a i n e d m a i n l y by activation m e t h o d . Energy spectra a n d a n g u l a r distributions have been d e t e r m i n e d a l t h o u g h only one o f the two e m i t t e d neutrons has been detected 1. z). T h u s it seems difficult to m a k e a n y definite statement as to the m e c h a n i s m o f the process, since the actual emission o f two neutrons c a n n o t be verified. Investigations o f the energy a n d angular correlations between the two n e u t r o n s will lead to a better knowledge o f the reaction m e c h a n i s m 3) a n d possibly to nuclear s p e c t r o s c o p y data. I n view o f the considerable experimental difficulties we w a n t e d first to o b t a i n s o m e i n f o r m a t i o n on the extent o f the correlations which m i g h t be expected. The m e a s u r i n g technique was so chosen as to yield the cross section value a(n, 2n) as o b t a i n e d b y the activation m e t h o d if no correlations occur or a lower value giving the u p p e r estimate o f the u n c o r r e l a t e d (n, 2n) events.

2. Experimental Procedure The e x p e r i m e n t a l set-up a n d the b l o c k d i a g r a m o f the electronic devices are to be seen in figs. 1 a n d 2, respectively. The neutrons are p r o d u c e d f r o m the T ( d , n ) H e 4 reaction b y m e a n s o f a 200 keV accelerator. Plastic scintillators 50 m m b y 230 m m for neutrons a n d 50 m m b y 0.1 m m for the recoil ~t-particles are used as detectors, 489

A..~D.~M et aL

490

they are all mounted on RCA 68-10/A photomultipliers. The (n, 2n) events are selected by fast coincidence circuits between the a- and the neutron detectors 4). The time delays are so chosen that no systematic coincidence due to 7-particles from the (n, 2n) and (n, n' ~) reactions m a y occur whereas the time conditions permit the counting of the (n, 2n) neutrons in the 0.1-7 MeV energy interval. The pulses from the two fast coincidence circuits are fed into a slow coincidence unit of 2 . 10 - 6 sec time ,A

t~eotrondeteftor$

A

B /

uferOn

0

trt'ttem

a ~elec/or ,\ .0 j" (t2)

&

reacficnlar#et

Fig. 1. The three arrangements o f the neutron detectors.

1..N.t7-=~5.t0" ,oJco,.c J "

[ seater

]

V---r---q

I

Idl.~cr,minatarl

co'fcL.._Jamp/if er ] Id'~c~iminat°rl $

] "t'=KS"/d° I

[neutron d~leclor I "

I 2

I scaler

I

]

Fig. 2. Block diagram of the electronic setup.

resolution. Thus, the number of coincidences covers those events only in which the counts of both neutron detectors occur in a given time interval after an c~-count. The threshold of the fast coincidence circuits was about 100 keV proton energy on the neutron side, while the a-side was set immediately above the noise level. The direction of the incident neutrons is given by the a-detector solid angle, thus no additional neutron collimation is required. The c~-counts determine also the neutron yield. The recorded quantities are the coincidences NA and NB between each of the neutron detectors and the a-detector, the coincidences NK between N A and NB and the number N~ of or-counts.

THE (n, 2n) REACTION

491

Targets of various sizes were used, the smallest was a 1 cm by 1 cm cylinder, the largest a 3.5 x 7 x 14 cm slab. The reaction target was mounted directly on the tritium backing. This gives the optimum ratio of true-to-random coincidences, the angular distribution being determined in any case by the solid angle of the a-detector. The chance coincidences are of a complex nature. However, if the detector pulses are delayed in a suitably way, the number of random coincidences could be experimentally determined. The correction amounted to 10-15 ~ depending on the geometry chosen. A correction was applied also for systematic coincidences due to material other than target material. The value of this correction term varied from 5 to 10 (e.g. the value of N t showed appreciable change when instead of the usual tritium target with 0.2 mm tungsten backing a 2 mm molybdenum backing was used).

3. Method of Evaluation

The present evaluation is based on the assumption that for the materials investigated (Bi and Pb) only neutrons from the (n, 2n) reaction emerge at 90 °. This assumption is justified, since in the case of heavy nuclei the (n, 2n) cross section is equal to the non-elastic cross section 5). In addition, let us assume that the neutrons evaporate independently of each other. As to their angular distribution, we assume axial symmetry. It follows from these assumptions that in the set-up shown in fig. la, the number of counts is given by NA = N,p(GA, + GA~-- GA, GA~) ~ N,p(GA, + GA~),

N. =

(1)

NK = N~p(GA, Ga2 + GA2 Ga,),

where p is the probability of the (n, 2n) reaction in the target, GA~ , GA2 , Ga, and Gas are the detection probabilities of the first and the second neutron in the detectors A and B. The values G depend in addition to detector solid angle and efficiency on the angular distribution and contain the effect of multiple scattering and are averaged over the neutron energies. Now, we calculate the ratio p = N A Na/2N~, N K from the measured number of counts. Since the detectors are identical and in symmetrical positions GAI -----GB, and GAs = GB2.Thus it can be seen that -

NANB -- p (GAt4-GA2)(GB'q-GB2) -- p (GAtI-GA2)2 ___~>p.

