ISSN 0020-4412, Instruments and Experimental Techniques, 2006, Vol. 49, No. 6, pp. 765–777. © Pleiades Publishing, Inc., 2006. Original Russian Text © V.M. Piksaikin, N.N. Semenova, V.I. Mil’shin, V.A. Roshchenko, G.G. Korolev, 2006, published in Pribory i Tekhnika Eksperimenta, 2006, No. 6, pp. 29–42.
NUCLEAR EXPERIMENTAL TECHNIQUE
A Method and Setup for Studying the Energy Dependence of Delayed Neutron Characteristics in Nuclear Fission Induced by Neutrons from the T(p, n), D(d, n), and T(d, n) Reactions V. M. Piksaikin, N. N. Semenova, V. I. Mil’shin, V. A. Roshchenko, and G. G. Korolev Institute of Physics and Power Engineering, pl. Bondarenko 1, Obninsk, Kaluga oblast, 249033 Russia e-mail:
[email protected] Received February 27, 2006
Abstract—A method and a setup based on this method are described, with which it has for the first time become possible to measure the energy dependence of the absolute total and relative yields of delayed neutrons and the half-lives of their precursors from neutron-induced fission of heavy nuclei in the course of one experiment. T(p, n)3He, D(d, n)3He, and T(d, n)4He nuclear reactions induced by high-energy charged-particle beams from the äÉ-2.5 electrostatic accelerator at the Institute of Physics and Power Engineering are used as sources of monoenergetic neutrons. The measured total delayed neutron yields from neutron-induced fission of 233U and 239Pu nuclei in the energy range of 0.37–4.7 MeV, as well as the relative yields of delayed neutrons and the halflives of their precursors from neutron-induced fission of 239Pu in the range of 15.8–17.9 MeV, are presented as an illustration of the method. The uncertainties of the data obtained by means of this method are shown to be significantly lower than the uncertainties of similar data measured using other techniques. PACS numbers: 25.85.Ec, 29.90.+r, 25.85.-w DOI: 10.1134/S0020441206060030
INTRODUCTION Interest in investigating the characteristics of delayed neutrons emitted in the final phase of heavy nucleus fission has been brought about primarily by the role that delayed neutrons play in safe operation of nuclear power plants based on chain fission reactions. The availability of precise physical data on delayed neutrons is a necessary condition for carrying out reliable analysis of nuclear reactor kinetics. However, the currently available delayed neutron databases incompletely satisfy the requirements specified for these data by a new generation of reactors characterized by a hard neutron spectrum, the use of a multicomponent nuclear fuel, and the presence of nuclear materials liable to transmutation. The most important characteristics of delayed neutrons as regards the kinetics and safe operation of nuclear reactors are absolute delayed neutron yield νd, relative yields ai and decay constants λi of separate delayed neutron groups, and energy spectra of delayed neutrons χi (En). The energy range of primary neutrons used in these tasks corresponds to the energy range of fission neutron spectrum. In addition, there are a number of applied problems in which obtaining the delayed neutron data at primary-neutron energies of 14 MeV is also a relevant task. First and foremost, these problems concern development of a technique
for nondestructive analysis of nuclide composition of nuclear fuel and a method for detecting and identifying nuclear materials in sealed containers. The libraries of evaluated nuclear data contain the values of above characteristics for thermal (2.53 × 10–2 MeV), fast (0.5 and 0.4 MeV in the ENDF/B-VI [1] and JEF [2] libraries, respectively), and high-energy (14 MeV) neutrons. It should be noted that the parameters of the delayed neutrons corresponding to the fast neutrons were estimated based on the experimental data obtained from reactor neutron spectra; however, the average energies of these spectra, weighted over the fission cross section, differ considerably from the values presented in the above libraries (2.75 MeV [3] and 3.1 MeV [4] in an experiment with 238U). The absence of detailed information about the energy dependence of delayed neutron parameters νd, (ai , λi), and χi (En) is due to the fact from that only a few experiments on monoenergetic neutron beams in a wide range of energies have been performed. The goal of this work was to develop a method and use it as a basis to create a setup for studying the energy dependence of the absolute yield of delayed neutrons and their temporary characteristics—the relative yields of separate delayed neutron groups and the half-lives of their precursors in neutron-induced fission of heavy nuclei.
