Measurements of angular and energy distributions of prompt neutrons from thermal neutron-induced fission

Measurements of angular and energy distributions of prompt neutrons from thermal neutron-induced fission

ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 598 (2009) 795–801 Contents lists available at ScienceDirect Nuclear Instrume...

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ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 598 (2009) 795–801

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Measurements of angular and energy distributions of prompt neutrons from thermal neutron-induced fission A.S. Vorobyev , O.A. Shcherbakov, Yu.S. Pleva, A.M. Gagarski, G.V. Val’ski, G.A. Petrov, V.I. Petrova, T.A. Zavarukhina Petersburg Nuclear Physics Institute, 188350 Gatchina, Leningrad District, Russia

a r t i c l e in fo

abstract

Article history: Received 11 March 2008 Received in revised form 28 August 2008 Accepted 13 October 2008 Available online 1 November 2008

The experimental setup and methodology used to measure prompt neutron angular and energy distributions from thermal neutron-induced fission are described. The neutrons are detected using two scintillation detectors, while the fission fragments are detected by multi-wire proportional detectors in conjunction with the TOF technique. To separate events corresponding to neutrons and g-quanta, a double discrimination by the pulse shape and the time-of-flight is applied. Some preliminary results of an experiment performed with the 235U target are presented and briefly discussed. The yield of ‘‘scission’’ neutrons has been estimated in the framework of a simple evaporation model and was found not to exceed 5% of the total neutron yield. Including an assumed of anisotropy of the fission neutron angular distribution in the center-of-mass system of fission fragments into the model calculation leads to an increase in the ‘‘scission’’ neutron yields inferred from the data. & 2008 Elsevier B.V. All rights reserved.

Keywords: Neutron-induced fission Fission fragments Neutron emission Scintillation detectors MWPD Neutron angular distribution Prompt fission neutron energy 235 U target

1. Introduction A large number of theoretical and experimental works have been dedicated to comprehensive study of the properties of fast fission neutrons. The average neutron multiplicity per fission, the shape of neutron energy spectra, neutron yields as a function of fragment mass and energy, neutron angular distributions relative to the fragment separation axis, and other characteristics have all been obtained as a result. As a result, one may now reliably state that the main part of the fast fission neutrons is emitted from the fission fragments that are fully accelerated in a Coulomb field of the nucleus. Such neutrons therefore have angular distribution directed mainly along the fission axis in the laboratory system. Given this, the main part of the fragment’s excitation energy is released through the neutron emission in a time of to1018 s, with the remainder taken away by the g-quanta. An analysis of angular and energy distributions of fission neutrons carried out in the framework of the statistical model leads to the conclusion that available experimental data could

Corresponding author. Tel.: +7 81371 46444; fax: +7 81371 36041.

E-mail address: [email protected] (A.S. Vorobyev). 0168-9002/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2008.10.017

be satisfactorily described under the assumption that fission neutrons are evaporated isotropically in the center-of-mass system of the moving fragments. However, as early as 1962, on the basis of analysis of experimental data on spontaneous fission of 252Cf, Bowman et al. [1] were able to estimate that about 10–20% of fission neutrons could be emitted by a fissioning nucleus. By now, several experimental works have been carried out with the purpose of measuring the contribution of such ‘‘scission’’ neutrons to the total yield of fast fission neutrons for 252Cf [1–6] and 235U [7–9]. The estimations obtained in these works range from 1% to 20%, so the very existence of such ‘‘scission’’ neutrons can hardly be considered proven (not to mention the measurement accuracy of such yield for various fissile nuclei). The recent work of Kornilov et al. [10–13], dedicated to the analysis of all available experimental data, has lead to the conclusion that only one experimentally observable effect can be taken as a proof in this matter, namely an excess of fission neutrons (about 30% and 60% for 252Cf and 235U, respectively) emitted at an angle near 901 in comparison with the calculation carried out using a model of neutron emission from the fully accelerated fragments. According to the opinions of these authors, the statistical and systematic error associated with the available experimental data does not allow one to unambiguously determine the emission mechanism of such neutrons. They proposed