2N~ N K

2(GA, GBaq- GA2 Ga,)

(2)

4GA, GA2

It follows that for independently evaporating neutrons we must have t3 > p.

(3)

Measurements have shown the detector efficiency averaged over the energy spectrum to be insensitive, or hardly sensitive to the shape of the energy spectrum~ If there

492

A. ~t>~,M e t

al.

is no correlation and the angular distributions of the two neutrons are taken to be equal (not necessarily isotropic), then GA1 = GA2 and/5 = p. The relationship between p and the (n, 2n) cross section is I 1-- exp ( -- 2~.)] , p - - a(n'2n) - -

(4)

O'at t

where L is the target length, and ~'att is the mean free path for attenuation. Owing to the markedly forward peaking of the elastic scattering 7), it is expected that )'att = 2r, where 2r is the reaction mean free path. This has been confirmed experimentally by measurements on targets of various lengths. Nevertheless, the cross section was determined from measurements on such short targets that L << ~att, thus p = L Z(n, 2n),

(5)

where 27(n, 2n) is the macroscopic (n, 2n) cross section. We should like to point out that by this method it was checked directly whether the neutrons emerge independently of each other, without making any particular assumption concerning the evaporation (e.g. symmetry to 90°). It is easily understood that the probability of the uncorrelated (n, 2n) reaction is less than the value of/~ determined by the above method, if part of the (n, 2n) neutrons are correlated with each other or with the incident neutrons. This holds also in the case when, in addition to the (n, 2n) reaction, the (n, n'7) reaction occurs. The angular correlation between the neutrons in the (n, 2n) reaction seems to be far from simple. For convenience it is assumed to be divisible into individual components, each of them associated with a given reaction mechanism. These mechanisms are assumed to be the following: a) Pure compound mechanism. Both neutrons evaporate from the compound nucleus independently of each other. In this case the angular correlation between the neutrons may occur only via the angular momentum of the compound nucleus 6). Then, using the set-up shown in fig. la, a higher value of ArK will be obtained than in the arrangement of fig. 1(c). b) Direct-compound mechanism. The incident neutron collides directly with the target nucleus and is ejected in the forward direction. The excitation energy of the residual nucleus is sufficient to cause a second neutron to evaporate. e) Compound-direct mechanism. Owing to the n-n interaction in the final state, two neutrons emerge simultaneously from the compound nucleus. The centre-of-mass of the emerging neutrons is not correlated with the direction of the incident neutron, but the angular correlation between the outgoing neutrons can be strong. d) Direct mechanism. Both neutrons leave the nucleus as a result of a direct interaction. Forward peaked angular distributions and angular and energy correlation of the two neutrons are to be expected 3). i

ThE (n, 2n) REACTION

493

4 Measurements and Results The values of N A, N B, N~ and ArKwere determined with and without target, measuring in each case the number of random coincidences as well. With each of the various targets 10 to 30 runs were made. The values given here are the averages. The error was estimated from the deviation from the mean. The evaluation was performed by making use of eq. (5) for small targets, and of eq. ,(4) for large targets. In the latter case the value of 2at t w a s also needed. It was found that ~'att = )'r, therefore the value given in the literature could be used. 4.1. THE Bi-TARGET Using a cylindrical target (1 x 1 cm) we obtained a(n, 2n) = 1.95+__0.08 b, as compared with 2.3+__0.3 b and 2.60+0.19 b (refs. 2, 7), respectively). The values of a as measured with targets of various lengths were in agreement with one another, using ar = 2.5 b (fig. 3).

¢era

½)'t

)'t

2),t torg o/leng/h

Fig. 3. The (n, 2n) reaction probability for targets of various lengths. O Measured points. + -- ÷ Calculated curve (from the total (n, 2n) cross section). In order to verify that the result is not being affected by a double scattering, measurements were performed also on targets with identical lengths but varying in cross section. The values of a thus obtained were in agreement to within 3 ~ accuracy. I f any of the conditions assumed is not fulfilled, this will lead to an underestimate of the contribution of correlated processes. The only effect possibly reducing the value of p would be the simultaneous response of both detectors to the same neutron, for instance, the cross-scattering of a neutron from one detector into the other or a crossscattered gamma. This effect would increase primarily the values of N~ leaving that of NA and NB essentially unchanged. This process seems to be quite improbable since for the given geometry (180 ° ) neutrons are cross-scattered only by multiple scattering. I f the second neutron detector responds to a gamma, arising from inelastic collision of the neutron with carbon in the first detector, the pulse from the excited carbon nucleus does not attain the threshold of the measuring apparatus. In spite of this, the apparatus was thoroughly tested for cross-scattering.

