The (n, 2n) cross section of 9Be in the energy region 2.0–6.4 MeV

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Nuclear Physics A129 (1969) 305--326; (~) North-Holland Publishing Co., Amsterdam

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Not to be reproduced by photoprint or microfilm without written permission from the publisher

THE (n, 2n) CROSS SECTION OF 9Be IN THE ENERGY REGION 2.0-6.4 MeV M. H O L M B E R G a n d J. H A N S E N

Research Institute o f National Defence, Stockholm 80, Sweden * Received 23 D e c e m b e r 1968

Abstract: The (n, 2n) cross section of 9Be was measured in the energy region 2.0-6.4 MeV and with an accuracy of about 8 % above 3.2 MeV. The two neutrons in the (n, 2n) reaction were detected by a large liquid scintillator by measuring the correlation time between the pulses due to the two neutrons. The (n, 2n) cross section increases rapidly above the threshold at 2.70 MeV for the inelastic neutron scattering to the 2.43 MeV level of 9Be, which subsequently decays by neutron emission. There also exists a small (n, 2n) crcss section in the energy range 2.0-2.7 MeV. E]

NUCLEAR REACTIONS 9Be(n, 2n), E : 2.0-6.4 MeV; measured or(E).

1. Introduction This p a p e r gives d a t a on the (n, 2n) cross section o f 9Be in the energy region 2.0-6.4 MeV. The study o f the (n, 2n) cross section in this energy range gives i n f o r m a tion a b o u t the nuclear m e c h a n i s m o f tbe (n, 2n) process as different nuclear reactions m a y c o n t r i b u t e to the cross section. The shape o f the excitation function is also o f i m p o r t a n c e for reactor calculations f r o m the viewpoint o f n e u t r o n e c o n o m y and helium p r o d u c t i o n . It has been k n o w n since the w c r k o f Fischer 1) that the "effective t h r e s h o l d " for the (n, 2n) process is at 2.70 MeV. This c o r r e s p o n d s to the inelastic n e u t r o n scattering to the 2.43 M e V level o f 9Be, which subsequently decays by n e u t r o n emission. A b o v e 2.7 M e V the cross section increases r a p i d l y and is a b o u t 0.5 b at 4 MeV. Below 2.7 M e V Fischer i) r e p o r t e d a cross section o f 15 m b at 2.57 MeV. But in the w o r k by M a r i o n et al. 2) the time-of-flight spectra o f the emitted neutrons suggested c o n t r i b u t i o n s besides the inelastic scattering to the 2.43 M e V level, i.e. three- o r f o u r - b o d y b r e a k - u p reactions (thresholds at 1.85 and 1.75 MeV, respectively) or inelastic neutron scattering to the b r o a d level at 1.7 MeV. In fact, M a r i o n et al. c o n c l u d e d that only a b o u t h a l f o f the (n, 2n) cross section at 3.5 M e V arose f r o m the 2.43 M e V level a n d this was s u p p o r t e d by the revised results o f Levin a n d C r a n b e r g 3). A n o t h e r possible reaction also leading to the emission o f two n e u t r o n s was p o i n t e d o u t by Bass et al. 4). The r e a c t i o n 9Be(n, ~)6He m a y lead, n o t only to the g r o u n d state, b u t also to the first t Preliminary results were reported at the Paris Conference on Nuclear Data for Reactors in Oct. 1966. 305

306

M. HOLMBERG AND .L HANSEN

excited state of 6He, which decays to an s-particle and two neutrons. The threshold for this reaction is also at about 2.7 MeV but there are no measurements below 14 MeV. The above discussion makes it clear that the cross section in the energy region below 2.7 MeV is of particular interest. The excitation function was also measured above 2.7 MeV, where the earlier measurements have given contradictory results. I-he measurements of the (n, 2n) cross section of Be have been performed with different experimental techniques. Fischer 1) used a neutron regeneration method and Marion et al. 2) combined the time-of-flight measurements with the total-minuselastic Drocedure. Ball et al. s) and Beyster et al. 6) used the sphere transmission method. All these measurements give the non-elastic cross section or the non-elastic minus the (n, ~) cross section. Direct measurements on the (n, 2n) neutrons have been performed in the range 6-14 MeV by Catron et al. 7) using a large liquid scintillator and in the range 3.24.5 MeV by Zubov et al. 8) using BF 3 counters. In the present measurement a large liquid scintillator was used as detector for the (n, 2n) neutrons, but the experimental method is somewhat different from that of Catron et al. 7).

2. Experimental method and arrangement 2.1. LARGE LIQUID SCINTILLATOR The large liquid scintillator has earlier been used in ~-measurements and is described by Asplund-Nilsson et al. 9). The scintillator tank was cylindrical and 50 cm in diameter x 50 cm in length and equipped with an axial channel, 6 cm in diameter. Six 12.7 cm photomultipliers were mounted on one of the ends. The tank contained 100 litres of the Gd-loaded scintillator N E 313. A fast neutron entering the scintillator gives rise to a prompt pulse due to the n - p scattering, if the neutron energy is above the discriminator bias at about 2 MeV. The neutron is thermalized in a few microseconds and diffuses in the scintillator until it is captured by a Gd nucleus and a new pulse due to the capture g a m m a rays occurs. The diffusion time of the thermalized neutron is determined by the amount of Gd salt. For the present scintillator the mean value is at about 20 ps. In the ~-measurements a fission chamber was placed at the centre of the tank. When a fission occurred, a coincidence pulse between the fission-chamber pulse and the liquid-scintillator pulse (due to fission gammas and n - p scattering of the fission neutrons) opened a gate, and the number of pulses in the gate was counted. The gate-length was chosen in such a way that the main part of the captured neutrons was contained in the gate. The pulses were counted by a beam switching tube and then accumulated in ten decade registers. In that way not only the ~-value but also the distribution of the fission neutron number was measured. This technique was originally used by Diven et al. 10). Ashby et al. 11) adapted a modified technique to the (n, 2n) measurements, since no definite pulse indicated

THE (n, 2n) CROSS SECTION OF 9Be

307

the (n, 2n) event. The accelerator was pulsed and the gate was opened for every ion burst. The number of (n, 2n) events could then be calculated from the neutron number distribution. But since the gate-length was of the order of 25/~s, the repetition rate of the accelerator pulsing system could only be about l0 kHz. For a Van de "\,\ , ",~,'', ~ \ ' ,~\ \~ ~ ~ " ~)~ / ;~:

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Graaff accelerator with a normal top terminal pulsing system of 1 M H z this will reduce the ion current by a factor of a hundred, if the pulse width is not increased. For our measurements a different method was used which did not produce this loss of the pulsed ion current. The repetition rate was 1 M H z and the gain in intensity was used to obtain a good collimation system in order to reduce the background .