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235 U as the most promising isotope for investigation as it was observed to provide the highest relative yield of ‘‘scission’’ neutrons in previous experiments [7–9] and as it follows from the systematics of light particle yield in ternary fission [14]. In the present work, performed at the PNPI RAS as part of an extensive research program on fission processes, we have performed measurements of the spectra of fast fission neutrons from the 235U(nth,f) reaction for fission fragments at 11 fixed angles between the neutron and light fragment directions in the range from 01 to 1801 in 181 intervals. In what follows, the methodology used to measure prompt neutron angular and energy distributions is described. We present processed experimental data and an analysis performed with the intent of deducing the yield of ‘‘scission’’ neutrons emitted in the vicinity of the rupture of a fissioning nucleus.

2. Measurement procedure The experimental set-up [15,16] shown in Fig. 1 was installed at the radial neutron channel N7 of the research reactor WWR-M equipped with a neutron guide 3 m in length. The flux density of neutrons of wavelength l 1.5 A˚ from the neutron guide outlet slit (3  40 mm2 in cross-section) was 2  107 cm2 s1. The collimated thermal neutron beam passes through a 100 mm thick Al-window in a cylindrical vacuum chamber striking a target of fissile material at a small angle of incidence. The uranium target, enriched to 99.99% purity, consisted of 280 mg/cm2 thick 235 U sprayed as UF4 on a self-supporting 70 mg/cm2 thick Ti backing, making a circular spot 15 mm in diameter. The fission fragments spectrometry was carried out by measuring the time-of-flight of paired fragments. The ‘‘time zero’’ mark, used as a start signal triggering the data acquisition system, was generated using a multi-wire proportional detector (MWPD) located within a 7 mm range from the fissile target and parallel to the target plane. The anode of the detector consisted of thin (+25 mm) gilded tungsten wires spanning a 1 mm spacing

T11

T21

Neutron Detector ND1

Delay MWP D Start Detector Arc N1

Arc N2

on a rectangular frame made of foil-coated fiberglass plastic. The sensitive area of the anode was 68  92 mm2. The cathode consisted of a mesh of +25 mm thick wires with a cell of 0.35  0.35 mm2 size. The anode to cathode spacing was 3.5 mm. A start MWPD was mounted together with the target holder-ring on a special frame located in the center of the reaction chamber in such a way that all hardware parts were well out of the path of the neutron beam. The MWPDs were also used to simultaneously detect fission fragments and to determine their direction of motion. Every stop detector consisted of a thin polished aluminum cathode and an anode in parallel with it. The last detector had a wire structure similar to anode of the start detector, with a sensitive surface area of 72  38 mm2. The operating voltage of all MWPDs was 400–500 V at the operating gas (isobutane) pressure of 4–6 Torr. The 16 rectangular fragment detectors were placed in two arcing formations (eight detectors in each) diametrically opposed to each other in the reaction chamber at a distance of 140 mm from the chamber axis. The neutron beam was directed along the chamber axis. Prompt fission neutrons were detected by two neutron scintillation detectors (stilbene crystals +50 mm  h50 mm and +40 mm  h60 mm mounted on the Hamamatsu-R6091 phototubes) positioned with a 901 angle between their respective axes at a distance of about 50 cm from the fissile target. Both neutron detectors were shielded by a cylindrical shield made of a 30 mm thick layer of lead and a 40 mm thick layer of polyethylene (not shown in Fig. 1). The neutron registration threshold was 150–200 keV. A double-discrimination method (pulse shape and time-of-flight) was used to separate the events produced by neutrons and g-quanta. A detailed description of this method is given below. During the experiment, multi-dimensional data were recorded in terms of the energies of the fission neutrons and their correlation with the direction of the separation axis of the paired fission fragments. Since in this experiment the position of neutron detectors was fixed, the relative angle of neutron emission was determined by the position of the fragment detector that recorded the fission event. In practice, the position of the detector was calculated using the difference of detector pulse arrival times at the two ends of the delay line connected to the output of each of the eight MWPDs located on a given arc. Each multi-dimensional fission event, triggered by a start detector, was characterized by the following 13 attributes:

 integral of the start detector pulse, Isd;  fission fragment flight times detected at 1st and 2nd ends of an Delay