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EXPERIMENTAL TECHNIQUE FOR MEASURING THE ENERGY DEPENDENCE OF THE DELAYED NEUTRON CHARACTERISTICS ON MONOENERGETIC NEUTRON BEAMS The method for measuring the total yield and the temporary characteristics of delayed fission neutrons consists in irradiating the sample under investigation by a prompt neutron burst or a neutron flux during a time interval comparable to the half-life of delayed neutron precursors and measuring the decay curve of the delayed neutron intensity [4]. If the sample is irradiated by a prompt neutron burst, the initial intensity of delayed neutrons is proportional to product aiλi . Therefore, it is profitable to use a “propmt neutron burst” to study the temporary characteristics of short-lived delayed neutron groups. In this case, the total number of recorded pulses is proportional to the total yield of delayed neutrons, which renders this method suitable for measurements of the absolute total yields. However, this requires a high-intensity neutron source (e.g., see [4]). As a rule, neutrons from this source have a wide energy distribution, which rules out the possibility of investigating the energy dependence of the delayed neutron characteristics. Irradiation of a sample over a time comparable to the half-life of the most long-lived group of delayed neutrons offers the chance to carry out combined measurements. The majority of the experiments aimed at studying the integral delayed neutron characteristics were performed on neutron beams from a reactor, a critical assembly, and a neutron generator [4]. Measurements on monoenergetic neutron beams with energies variable over a wide range (e.g., see [5]) were made only in a few experiments, the prime objective of which was to study the relative yields and half-lives of separate delayed neutron groups. The method proposed in this paper is based on the use of monoenergetic neutron beams generated in charged-particle-induced nuclear reactions on the äÉ-2.5 electrostatic accelerator. The neutron beam intensity provided by the accelerator is substantially lower than the intensity of neutron beams from a reactor or a critical assembly. Therefore, to achieve sufficient statistical accuracy of data, measurements are made in a cyclical mode. Each cycle consists in irradiating the sample under investigation by a neutron beam with a fixed energy, transporting the sample to a neutron detector with the aid of a pneumatic system, and measuring the time dependence of the delayed neutron intensity. By varying the irradiation time, the time between the end of irradiation and the start of the counting of delayed neutrons, and the measurement time for the delayed neutron intensity decay curve, it is possible to increase the contribution of one or another group of delayed neutrons to the integral neutron activity decay curve, thus improving the resolution of the method. The basic expression for the time dependence of the delayed neutron intensity, measured during cyclical
irradiation of fissile samples in neutron flux ϕ(En), has the form m
N ( tk ) = A
ai
∑ T ---λ- ( 1 – e i
i=1
Ti = (1 – e
– λ i t irr
– λ i ∆t k
)e
–λi tk
(1)
+ B∆t k ,
i
– nλ i T ⎞⎞ ⎛ n –λi T ⎛ 1 – e -------------------------⎟ ⎟ , e ) ⎜ -----------------– ⎜ –λi T –λi T 2 ⎝(1 – e ) ⎠⎠ ⎝1 – e
A = ε n σ f ϕN f ν d , where N(tk) are the neutron detector counts recorded in time channel tk with duration ∆tk, νd is the total yield of delayed neutrons per fission event, B is the neutron background intensity, λi and ai are the decay constant and relative yield of the ith delayed neutron group, n is the number of the measurement cycles, m is the number of delayed neutron groups, T is the duration of one cycle (including the irradiation and delayed neutron registration times), tirr is the irradiation time, εn is the neutron detector efficiency, ϕ is the neutron flux, σf is the fission cross section of the fissile nuclide, and Nf is the number of nuclei in the sample. The method we propose allows for two types of experiments. In the first of these, the energy dependence of the relative yields of delayed neutrons and the half-lives of their precursors are measured. Depending on the experimental conditions (the background radiation level, the properties of the nuclide sample under investigation, etc.), we