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Fig. 3. Time-of-flight spectra o f the incident n e u t r o n s with the large liquid scintillator as n e u t r o n detector. T h e spectra were m e a s u r e d with no sample (upper figure) a n d t h e carbon-scatterer in position, respectively. T h e lower s p e c t r u m s h o w s h o w the fast n e u t r o n p e a k was r e m o v e d by the anti-coincidence circuit. Note that the time of-flight s p e c t r u m of those n e u t r o n s , which are slowed down a n d captured by G d nuclei, is flat within the actual time-interval (1 /,s).

and to obtain a good energy resolution of the incident neutrons by the use of a thin target. The experimental set-up is shown in fig. 1.

THE (n, 9n) CROSS SECTION OF 9Be

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2.2. T I M E D I S T R I B U T I O N

With the present method the distribution of the time between two successive liquid scintillator pulses was measured in the range up to 40 ps. The prompt pulse preceding the capture pulse was first removed. Hence the time distribution should be nearly flat for a random distribution of the remaining pulses. However, for an (n, 2n) event there was still a time correlation between the capture pulses of the two neutrons and accordingly the (n, 2n) events could be separated from the random distribution. The block diagram of the electronic circuits is shown in fig. 2. The photomultiplier pulses were added in a distributed amplifier which delivered a standard pulse c f 0.1 ps duration. In the unit (B) this pulse was in a coincidence with the pulse from the pick-up tube of the Van de Graaff accelerator. The coincidence unit was equipped with a variable time-delay for the pick-up pulse. It was also possible to continuously vary the resolution between 7C and 130 ns. The output pulse of the coincidence unit had a length of 0.6 ps and was fed to the anti-coincidence unit (C), where the prompt neutron pulse was removed. To obtain the proper adjustment of the coincidence unit the stop pulses to the time-to-pulse-height converter (D) were taken from the pick-up tube and the time-of-flight spectrum of the incident neutrons was analysed in a multichannel analyser. This spectrum is shown in figs. 3a and 3b while fig. 3c shows how the fast neutron peak has been removed in the anti-coincidence circuit. In the time distribution measurement the liquid-scintillator pulses which passed through the anti-coincidence circuit were used both to start and to stop the converter (D). The start pulse was delayed by 0.12/~s relative to the stop pulse. With this arrangement the time between two successive pulses was measured. The sweep time of the converter was about 40 ps. If no stop pulse occurred during that time interval there was no output pulse from the converter. The converter did not start on the pulse which had stopped it. The pulses before and after the anti-coincidence unit and the number of output pulses from the converter were counted by fast scalers. The time distribution of the captured neutron, the f(t) curve, is shown in fig. 4. The curve was measured with the arrangement described above and with a Po-Be source placed at the centre of the scintillator tank. The gamma ray and the proton recoils due to the neutron in the reaction 9Be(~, n~)12C gave a start pulse to the timeto-pulse-height converter which was followed by the stop pulse from the correlated neutron capture. The recorded distribution gave t h e f ( t ) curve superimposed on a small background. The distribution of the time between the two captured neutrons in an (n, 2n) event could then be calculated from the f ( t ) curve, since the start pulse was given by the first captured neutron and the stop pulse by the second. This calculated distribution, the 9(t) curve, is also shown in fig. 4. The distribution of the time between two successive pulses which are randomly distributed is given by exp(--Rt), where R is the counting rate and t is time. For the actual counting rates (2500 counts/s) and a time interval of 40 ps the deviation from a flat spectrum is about 10 ~. But there are also effects disturbing the ideal shape of the time distribution curve. In fact, some of the natural background pulses from the

310

M. HOLMBERG AND J. HANSI~N

large liquid scintillator (500 counts/s) are correlated in time and give a distribution with a marked slope at the beginning o f the time-spectrum (seefig. 4). This time correlation is probably due to cosmic rays ~2). However, the deviation from a random distribution is suppressed when the counting-rate is increased by using a 6°Co source as a 600• e

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seen from fig. 4. It follows from the above discussion that the recorded time distribution for a scatterer with a non-vanishing (n, 2n) cross section is o f the form exp( - Rt) + +ag(t), where a is a measure of the cross section. The number of (n, 2n) events can then be calculated directly from the time distributions but difficulties are involved in the background subtraction, especially for small cross sections. Therefore the number of (n, 2n) events was determined by a more accurate procedure.

THE

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For a random distribution of the pulses the probability for a stop pulse to occur in the time interval k was given by

l R e - R t d t = ( 1 - e -Rk) ~ 0.1

for R = 2500counts/s and k = 40ps.