18°

arc N1, T11 and T12, respectively;

 integral of the pulse detected at one end of an arc N1, Id1;  fission fragment flight times detected at 1st and 2nd ends of an arc N2, T21 and T22, respectively;

235

 integral of the pulse detected at one end of an arc N2, Id2;  time-of-flight of the neutron detected by detector ND1, T1;  total and partial integrals of the pulse from the neutron

U Target

detector ND1, I1t and I1s, respectively;

Neutron Detector ND2

T22

T12

2 x 8 MWPD Stop Detectors Fig. 1. Schematic view of the experimental setup (no scale).

 time-of-flight of the neutron detected by detector ND2, T2;  total and partial integrals of the pulse from the neutron detector ND2, I2t and I2s, respectively.

The total counting rate was about 100 events/min for both neutron detectors. About half of the events were related to neutrons. More than two months of measurement time was necessary to accumulate about 2  106 events accompanied by neutron registration. The measurements were carried out in

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weekly cycles. The data accumulated over each cycle were processed separately.

3500

10000 Counts

2500

Counts

100

A common feature of fission events registered by all MWPDs located on the arc N1 is that the measured angular distribution of fission neutrons is determined relative to the course of fission fragments moving in direction of a neutron detector. At the same time, the stop MWPDs located on arc N1 are not shielded by a start detector. Therefore, the correction for the limited transparency of the start detector is minimal in this case and can be neglected. It should be mentioned that the correction related to variation of angular distribution of fission fragments due to transmission through the target backing and due to the neutron emission is negligible. We note that such scheme of experimental set-up, with two neutron detectors, guarantees identity of conditions of the neutron spectra measurements at various angles relative to the fission axis, namely: the magnitude and composition of the background, the efficiency of the neutron detectors, and neutron re-scattering by the parts of experimental set-up. The first stage of the experimental data processing consists of the application of some corrections to the raw data, which are discussed below.

1 2 3 4

3000

(a)

3. Data processing and analysis of the experimental data

797

2000 1500 1000 500

100

10

850

875 900 925 950 Time-of-Flight, channel

(b) Background

1 1000

1500

2000 2500 3000 Neutron TOF Channel

3500

Fig. 2. Time-of-flight spectrum for fission neutrons of 235U: (a) initial spectrum; (b) after subtraction of the g-quanta contribution via pulse shape discrimination. The background is shown as a straight line. The timing channel width was equal to 0.05 ns. The inset shows a peak corresponding to the fission g-quanta: (1) raw spectrum; (2) spectrum corrected for pulse-height dependence of timing jitter of the start MWPD; (3) spectrum corrected for effect (2) and the dependence on the integral of the neutron detector pulse; (4) spectrum corrected for effects (2), (3) and for the difference of light and heavy fission fragment times-of-flight corresponding to distance between fissile target and start detector.

3.1. Correction for time uncertainties in the time-of-flight measurements

T ¼ ðN0 þ M þ DtÞ  dT þ T del

(1)