494

A. ADAMet

aL

The threshold energy for the (n, 2n) reaction in carbon is a b o u t 20 MeV. Consequently, the value of NK with or without carbon target must be the same. However, ArK measured with the carbon target was found to be about I0 ~o higher. The reason for this is that the counting efficiency of the coincidence circuit outside the resolution time proper does not drop immediately to zero, thus (n, n'v) coincidences were also counted, though with less probability. In the case of Bi- and Pb-targets these coincidences were only a small fraction of the total number of counts and anyhow they only may increase the value of p. Owing to the detection of (n, n'v) coincidences this method seemed inadequate" for checking the cross-scattering effect. It is possible to determine p from each of the values N A, NB and ArK individually, if the average efficiency of the detectors is known, since only (n, 2n) neutrons are assumed to emerge at 90 °. The p thus obtained is, of course, less accurate than that determined by the above method because of the relatively large error in the efficiency, yet adequate for checking the cross-scattering. After having measured the detector efficiency, the energy spectrum of the (n, 2n) neutrons for bismuth was determined 9). Averaging the efficiency over the measured energy spectrum, p as determined from NA and NB was found to be 0,255 + 0.023 and from NK 0.252 _0.046as compared to t5 = 0.267+_0.006 and to 0.34 to be expected from the (n, 2n) cross section obtained by the activation method. The errors in the experimental values contain the uncertainty in efficiency. If cross-scattering were responsible for the lower value measured in the present experiment, then from N A and NB we would have obtained 0.34 and from NK a higher value by counting "cross-scattering coincidences", too. Thus, it is thought that crossscattering did not interfere in the measurements and the lower value in the present experiment suggests the existence of correlated events. Consequently, the cross section value obtained from the measurement must be actually the upper limit of the uncorrelated reactions. Altering the time resolution of one of the coincidence circuits in order to have GAI ---- GA2 the measured value of/~ remained the same as above. It was concluded from this that GBI = G82. The detectors were placed as shown in fig. 1 (b). A higher value io = 0.283 +_0.005 was obtained. The increase in the measured value of/~ can be attributed now to the contribution of neutrons from direct interactions. In this altered geometry crossscattering is more plausible, but this would lead to a decrease in/5. Measurements were made also using the set-up in fig. 1 (c) in an attempt to find any angular correlation due to the angular momentum of the compound nucleus. There was no indication of such correlation, since the value of N K was found to be the same as in the set-up (la). 4.2. THE Pb-TARGET In the measurements on natural lead, the cross section was found to be tr = 1.8__+0.2 as compared to the reported s) tr(n, 2 n ) = 2.74_0.20b.

THE

(n, 2n)

REACTION

495

5. Conclusions Even considering the uncertainty of the (n, 2n) cross section data, it can be stated that the values obtained in the present experiments are lower than those measured by the activation method or some other method insensitive to the angular distribution of the emerging neutrons. The contribution of the uncorrelated events, i.e. the "purecompound" cross section is 70-80 ~ at most of the total (n, 2n) cross sections in lead and bismuth. Considering the evaluation method used, the lower value in the present experiments suggests the contribution of the "compound-direct" mechanism to be hardly substantial. Thanks are due to Mr. E. Pgtsztor and Mr. I. Veress for the reliable operation of the accelerator as well as to all workers in our group for building the measuring apparatus and for their help in the experiments.

References 1) 2) 3) 4) 5) 6) 7) 8) 9)

G. K. O'Neil, Phys. Rev. 95 (1954) 1235 L. Rosen and L. Stewart, Phys. Rev. 107 (1957) 824 V. V. Komarov, A. B. Kurepin and A. N. Popova, JETP 38 (1960) 1824 S. De Benedetti and H. J. Richings, Rev. Sci. Instr. 23 (1952) 37 Benveniste, Geneva 1958. Vol. 15. p. 3. P/2494 T. Ericson and V. M. Strutinski, Nuclear Physics 8 (1958) 284 W. G. Cross and R. G. Jarvis, Nuclear Physics 15 (1960) 155 V. J. Ashby et al., Phys. Rev. 111 (1958) 616 A. Ad6m et aL, to be published