The corresponding probability for an (n, 2n) event was about 0.9 and hence the (n, 2n) cross section could be determined from the difference in probabilities. Experimentally this was realized by counting the number of output pulses (X) from the converter as a function of the number of input pulses (N). For a random distribution we have

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where X is the experimental number of output pulses from the converter, the index r indicates a random distribution, N the total number of input pulses, k the sweep time of the converter ( = 38.5 ps) and T the time of the experimental run. The approximation in (1) is valid for the actual counting rates. An experimental set of values of X, as a function of N was obtained by measurements on carbon scatterers. When the measurements were extended to scatterers with a non-vanishing (n, 2n) cross section, the number of (n, 2n) events was given by the difference ( X - X r ) , where the proper value of X, was obtained by iteration from the experimental value of N. Experimental points of X as a function of N are shown in fig. 5. The spread of the points along the N-axis depends both on small changes in the counting rate and on the fact that samples with different lengths were used. The difference X - X r in fig. 5 corresponds to an (n, 2n) cross section of 15__+3 mb. It should be pointed out that (1) is valid only if the counting rate, R, is approximately constant during the experimental run. This follows from the Schwarz inequality x~T)--0.85 kN2 =0.85k T

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with equality only for R(t) = constant. Since the counting rate was dependent on the stability of the ion beam current, the input pulses to the converter were fed to a ratemeter and recorded (fig. 2). Hence the counting rate could be checked during the whole measurement and only runs with small variations were accepted. 2.3. T A R G E T A R R A N G E M E N T A N D C O L L I M A T O R

The incident neutrons were produced at the 5.5 MeV Van de Graaff accelerator at Studsvik. The T(p, n)3He reaction was used on thin adsorbed tritium targets with gold backings. The target thickness was about 25 keV for 4 MeV protons. ~/he proton energy was measured with a nuclear magnetic resonance Gauss meter. The neutrons above 4.6 MeV were produced by the D(d, n)3He reaction and thin adsorbed targets were used. The target beam spot was determined by a Ta diaphragm, 8 m m in diameter.

312

M. HOLMBERG AND J. I-IANSI~N

The collimator consisted of a central part of iron, 20 cm square and 1.5 m long. It was equipped with a conical hole, l0 m m in diameter at the entrance and 40 m m at the end and was surrounded by a lead and paraffin shield of the same length, but between 60 and 100 cm square. The large liquid scintillator tank was shielded by 20 cm of paraffin and 5 to 10 cm of lead. The collimator system was checked by measuring the time-of-flight spectra of the incident neutrons with and without a scatterer in the tank. The prompt neutron peak was almost absent without the scattering sample, as may be seen from the spectra

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shown in fig. 3. Nevertheless the background increased from 500 counts/s to about 1800 counts/s for the beam on the target. This corresponded to a neutron flux of about 2500 n/sin the area of the scattering sample. 2.4. (n, 2n) T A R G E T A N D N E U T R O N F L U X

The Be samples were in the form of disks, 3 cm in diameter and with a length corresponding to about ½ of the total mean free path. The C samples had the same

THE

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313

diameter and the lengths were chosen to give counting rates corresponding to the Be runs. The incident neutron flux was measured by means of a plastic scintillator, 3 cm in diameter and 2.54 cm thick. It was mounted on a photomultiplier tube (AVP 56) and located at the centre of the channel through the scintillator tank. The pulses were shaped in a tunnel diode circuit with two discriminators 13). This admitted a discriminator setting which corresponded to about 5 keV in g a m m a energy. The proton recoil spectrum was measured in a 256-channel analyser for each incident neutron energy. The proton recoil pulses were observed in coincidence with the pulses of the fast neutron peak in the time-of-flight spectrum. Because of the low discriminator setting the full spectrum could be recorded and hence the number of proton recoils was determined. The efficiency of the plastic scintillator was calculated from ~p m

nH ~H + knc t~c [ 1 - e - ( . . . . +.c~c)a], /'/H O'H + / ' / C O'C

where nil, n c are the number of hydrogen atoms and carbon atoms per c m 3, respectively, d is the thickness of the scintillator and k the proportion of the scattering events against carbon which lead to a subsequent scattering against a hydrogen nucleus. The value of k for each incident neutron energy was calculated by means of the Monte-Carlo program written by Zetterstr~Sm 14) using the elastic cross sections and the angular distributions for carbon. A long counter at a distance of 5 m from the target was used as a monitor of the neutron flux. 2.5. NEUTRON DETECTOR EFFICIENCY The efficiency of the large liquid scintillator was determined from the ratio between the observed and the absolute ~-value of 252Cf. This latter was taken to be 3.772+ +0.020 (ref. 15)). The shape of the efficiency curve as a function of neutron energy was taken from Asplund-Nilsson et al. 16). This curve was determined for a spherical scintillator of the same volume (100 l) by a scattering experiment. Its shape is assumed to be correct to within a few percent, also for the present detector. Below 2 MeV neutron energy the efficiency curve was flat and the efficiency was (85+2)~o. In the (n, 2n) measurement the efficiency of the detector was reduced in the following ways: (i) The pulses within the time interval which corresponded to the prompt neutron peak were missed. This fraction (10 ~ ) was determined by counting the pulses before and after the anti-coincidence unit, when a flat time-of-flight spectrum was used. This spectrum was obtained by taking the start signals from the liquid scintillator (6°Co source) and the stop signals from the Van de Graaff accelerator but with no beam on the target. The error was estimated to be less than 0.5 ~ .

314

THE (n, 2n) CROSS SECTION OF aBe

(ii) A n (n, 2n) event was missed if the time between the two capture pulses exceeded the sweep time of the converter (38.5 ps). The missed fraction was determined from the distribution of the time between the two capture pulses, the g(t) curve, fig. 4. The correction was (10_+ 1) %. (iii) A n (n, 2n) event was missed, if the two capture pulses came within 0.12 ps, i.e. the time delay between the start and stop o f the converter. This fraction was also determined from the time distribution curve and was (1.5_+0.5) %. (iv) D e a d time of the converter. This correction was (2_+0.5) %.