where T/dT is a channel number in which a neutron or fragment has been registered, N0 is a channel number corresponding to ‘‘time zero’’, M is the time-of-flight (in channels), dT is the channel width (0.05 ns), Dt is the (in channel) correction for timing uncertainties, Tdel is the difference of delays between start and stop registration channels. For all detectors used in this experiment, constant fraction discriminators were employed to obtain timing marks. Despite this, it became necessary during the processing of the data to take into account the correlation between the pulse-height of detected signals and the position of the corresponding timing mark. Thus, in a measurement of the time-of-flight spectrum of fission neutrons, a correction was applied both to the start fragment detector and to the stop neutron detector. A difference of heavy and light fragment time-of-flight measurements from the target to the start detector was also taken into account. All enumerated corrections were applied to the raw spectrum. As a result, the FWHM of the ‘‘fragment-g-quantum’’ coincidence curve decreased from 2.5 to 1.2 ns (inset of Fig. 2). 3.2. Correction for neutron detector background For reliable separation of neutron and g-quanta events, a double discrimination (by means of the pulse shape and time-offlight) has been used. As is well known, a decay curve of stilbene consists of fast (de-excitation time 4 ns) and slow (270 ns) components. In the case of neutron registration, the slow component contribution is considerably higher than in the case of g-quantum registration. This difference was used here for initial separation of neutron and g-quantum events. To achieve this, the total It and partial Is integrals (over 300 ns time intervals) have been measured for every neutron detector pulse using a ‘‘chargeto-digital’’ converter. The window corresponding to the partial

Partial Integral [arb. units]

300 The time-of-flight of fission neutrons or fragments MdT was calculated using the following expression:

Neutrons

250 200 150 γ - quanta

100 50

100

200 300 Total Integral [arb. units]

400

500

Fig. 3. Separation of fission neutrons and g-quanta using a correlation between total and partial integrals of the neutron detector pulse.

integral was delayed for 30 ns relative to the window corresponding to the total integral. Two-dimensional neutron detector pulse distributions (shown in Fig. 3) were used both for on-line quality control of neutron-g-quantum separation during the measurements and for the subsequent experimental data processing. The region of events corresponding to neutron events is marked by two curves. Fig. 2 shows the fission neutron time-of-flight spectrum before and after g-quanta background subtraction, we see that pulse shape discrimination enables g-quanta background suppression by about a factor of 200. The residual background component (related to the neutron scattering and insufficient neutron-gamma separation in low energy region) was approximated by the straight line drawn using average values corresponding, respectively, to the left (100–500 channels) and right (3000–3500 channels) edges of distribution (b) shown in Fig. 2. The contribution of this

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component of the background averaged over all angles did not exceeded 8% of the neutron events remaining after subtraction of both background components.

500 3.3. Correction for the fragment detector efficiency

NS ðT; yÞ ¼ C1ðyÞ  C2ðyÞ  NB ðT; yÞ

(2)

C1ðyÞ ¼ N f ðRÞ=Nf ðyÞ

(3)

C2ðyÞ ¼

8 > > > > > > > > if yp90 > > > > < > > > > > > > > > if yX90 > > > :

8 > > > > <1 Nf ð180  yÞ > > > > : Nf ðyÞ 8 Nf ðyÞ > < Nf ð180  yÞ > : 1

400 Counts

The mass and energy distributions of fission fragments obtained for each of stop MWPDs coincide with an accuracy of correction for the transmission of the fragment through the target and the target backing materials. The number of neutrons NS(T,y) registered by a neutron detector at angle y with respect to the direction of movement of light fragments after correcting for efficiency differences of the MWPDs, can be written using:

300

200

100

0 1600

1800

2000

2200

2400

Fragment TOF channel if

Nf ð180  yÞ p1 N f ðyÞ

1000

otherwise (4)

800

Nf ð180  yÞ p1 N f ðyÞ otherwise

where NB(T,y) is a number of fission neutrons detected at angle y after background subtraction; C1(y) is a coefficient accounting for differences in solid angles and efficiencies of fission fragment registration (on average, 7%); Nf(y) is the number of fission fragments detected by one of the MWPDs in the arc N1; R is a reference angle corresponding to the MWPD in the arc N1 for which the maximum number of fission events was registered; C2(y) is a correction accounting for the difference in registration efficiency for light and heavy fragments by the start detector (p2%).

Counts

600

400

200

0 -300

-200

-100

0

100

200

300

T11 - T22 , channel 3.4. Correction for complementary fragment contribution This correction, caused by incomplete separation of light and heavy group of fission fragments, is accounted for by solving the system of (

N S ðT; yÞ ¼ ð1  f 1ÞNA ðT; yÞ þ f 1NA ðT; 180  yÞ N S ðT; 180  yÞ ¼ f 1NA ðT; yÞ þ ð1  f 1ÞNA ðT; 180  yÞ

(5)

where NA(T,y) is the number of registered neutrons corrected for an incomplete separation of light and heavy group of fission fragments; f1 is the fraction of heavy fragments in a light fragment group. For events in which only one fragment of the two is detected, f1E2–5%. When both complementary fragments are detected, f1p0.5% (Fig. 4). 3.5. Correction for angular resolution The angular resolution correction was applied by means of the following expression: NðT; yÞ ¼  s2 =2½N A ðT; y  18Þ þ N A ðT; y þ 18Þ þ ð1 þ s2 ÞN A ðT; yÞ

(6)

Fig. 4. (a) Time-of-flight spectrum of fission fragments detected by MWPDs of arc N1. (b) Number of fission fragments as a function of time-of-flight difference for fragments registered by two opposite detectors of arcs N1 and N2.

where a variance of the angular distribution of fission neutrons was given by !2 360  ðMWPD lin: widthÞ s2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ln 2 2pðMWPD  235 U dist:ÞðMWPD ang: widthÞ 0:138

3.6. Correction for neutron detector efficiency The energy spectrum of fission neutrons N(En,y) was obtained in non-relativistic approximation from the measured time-offlight spectrum N(T,y) for each of the two neutron detectors with the following expression: Ni ðEn ; yÞ ¼ Ni ðT; yÞ

ðM dTÞ3 C2ðRÞ þ C2ð180  RÞ Oi N f ðRÞ ð72:3Di Þ2

(7)

where M  dT is the neutron time-of-flight calculated using Eq. (1); Di is the distance from the target to the i-th neutron detector (i=1,2), corrected for average range of neutrons in stilbene;

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O1=0.013 sr and O2=0.008 sr are the solid angles of neutron registration, accordingly. Since the integral (total) spectrum of prompt fission neutrons from the reaction 235U(nth,f) in the energy range from 0.03 to 9 MeV, NStd(En), is known to within about 3% [17], the registration efficiency of the i-th neutron detector ei (En) was determined using following expressions: Rp 2p 0 N i ðEn ; yÞ sinðyÞ dEn dy (8) i ðEn Þ ¼ NStd ðEn Þ NStd ðEn Þ ¼ ð0:95342 þ 0:04909En  0:0092331E2n þ 0:00024973E3n ÞMðEn ; hEn iÞ pffiffiffiffiffi 2 En expðEn =T m Þ ; MðEn ; hEn iÞ ¼ pffiffiffiffi 32 pT m

Tm ¼

(9) 2hEn i 3

(10)

where M(En,/EnS) is a Maxwellian distribution with average energy /EnS=1.971 MeV. Then the number of fission neutrons emitted at angle y with respect to the direction of movement of light fragments in the laboratory system per unit solid angle and corrected for registration efficiency of the i-th neutron detector, ni (En,y), was calculated by ni ðEn ; yÞ ¼

N i ðEn ; yÞ i ðEn Þ

(11)

Additionally, these neutron spectra ni(En,y) were normalized to the average fission neutron multiplicity of 235U from thermal neutron-induced fission, /nS=2.43, which is known with high accuracy: Z 1Z p ni ðEn ; yÞ sinðyÞ dEn dy (12) hni ¼ 2:43 ¼ 2p 0