3. Experimental procedure The electronic equipment was first checked by measurements o f the time spectra for r a n d o m l y distributed pulses. The large liquid scintillator pulses were used to

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315

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The Be scatterer was then placed at the centre of the scintillator tank and the adjustment of the coincidence-anti-coincidence circuit was checked by measuring the time-of-flight spectrum of the incident neutrons. This was repeated two times at each energy of the incident neutrons. After performing these preliminary experiments eight to twelve 10 min runs were made for recording X, N and the time distribution alternately for the Be scatterer and the C scatterers. Two 5 min runs with the plastic scintillator at the centre of the tank were made and the experimental cycle was repeated for the next incident neutron energy. Some typical time distributions for the Be scatterer and C scatterer are shown in fig. 6. Experimental points for X as a function of N are shown in fig. 5. The number o f (n, 2n) events, N n , 2 n , w a s given by the difference (X-Xr), where Xr indicates the proper random distribution for the Be run. The difference was determined by iteration :starting from the experimental N value. The good stability of the electronic circuits made it possible to detect differences (X-X,) of about 0.5 % of the Xr value.

4. Data handling 4.1. CROSS

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The runs with the plastic scintillator were ncrmalized to the flux monitor and the (n, 2n) cross section, an,2n, was calculated from the expression: 0"n, 2n O"t

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where o"t is the total cross section, A the number of atoms per cm 2, R the ratio of (n; 2n) events produced by elastically scatteled neutrons to the (n, 2n) events resulting directly from first collisions of incident neutrons, Np the number of counts recorded by the plastic scintillator, ep the efficiency of the plastic scintillator, en,2. the effici2 where ~n is ency of the large liquid scintillatcr for (n, 2n) detectiGn, i.e.e., 2, = en, efficiency of the large liquid scintillator for neutron detection and N,, 2n the number of (n, 2n) events recorded by the large liquid scintillator. The total cross section of Be was taken from the compilation by Doherty iv). The multiple scattering correction, R, was calculated by the use of the Monte-Carlo program written by Zetterstr~Sm ~4). For these calculations the angular distributions o f the elastically scattered neutrons were taken from BNL 400 18). The multiple scattering correction was 14 °//o at 4.2 MeV and the error was estimated to be less than 2 O//o.The following corrections were applied to the Be cross sections calculated from eq. (2): (i) Variation of neutron detector efficiency with neutron energy. This correction must be calculated on some assumption about the energies of the emitted (n, 2n) neutrons. It was assumed that the (n, 2n) reaction above 4 MeV proceeds by inelastic excitation to the levels of 9Be at 2.43 MeV (60 %), 3.04 MeV (30 %) and 10 % by excitation to the 1.7 MeV level or by direct break up reactions. This assumption is

316

M. HOLMBERG AND J. HANSEN

rather arbitrary, but is partly justified in sect. 5. For the 2.43 MeV level the energy distribution of the first neutron in the lab system was calculated using the angular distributions for inelastic scattering to this level measured by Levin and Cranberg 3). The energy of the second neutron will be less than 1 MeV whether this level decays to the ground state of aBe or via 9Be* ~ 5 H e + 4 H e ---, 2 4 H e + n (ref. 19)). T h e calculations for the remaining levels were performed in a similar way. It should be pointed out that the correction is only of importance above 4 MeV of incident neutron energy because of the fiat energy response of the liquid scintillator for neutrons below 2 MeV. The correction was 8 ~o at 6.4 MeV. (ii) Absorption of the (n, 2n) neutrons by the (n, ~) process in the Be sample. This correction was calculated using the above assumptions for the energies of the two neutrons. The correction was 2 ~o at 6.4 MeV with an estimated error of 1 ~ . (iii) Neutron escape along the axial channel of the scintillator tank. This correction depends on the fact that the emitted (n, 2n) neutrons are not emitted isotropically. The correction was (2 + 1) ~. (iv) Spectrum of the incident neutrons. At the higher energies (n, 2n) events were induced by low-energy neutrons. The fraction of these neutrons was determined from the time-of-flight spectrum measured with the plastic scintillator and the correction was calculated by the use of the excitation function for the (n, 2n) cress section. The correction was ( 3 _ 1) ~o at 6.40 MeV. (v) Neutron flux correction. The runs with the plastic scintillator must be corrected for the neutrons which are scattered back into the scintillator by the photomultiplier. A calculation was performed in which only the plain glass front surface of the photomultiplier was taken into account. The correction was (2 + 1) ~. 4.2. ABSOLUTE (n, 2n) CROSS SECTIONS The accuracy of the (n, 2n) cross sections determined from eq. (2) is mainly limited by the uncertainties in the determination of the neutron flux and of the efficiency of the large liquid scintillator. Therefore the absolute cross sections were checked at a few energies with a method which does not depend on these figures. Furthermore, any systematic error due to the special technique involved in the detection of the (n, 2n) neutrons may be detected. This method is based on the fact that the (n, 2n) neutrons give no pulse in the fast neutron peak of the time-of-flight spectra before about 2 MeV above an (n, 2n) threshold. This means that in the energy region up to 4 MeV the pulses in the neutron peak are mainly due to the elastically scattered neutrons. The number of pulses in the fast neutron peak and the number of capture pulses, i.e. the number of pulses randomly distributed, were measured simultaneously for each run, figs. 2 and 3. After a background subtraction we obtain the quotient, k, between these numbers for the C scatterer and Be scatterer, respectively

L0"el_l C

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THE (n, 2n) CROSS SECTION OF 9Be

317

and consequently a,, 2, -

kc kB~ (a t - an, ,)Be" kc + kBe

(3)

The above formula was corrected to include: (i) Multiple scattering correction. (ii) The n u m b e r o f p r o m p t pulses due to (n, 2n) neutrons. This correction was calculated by using the measured (n, 2n) cross sections and the function kc = f(E.). (iii) The efficiency for the elastically scattered neutrons is lower than for the (n, 2n) neutrons. The energy distribution of the elastically scattered neutrons was calculated using the angular distributions from B N L 400 is). The efficiency curve of the large liquid scintillator was used for the correction. There is also a small difference in the energy distributions of the neutrons scattered elastically from C and Be. This correction was calculated in a similar way. The error in the (n, 2n) cross section calculated from eq. (3) was 6 ~o at 3.8 MeV, where the error due to the corrections was estimated as 4 °/o. A n error of 5 ~ in the total cross section only adds about 1 }o to the error in the (n, 2n) cross section. F o r comparison, the (n, 2n) cross sections determined from eqs. (2) and (3), respectively, are listed in table 2. 4.3. S O U R C E S

OF ERRORS

The contributions to the absolute error in cry,2n at 4.2 MeV are given in table l which shows that the error is mainly due to the uncertainty in e., 2n and %. Therefore the consistency o f these figures was determined in separate measurements. The TABLE 1 The contributions to the error of %. 2. in the energy region above 2.80 MeV Parameter

Error (~)

Relative error (~) a)

en, 2n

5

2-3

ep

3

1-2

No

3-4

3~ ,

Am, 2.