0

In the final stage of experimental data processing, the results obtained independently for two neutron detectors were combined to produce the final energy and angular distributions of fission neutrons, n(En,y). 4. Discussion As mentioned above, it is well established that the prompt neutrons in low energy fissions are emitted mainly from fully accelerated fragments and the yield of ‘‘scission’’ neutrons may range from 1% to 20% of the total prompt neutron yield. The wide scatter of the published data on ‘‘scission’’ neutron yield is caused mainly by the different shape of the neutron spectrum in the center-of-mass system used in analysis. This follows as the yield of these neutrons is usually determined by comparing experimentally observable variables in the laboratory system with those calculated on the basis of the assumption that neutrons are emitted only from fully accelerated fragments. A more constitutive approach to the problem consists of obtaining the neutron spectrum in the center-of-mass system without resort to any model representation, using only experimental data. In order to obtain the contribution of the neutrons corresponding to the ‘‘principal’’ mechanism of neutron emission (evaporation from fully accelerated fragments), we used the spectra of fission neutrons obtained at small angles as measured relative to the dedicated directions of motion of light (y=01) and heavy (y=1801) fragments. For such small angles, the contribution of the ‘‘minor’’ mechanism in neutron emission is expected to be minimal, so that the contribution of neutrons emitted by a complementary fragment can be correctly taken into account. A circumstance of no small importance is the fact that, in these cases, it is possible to obtain a neutron spectrum in the center-of-mass system, which is

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practically unrestricted in the low energy range. Admittedly, in this case, the shape of the neutron spectrum and the number of neutrons obtained in the center-of-mass system both depend on the fragment velocities. As an evaluation, one can use a spectrum written in the center-of-mass system treating the case of two fragments characterized by the average parameters. Taking the example of 252Cf, it was shown by Madland [18] that a transition from the velocity distributions of fragments to the model of two fragments with average parameters has only a minor influence (2%) on the total neutron energy distribution. For a neutron emitted by a fragment, the neutron center-ofmass energy Ecm, the neutron energy in the laboratory system En, the fragment energy per nucleon Ef, and the neutron emission angles in the center-of-mass ycm and laboratory system ylab are related by Ecm ¼ En þ Ef  2 cosðylab ÞðEn Ef Þ1=2

(13)

Ef ¼ TKE½1=mf  1=A

(14)

ðEcm Þ1=2 cosðycm Þ ¼ ðEn Þ1=2 cosðylab Þ  ðEf Þ1=2

(15)

where A is the mass number of the fissioning nucleus, mf and TKE are the initial fragment mass and total kinetic energy of fission fragments, respectively. The number of neutrons n(En,y) with energy En per unit energy range and solid angle, registered at angle y with respect to the direction of motion of light fragments in the laboratory coordinate system, can be written as a sum of prompt neutrons emitted from light nL(En,y) and heavy nH(En,180y) fragments: nðEn ; yÞ ¼ nLðEn ; yÞ þ nHðEn ; 180  yÞ.

(16)

The number of neutrons nlab (En,O) with energy En, registered at the solid angle O with respect to the direction of motion of fragments in the laboratory coordinate system, is related to the analogous amount of neutrons ncm(Ecm,Ocm) in a center-of-mass system by the relations: nlab ðEn ; OÞ ¼ ðEn =Ecm Þ1=2 jðEcm ; Ocm Þncm ðEcm Þ

(17)

jðEcm ; Ocm Þ ¼ 1 þ A2 Ecm ð3 cos2 ðOcm Þ  1Þ=2

(18)

where the function j(Ecm,Ocm) is the angular distribution of neutrons in the center-of-mass system and the parameter A2 defines the value of the angular anisotropy. In the first step of calculations, it was assumed that neutrons registered at 01 and 1801 angles were emitted solely by the light and heavy fragments, respectively. In the second step, the neutron contribution to the complementary fragment was subtracted (Fig. 5). Then, using the energy spectra for 01 and 1801 angles obtained in this way in the laboratory system, the neutron energy spectra for light and heavy fragments were obtained in the centerof-mass system. In doing so, it was assumed that the specific energy per nucleon for light and heavy fragments, respectively, was EL=1.025 MeV and EH=0.476 MeV. The reference spectra obtained in the center-of-mass system (Fig. 6) were used for calculation of neutron energy and angular distributions in the laboratory system. The number of fission neutrons and their average energy for fixed angles in the laboratory system (obtained experimentally and calculated using an assumption about isotropic emission from fully accelerated fragments) are shown in Figs. 7 and 8. The errors of the obtained experimental data are comparable with the point’s size. In these figures, the experimental results of Skarsvag and Bergheim [7] are also shown. These authors came to a conclusion that about 15% of neutrons are emitted during the fission process itself. The energy dependence of the ratio of neutron yields

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0.21

0.8 n (θ) [neutron / fission / sr]

 = 0°

0.18 0.15

0.09

0.6

Model calculation

0.4

Skarsvag (1963) 0.2

0.06 0.0

0.03

0

0.12

18

36

54

72 90 108 126 144 162 180 θ [degree]

Fig. 7. Fission neutron yield as a function of the angle between neutron exit direction and the direction of motion of the light fragments.