2

2

corrections

3

< 3

total

8

5-6

• ) Those systematic uncertainties, which are the same for all incident energies, are not included. neutrons scattered from samples o f c a r b o n were counted by the large liquid scintillator with the "sample in" and "sample o u t " technique. The incident neutron flux was measured with the plastic scintillator and hence the quotient en/% could be calculated by the use o f the total ( = elastic) cross section of carbon. Since the energy o f the

318

M. H O L M B E R G A N D J .

HANSEN

scattered neutron depended on angle, a correction was calculated from the angular distributions of scattering by carbon. The corrected values are shown in fig. 7 together with the calculated shape cf the quotient e,/ep (based on ~ (252Cf) = 3.772_+0.020). The measured values agree with the calculated ones to within the given uncertainties. There are also possible systematic errors caused by the special technique used for the (n, 2n) detection. A different method used to check such sources of error has been described in the preceding section. However, this method does not work for small (n, 2n) cross sections as it gives an essentially constant error in the cross sections ( + 0.04 b). Most of this study gives data in the energy region, where the (n, 2n) cross sections are small. Therefore we must consider the possibility of systematic errors, which may dominate for the small cross sections.

3s1 3.0~:p 2,5-

2.0-

1.5 1.5

2.0

25

&O

35

4.0

4 5

5.0

INCIDENT NEUTRON ENERGY, MeV Fig. 7. The experimental a n d the calculated quotient, en/ev, between the efficiencies o f the large liquid scintillator and the plastic scintillator as a function o f incident n e u t r o n energy.

We have used the carbon data as a reference standard. This may cause an error, since the cross sections and the angular distributions for elastic scattering are different for Be and C. In principle, this should only affect the counting-rates, since the pulses are randomly distributed irrespective of the origins of the pulses (background-, capture-pulse etc.). This is valid when one neutron is emitted per event and when the prompt neutron pulse is removed. However, it was found that a small fraction of the prompt neutrons was not removed by the anti-coincidence circuit. This was observed in measurements of the Xr(N ) function by using a 6°Co source and varying the counting-rate by moving the source. 7he Xr-values for the carbon points below 3 MeV of incident energy were 1-2 ~o higher than this function and the shift increased to about 3 ~ at 4.8 MeV. This means that a correlation was present. It was interpreted as an effect of those neutrons which were scattered several times in the iron collimator or in the shield, but still with energies above the discriminator bias of the

THE (n, 2n) CROSS SECTION OF 9Be

319

detector. The flight path was longer and had a continuous distribution. Consequently these neutrons were not removed by the anti-coincidence circuit. This small contribution of correlated pulses might depend on the cross sections and the angular distributions of the scattered neutrons. It was found that this contribution was almost independent of whether the sample was in position or not. This fact gave an opportunity to investigate the limits of any (n, 2n) cross section for carbon. We did not make full use of this possibility since it would have increased the accelerator time considerably. We preferred to use the carbon data as a reference standard for a random distribution (i.e. an, 2n = 0) and tried to investigate experimentally the validity of this assumption when applied to the Be-runs. In general the Xr(N ) curve for carbon did not shift (compared to the 6°Co curve) when the energy was changed, at least in the energy region below 3 MeV. There were no deviations at the carbon resonance of 2.9 MeV or at the resonance of 2.08 MeV, where the angular distribution changes drastically. Furthermore, the carbon data were checked in the whole energy range 2-6.5 MeV by test runs. Samples of CH, CH2, H20 and D20 (below 3.2 MeV) were used, but no deviations from the Xr(N) curve for carbon were observed. This was taken as a guarantee that the proper random distribution was used. The Be-points were above the Xr(N ) curve measured with the carbon samples down to 2.0 MeV, where the two sets of points coincided. The recorded time distributions were frequently used to check data from the X versus N runs. Subtraction of the time distribution for carbon from the one with Be should give (see subsection 2.2):

Ag(t)+e-nB~'--ke-Rc' ~ ag(t)+(Rc-Rse)t+k'.

(4)

The g (t)function decreases with time. Since the middle term in eq. 4 also gives a decrease for RBe > Rc, this effect was taken into account when the number of (n, 2n) events was checked using the difference between the time distributions. The correction was almost negligible since the counting rates for the Be and C samples were about the same. The correction was also checked by comparing such differences for which Rc > RBe, i.e. where the difference (4) should increase with time if the (n, 2n) cross section was zero. This was never observed except at 2.0 MeV. If any contribution from correlated pulses due to prompt neutrons was also present in the difference (4), this should have shown up as a f ( t ) function. This was never observed. The number of (n, 2n) events, N,,2n, was determined from the X ( N ) function by an iteration proceeding and the result was cbecked by using the time distributions. Corrections were necessary, since the time-to-pulse-height converter could be started by some kind of pulse (background-, capture-pulse etc.) and stopped by another. It has been mentioned above that this should not affect the random distributions, but it might result in the loss of (n, 2n) events. By considering the various combinations it was found that the method of determining Nn, 2n from the X(N) function gave small corrections. This was not always the case, when the time distributions were used. For example, when the start signal is initiated by a background pulse and the

M. HOLMBERG AND S. HANSEN

320

TABLE 2 Be(n, 2n) cross sections in b Incident energy (MeV)

~rn. 2n(b)

3.40 3.80 4.20

eq. (2) a)

eq. (3) b)

0.47i0.03 0.51 ± 0 . 0 4 0.51 ± 0 . 0 4

0.444-0.03 0.50±0.03 0.51 3-0.04

a) Based on ~(~so-Cf) = 3.7723_0.020 a n d a calculated efficiency o f the plastic scintillator used for the n e u t r o n flux m e a s u r e m e n t . b) Based on the total cross section o f Be. N o t e that the error in the total cross section can be neglected c o m p a r e d to other errors. TABLE 3 Be(n, 2n) cross sections in b Incident energy a) (MeV)

an. 2, b~ (b)

2.00 2.10 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.62 2.65 2.68 2.75 2.80 2.85 2.90 3.10 3.20 3.40 3.60 3.80 4.20 4.80 5.80 6.40

0.0003 ± 0 . 0 0 2 0.003 ± 0 . 0 0 2 0.009 ± 0 . 0 0 2 0.011 ± 0 . 0 0 2 0.016 ± 0 . 0 0 2 0.015 ± 0 . 0 0 2 0.016 ± 0 . 0 0 2 0.019 ± 0 . 0 0 3 0.024 --0.003 0.023 ± 0 . 0 0 3 0.027 ± 0 . 0 0 3 0.029 ± 0 . 0 0 3 0.032 3-0.003 0.035 ___0.004 0.15 3-0.02 0.20 ± 0 . 0 2 0.25 3-0.02 0.27 3-0.03 0.37 3-0.03 0.42 3-0.03 0.47 i 0 . 0 3 0.48 ~ 0 . 0 4 0.51 ± 0 . 0 4 0.51 3-0.04 0.54 3-0.04 0.58 ± 0 . 0 5 0.58 3-0.05

Relative error e)

0.002

0.002 0.003 0.003 0.003 0.015 0.015 0.015 0.02 0.025 0.03 0.03 0.03 0.03 0.03 0.03 0.04 0.04

a) T h e energy spread is a b o u t ± 15 keV at 3 MeV. b) Based on ,7 (25~Cf) = 3 . 7 7 2 ± 0 . 0 2 0 a n d a calculated efficiency o f the plastic scintillator used for the n e u t r o n flux m e a s u r e m e n t , f o r m u l a (2). e) T h o s e systematic uncertainties, which are the s a m e for all incident energies, are not included.

THE (n, 2n) CROSS SECTION OF 9Be

321

stop signal is due to the first of the two capture pulses f r o m the (n, 2n) neutrons, this (n, 2n) event is recorded (there is an output pulse from the converter), but does not give the proper time distribution, i.e. the g ( t ) curve. The difference between the time distributions shown in fig. 6 is corrected for such effects. The good agreement with the calculated g ( t ) function was taken as an indication that we have correctly considered the various combinations.

5. Results and discussion The corrected values o f a., 2, are given in tables 2 and 3 and are also shown in fig. 8. The cross sections measured by Ball et al. 5), Beyster et al. 6) and C a t r o n et al. 7) are also shown. In fig. 9 o-,, 2, is shown in the energy region 2.0-2.? MeV.

:1 0.4-

0.3-

0.2-

0.1-

0

aeoo~ I 2

I I 2.70 3

INCIDENT

I 4

NEUTRON

[ 5

I 6

I 7

ENERGY, M e V

Fig. 8. The (n, 2n) cross section for Be as a function of neutron energy. The solid circles represent the present data. The stated uncertainties are the relative errors. The open circles are from Beyster et al. O, the open triangle is from Catron et al. 7) and the solid square is from Ball et al. 5).

The present result at 4.2 MeV is in agreement with the cross section at 4.07 MeV reported by Beyster et al. 6) and there is also g o o d agreement with the measurement o f C a t r o n et al. 7) at 6.5 MeV. However, our results disagree with those o f Fischer 1) for the shape o f the excitation function above the threshold at 2.7 MeV. In the data compilation by D o h e r t y 17) the recommended (n, 2n) cross sections were a c o m p r o mise between the results of Fischer 1), Levin and Cranberg 3), Beyster et al. 6), Ball et al. s) and Fowler et al. 2o). The present results are in very g o o d agreement with the r e c o m m e n d e d excitation function above 2.8 MeV incident neutron energy.

322

M. HOLMBERG AND J. HANSEN

Below 4 MeV incident neutron energy the (n, 2n) process m a y proceed by the following reactions: Threshold (MeV) n + 9Be ~ 2n + 24He

F (keV)

1.75

(5.1)

1.85

(5.2)

Q = - 1 . 5 7 1 MeV 2n+SBe ~ 2n+24He Q = - 1 . 6 6 5 MeV n + 9Be* ~ 2n + 24He * Excited levels of 9Be at

1.67 MeV

1.85

200

(5.3a)

2.43

2.70

< 1

(5.3b)

3.03

3.4

265

(5.3c)

1.80 MeV

2.70

100

(5.4)

4He + 6He* --+ 2n + 24He Excited level of 6He at

The Q-values and the data on the energy levels were taken from Lauritsen and Ajzenberg-Selove 21). {3" n,2n

L,0-

30-

20-

,0

0 ts

I ~1 1.9 2.0

I 2.1

INCIDENT

i 2.2

I 2,3

NEUTRON

i 2.~

I 2.5

I 2.6

I 2.7

ENERGYjMeV

Fig. 9. The (n, 2n) cross section for Be as a function o f neutron energy in the energy region 2.0-2.7

MeV. The solid curve is the calculated relative cross section, normalized at 2.60 MeV. The calculation is based on the assumption of a resonance level of 9Be at 1.70 MeV, which subsequently decays by neutron emission. As has been mentioned, earlier experiments have indicated that the reaction (5.3b) gives the largest contribution to the (n, 2n) cross section. However, it was * We have only indicated the final products, not the decay schemes of the excited levels.