 = 180°

0.10 0.08 0.06 0.04 0.02

1 Neutron energy, En [MeV]

10

Average neutron energy, [MeV]

n (En, θ) [neutron / fission / sr / MeV]

0.12

neutron detector ND1 neutron detector ND2 average

3.0 neutron detector ND1 neutron detector ND2 average

2.8 2.6 2.4 2.2

Model calculation

2.0 1.8 1.6

Skarsvag (1963)

1.4 1.2 0

Fig. 5. Spectrum of fission neutrons in laboratory system: experiment—full circles with error bars; model calculation (contribution of fission neutrons from complementary fragment)—open circles.

18

36

54

72 90 108 126 144 162 180 θ [degree]

2.0 1.8

Light fragments Heavy fragments

N(0°) / N(90°)

Experiment

1.6

Model calculation

100

1.4

Ratio

Ratio to MaxwellianTm = (2/3)

Fig. 8. Angular dependence of the average neutron emission energy in the laboratory system.

1.2

10 1.0 N(180°) / N(90°) 0.8 0.01

1 0.1 Neutron energy, Ec.m. [MeV]

10

1 1

2

3 4 5 6 7 Neutron energy, En [МeV]

8

9

10

Fig. 6. Ratio of the prompt fission neutron spectrum from light and heavy fragments in the center-of-mass system to the Maxwellian spectrum with adjusted parameters.

Fig. 9. Ratio of the fission neutron yields as a function of neutron energy for angles 01, 1801 and 901 in the laboratory system.

measured at 01 and 901, as well as that at 1801 and 901, is shown in Fig. 9. On the whole, the calculated model energy and angular distributions agree rather well with the experimentally obtained

distributions. However, there is a minor distinction which is most clearly demonstrated in Fig. 10, where it is shown the angular dependence of the ratio of experimentally obtained neutron yield to calculated one. A maximal difference between the model

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1.3 neutron detector ND1 neutron detector ND2 average

N (θ)exp / N (θ)model

1.2

anisotropy A2 = 0.04 1.1

1.0

801

of the 235U(nth,f) fission neutrons with a theoretical distribution, calculated using the model of isotropic emission of neutrons from fully accelerated fragments shows that, in the integral spectra a difference in the neutron yield, which could be assigned to a contribution of ‘‘scission’’ neutrons, does not exceed 5%, while a maximum effect is 10% at the angles near 901. Introduction of anisotropy of the fission neutron angular distribution in the center-of-mass system of fission fragments into the model calculation leads to an increase in the ‘‘scission’’ neutron yields inferred from the data.

0.9 Acknowledgements

0.8

0

18

36

54

72 90 108 126 144 162 180 θ [degree]

Fig. 10. Angular dependence of experimental and calculated fission neutron yields.

calculation and the experiment is 10% for the angles near 901. For the total spectra (integrated over all angles) this difference does not exceed 5% therewith. Special attention must be given to the fact that, for angles 301 and 1501, the model calculation gives overestimated values of fission neutron yield as compared with the experiment. Such a discrepancy, as our model calculation shows, may be related to presence of anisotropy of the fission neutron angular distribution in the center-of-mass system (A2E0.02–0.08). For example, introduction of anisotropy with A2=0.04 into the model calculation leads to an increase in the neutron yield ratio from 10% to 15% for angles close to 901.