THE (n, 2n) CROSS SECTION OF 9Be

323

suggested by Bass et aL 4) that the (n, ct) excitation of the 1.80 MeV level of 6He also may contribute. The thresholds for (5.3b) and (5.4) are almost identical, but in principle the two reactions may be separated because of the large width of the 1.80 MeV level. The (n, ct) measurements make use of the fact that 6He in the ground state is a fl-emitter with a long half-life, 0.8 sec. Consequently these measurements give no information about the reaction passing through the excited state at 1.80 MeV. A direct (n, ~t) measurement at 14 MeV by Gangas et aL 22) indicated that the cross section leading to the excited state at 1.80 MeV was of the same order as to the ground state. The present results show an (n, 2n) cross section below the threshold at 2.7 MeV for the inelastic neutron scattering to the 2.43 MeV level of 9Be. This cross section is observable down to about 2.0 MeV. In the energy region 2.6-2.7 MeV, where one might expect a contribution from the reaction (5.4) no increase of the cross section is found. This is not surprising since we can expect a suppressed (n, ~) cross section in a region above the threshold because of the Coulomb barrier. Use of the formula O'n, = ~,~ e - 2nr/=,

/]:t - -

Z 1 Z2 e 2

,

hv~ gives no contribution of importance within about 1 MeV above the threshold. But only 300 keV above the threshold the present results give an (n, 2n) cross section of 0.4 b. This shows that the contribution from the 2.43 MeV level of 9Be must be dominant. The (n, 2n) cross section below 2.7 MeV is of the order 15-25 mb with an extrapolated observed threshold at about 2.0 MeV. It follows from the above that the crcss section is due to one of, or a combination cf, the reactions (5.1), (5.2) or (5.3a). If we consider tbe probability for a four body break-up reaction as negligible, we may discuss the two alternatives (5.2) and (5.3a). The thresholds for the two reactions are at about 1.85 MeV, and therefore tbe observed experimental threshold seems to be too high. However, this contradiction is removed, if we assume the reaction (5.3a), i.e. the inelastic neutron scattering to the 1.7 MeV level of 9Be, which subsequently decays with neutron emission. The effects observed with various reactions at about 1.7 MeV in 9Be have been thorougly discussed in the literature and it has been questioned if there exists a resonance level at 1.7 MeV. An extensive account with references to earlier works is given by Lucas et al. 23). However, a i + level at about 1.7 MeV fits naturally in the shell-model calculations 24) and in a recent measurement by Imhof et al. 25) the gamma-ray transition between a level at 16.97 MeV and the 1.7 MeV level was observed. In the (p, p') experiments the inelastically scattered protons to the 1.7 MeV level showed a broad distribution (300 keV) with a sharp cut-off, which corresponded to Q = - 1 . 6 7 5 MeV. The asymmetric shape of the proton distribution was fairly well explained by Barker and Treacy 26) on the basis of R-matrix theory. Following

324

M. HOLMBERG AND J. HANSON

the treatment and notation by Barker and Treacy, the cross section for the reaction a + A --. b + B ,

B --* c + C ,

n + 9 B e ~ n + 9 B e *,

9Be* --* n + SBe,

is written

try(E) = (l~attbkb/4n z h ~ k , ) l ( B + b , E b I H ' I A + a , Ea)lZ pt(E), where E is the energy of the nucleus B above the threshold for break-up into c + C and where the density of states function is given by

pl(E) = const

2+(½r,) 2'

In the present case, assuming emission of s-wave neutrons, F~ is given by Fo = 2kcaoYo2. Barker and Treacy calculated the reduced width of the ½+ state for a channel radius a0 = 4.35 fm, giving ~o2 = 1.01 MeV. The 9Be(y, n)SBe cross section was then fitted with E, = Eo = 0.11 MeV (measured from the S B e + n threshold at 1.667 MeV). We have used these parameters in calculating the distribution of no(E) for different values of ka, assuming s-wave neutrons for the inelastically scattered neutron. The relative reaction cross section as a function of incident neutron energy was then given by the integrated distributions. The calculated cross section normalized at 2.6 MeV is shown in fig. 9 and is in good agreement with the experimental points at the threshold. The good fit may be a reason for ascribing the (n, 2n) cross section below 2.7 MeV to the inelastic neutron scattering to the 1..7 MeV level. We conclude that the (n, 2n) cross section of 0.30 b at 3 MeV is dominated by inelastic neutron scattering to the 2.43 MeV level. Marion et aI. 2) reported values of about 0.25 +0.04 b for o,, (2.43) at 3.5 MeV and 4 MeV. These values were obtained by integrating angular distributions. In addition the inelastic excitation curve was measured in the energy region below 3.5 MeV at one fixed angle (45 ° lab. system). The cross section was found to have a maximum between 3.2 and 3.3 MeV. Assuming an isotropic angular distribution the integrated cross section was 0.40 b at the maximum. In the present experiment no maximum was found at these energies for the (n, 2n) cross section. However, we can get rough agreement with the results of Marion et al. by assuming contributions due to the broad 3.03 MeV level from about 3.2 MeV of incident neutron energy. This also explains the statement by Marion et al. that the direct break-up reaction or the 1.7 MeV level contributed to a large extent. This conclusion was drawn from the observation that in the time-of-flight spectra of the emitted neutrons two groups and a continuum of neutrons were found besides the peak corresponding to the inelastic scattering to the 2.43 MeV level. The first group