5. Conclusion The experimental setup and methodology of the measurements of the angular and energy distributions of prompt fission neutrons are described. The neutrons were detected by means of two scintillation detectors, while the fission fragments were detected by multi-wire proportional detectors in conjunction with the time-of-flight technique. A double discrimination was applied to separate events corresponding to neutrons and g-quanta: discrimination by pulse shape and that by the time-of-flight. In the course of experimental data processing, a few corrections were introduced to account for neutron detector background, angular resolution of fragment detectors and neutron registration efficiency. The energy spectra and angular distributions of fission neutrons have been measured for thermal neutron-induced fission of 235U. A comparison of the measured angular distribution

It is a pleasure to acknowledge the help of D.V. Nikolaev, D.O. Krinitsin and L.S. Falev in adjustment of the equipment and conducting the experiment. The authors are grateful to T.E. Kuz’mina and S.M. Soloviev from Khlopin Radium Institute for producing the 235U target. This work was carried out under support of the INTAS Grant 03-51-6417 and a partial support of the ‘‘Russian Science Support Foundation’’. References [1] H.R. Bowman, S.G. Thompson, J.C.D. Milton, W.J. Swiatecki, Phys. Rev. 126 (1962) 2120. [2] V.M. Piksaikin, P.P. Dyachenko, L.S. Kutsaeva, Sov. J. Nucl. Phys. 25 (1977) 723. [3] P. Riehs, Acta Phys. Austriaca 53 (1981) 271. [4] E.A. Seregina, P.P. Dyachenko, Sov. J. Nucl. Phys. 42 (1985) 1337. [5] C. Budtz-Jorgensen, H.-H. Knitter, Nucl. Phys. A 490 (1988) 307. [6] O.I. Batenkov, A.B. Blinov, et al., IAEA Report INDC (NDS)-220, Vienna, 1989, p. 207. [7] K. Skarsvag, K. Bergheim, Nucl. Phys. 45 (1963) 72. [8] S.S. Kapoor, R. Ramanna, P.N. Rama Rao, Phys. Rev. 131 (1963) 283. [9] M.S. Samant, R.P. Anand, R.K. Choudhury, et al., Phys. Rev. C 51 (1995) 3127. [10] N.V. Kornilov, A.B. Kagalenko, in: A.M. Sukhovoj (Ed.), IInd International Seminar on Interaction of Neutrons with Nuclei ‘‘Neutron Spectroscopy, Nuclear Structure, Related Topics’’, ISINN-2, Dubna, April 26–28, 1994, JINR, Dubna, E3-94-419, 1994, p. 116. [11] N.V. Kornilov, A.B. Kagalenko, F.-J. Hambsch, in: A.M. Sukhovoj (Ed.), VIIth International Seminar on Interaction of Neutrons with Nuclei ‘‘Neutron Spectroscopy, Nuclear Structure, Related Topics’’, ISINN-7, Dubna, May 25–28, 1999, JINR, Dubna, E3-98-212, 1999, p. 241. [12] N.V. Kornilov, A.B. Kagalenko, F.-J. Hambsch, Sov. J. Nucl. Phys. 64 (2001) 1462. [13] N.V. Kornilov, A.B. Kagalenko, S.V. Poupko, et al., Nucl. Phys. A 686 (2001) 187. [14] G.V. Val’skii, Sov. J. Nucl. Phys. 67 (2004) 1288. [15] G.V. Val’skii, A.M. Gagarskii, I.S. Guseva, et al., PNPI Preprint-2546, Gatchina, 2003. [16] A.S. Vorobyev, O.A. Shcherbakov, Yu.S. Pleva, et al., PNPI Preprint-2753, Gatchina, 2008. [17] N.V. Kornilov, A.B. Kagalenko, K.I. Zolotarev, in: A.M. Sukhovoj (Ed.), VIth International Seminar on Interaction of Neutrons with Nuclei ‘‘Neutron Spectroscopy, Nuclear Structure, Related Topics’’, ISINN-6, Dubna, May 13–16, 1998, JINR, Dubna, E3-98-202, 1998, p. 242. [18] D.G. Madland, IAEA Report INDC(NDS)-251, Vienna, 1991, p. 201.