THE (n, 2n) CROSS SECTION OF 9Be

325

was a s c r i b e d to the n e u t r o n decay o f the 2.43 M e V level to the 8Be g r o u n d state. T h e b r a n c h i n g r a t i o was e s t i m a t e d to be (12 4-5) %. T h e second g r o u p a n d a p p a r e n t l y also the c o n t i n u u m were ascribed to a direct b r e a k - u p r e a c t i o n o r to the 1.7 M e V level. But the 3.03 M e V level decays p r e d o m i n a n t l y (90-100 %) to the abe g r o u n d state 27) a n d the energy o f the e m i t t e d n e u t r o n c o r r e s p o n d s very well to this latter group. T h e c o n t i n u u m m a y be ascribed to the decay 9Be*(2.43) --* 5 H e + 4 H e ~ 2 4 H e + n . T h e a b o v e discussion suggests t h a t m e a s u r e m e n t s o f the excitation functions for the inelastic n e u t r o n scattering t o the levels at 2.43 M e V a n d 3.03 M e V are required. A f t e r the m a n u s c r i p t was c o m p l e t e d a m e a s u r e m e n t by E a t o n a n d W a l k e r 28) o n the non-elastic cross section o f 9Be in the energy region 2.3-5.2 M e V was r e p o r t e d . The sphere t r a n s m i s s i o n technique was used a n d the neutrons ~vere detected by a 238U t h r e s h o l d detector. A f t e r s u b t r a c t i o n o f the (n, e) cross section the (n, 2n) cross sections are significantly a b o v e the present values (10-30 %). T h e stated errors are larger than in the present experiment, b u t in general the deviations are n o t within the limits o f the errors. D a t a on the (n, 2n) cross section o f Be were requested several years ago b y P r o f e s s o r H. G o l d s t e i n , C o l u m b i a University, N.Y. W e are i n d e b t e d to H.-O. Z e t t e r s t r 6 m for p e r f o r m i n g the M o n t e - C a r l o calculations, a n d the s t i m u l a t i n g discussions with him a n d L. W a l l i n have been o f great value to us. W e w o u l d also like to express o u r g r a t i t u d e to D. L u n d b e r g a n d L. E. Persson for their skillful assistance with the m e a s u r e m e n t s . W e wish t o t h a n k the five experts B. Jonsson, L. Larsson, T. Larsson, L. N o r e l l a n d P. T y k e s s o n o f the V a n de G r a a f f accelerator at Studsvik for their careful o p e r a t i o n o f the accelerator. F i n a l l y we also wish to t h a n k Dr. D. S. M a t h e r , A l d e r m a s t o n , E n g l a n d a n d Dr. M. D. G o l d b e r g , B r o o k h a v e n , U S A for v a l u a b l e c o m m e n t s o n the m a n u s c r i p t .

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15)

G. J. Fischer, Phys. Rev. 108 (1957) 99 J. B. Marion, J. S. Levin and L. Cranberg, Phys. Rev. 114 (1959) 1584 J. S. Levin and L. Cranberg, WASH 1029 (1960) 44; and WASH 1028 (1960) 26 R. Bass, T. W. Bonner and H. P. Haenni, Nucl. Phys. 23 (1961) 122 W. P. Ball, M. MacGregor and R. Booth, Phys. Rev. 110 (1958) 1392 J. R. Beyster, R. L. Henkel, R. A. Nobles and J. M. Kister, Phys. Rev. 98 (1955) 1216 H. C. Catron, M. D. Goldberg, R. W. Hill, J. M. Leblanc, J. P. Stoering, C. J. Taylor and M. A. Williamson, Phys. Rev. 123 (1961) 218 Yu. G. Zubov N. S. Lebedeva and V. M. Morozov, Neytronnaya fizika (Moscow, 1961) 298 I. Asplund-Nilsson, H. Cond6 and N. Starfelt, Nucl. Sci. and Eng. 20 (1964) 527 B. C. Diven, H. C. Martin, R. F. Taschek and J. Terrell, Phys. Rev. 101 (1956) 1012 V. J. Ashby, H. C. Catron, L. L. Newkirk and C. J. Taylor, Phys. Rev. 111 (1958) 616 D. S. Mather, private communication H. Cond6, G. During and J. Hans6n, Ark. Fys. 29 (1965) 307 H.-O. Zetterstr6m, unpublished C. H. Westcott, K. Ekberg, G. C. Hanna, N. J. Pattenden, S. Sanatani and P. M. Attree, Atom. En. Rev. 3 (1965) 3

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M. H O L M B E R ( 3 A N D J. H A N S E N

16) I. Asplund-Nilsson, H. Cond6 and N. Starfelt, Nucl. Sci. and Eng. 16 (1963) 124 17) G. Doherty, AEEW-MS13 (1965) 18) M. D. Goldberg, V. M. May and J. R. Stehn, Angular distributions in neutron-induced reactions, 2nd ed. Vol. 1, Z = I to 22, Brookhaven Nat. Lab. USA, Report BNL 400 (1962) 19) J. MOsner, G. Schmidt and J. Schintlmeister, Nucl. Phys. 64 (1965) 169 20) J. M. Fowler, S. S. Hanna and G. E. Owen, Phys. Rev. 98 0955) 249 21) T. Lauritsen and F. Ajzenberg-Selove, Nucl. Phys. 78 0966) l 22) N. Gangas, S. Kosionides and R. Rigopoulos, Phys. Lett. 12 (1964) 233 23) B. T. Lucas, S. W. Cosper and O. E. Johnson, Phys. Rev. 133B (1964) B963 24) C. Adler, T. Coreoran and C. Mast, Nucl. Phys. 88 (1966) 145 25) W, L. [mhof, L. F. Chase and D. B. Fossan, Phys. Rev. 139B (1965) B904 26) F. C. Barker and P. B. Treacy, Nuel. Phys. 38 0962) 33 27) P. R. Christensen and C. L. Cocke, Nucl. Phys. 89 (1966) 656 28) J. R. P. Eaton and J. Walker, Neutron cross sections and technology, Proc. of a Conference, Washington, D. C., March, 1968 (NBS special publication 299, U.S. Department of Commerce - National Bureau of Standards, 1968) p. 169