selected irradiation times of 15, 180, and 300 s; the data acquisition time for delayed neutrons was 224.5, 424.5, 524.5 or 724.5 s. In this case, the time scale was variable: 0.01 s (150 channels), 0.02 s (150 channels), 0.1 s (200 channels), 1 s (200 channels), and 10 s (0, 20, 30, or 50 channels). The above parameters have not been fixed; they can be changed depending on the goal and conditions of each particular experiment. After a correction for the dead time of the neutron detector is applied, the decay curves of delayed neutron intensity N(tk) are analyzed using the iterative method of least squares with the purpose of estimating relative yields of delayed neutrons ai, halflives of their precursors Ti (Ti = ln2/λi ), saturation activity A, and background intensity B [6]. In this case, the delayed neutron precursors are represented by a sixgroup model. The decay curves measured at relatively short irradiation times are used to estimate the parameters of the short-lived delayed neutron groups, and the decay curves corresponding to longer exposure times are used for groups with longer half-lives. Experiments of the second type are performed with the aim of investigating the energy dependence of the total delayed neutron yield. Depending on the background conditions of an experiment, the irradiation time is several times greater than or comparable to the half-life period of the most long-lived delayed neutron precursor—87Br (T1/2 = 55 s). Two methods utilizing Eq. (1) are used to obtain the total delayed neutron yields. The first of
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these is based on summation of counts N(tk) recorded within time interval (t1, t2), takes into account the background level, and involves time parameters (ai , λi) and background intensity B that are obtained from the analysis of the relevant delayed neutron activity decay curve
767 2 n
n p, d
t2
∑ N (t ) – B(t k
2
n
– t1 )
t1 -, ν d = -----------------------------------------------------------------6 a i –λi t1 –λi t2 〈 ε n〉 R s T i ---- ( e –e ) λi
(2)
3
∑
i=1
R s = σ f ϕN f ,
1
where Rs is the rate of a fission reaction in the sample under investigation. The other method (known as “extrapolation to the instant of time corresponding to the end of irradiation”) uses delayed neutron saturation activity A, determined by processing the delayed neutron intensity decay curve A ν d = ---------------- . 〈 ε n〉 R s
Fig. 1. Layout of the sample under investigation and the fissile layers of a fission chamber with reference to the accelerator target: (1) 237Np or 239Pu fissile layers of the fission chamber, (2) sample under investigation, and (3) tritium or deuterium target. (0)
E p can be calculated according to the expression [9] (also see [10]):
(3)
The use of both approaches for obtaining dependence νd(En) in a single experiment makes it possible to lower the probability of systematic errors that may occur in the course of measurements. From the above expressions, it is evident that both methods require information on neutron detector efficiency εn and rate of the fission reaction in the sample under investigation Rs(En). The value of εn is measured in a separate experiment (see below) and represents only the characteristic of the neutron detector itself, while quantity Rs(En) characterizes the whole experiment and depends on a variety of factors (the geometry of the experiment; the mass, size, and design of the sample under investigation; the properties of the neutron source; etc.). Therefore, determining the value of Rs(En) is the most complicated task from the standpoint of the methods involved. In most studies of the delayed neutron properties carried out with thermal and fission neutrons, the reaction rate in a sample was determined by measuring the γ and β activities of the fission products accumulated in the irradiated sample [7, 8]. However, the use of these kinds of techniques in investigations of energy dependence νd(En) in a wide range of energies is complicated due to a lack of reliable data on the energy dependence of the respective fission-product yields. In order to determine the rate of fission reactions in a sample, it is necessary that the neutron flux through the sample be known beforehand. Spectrum Φ(r, W, E) of neutrons emitted within solid angle (W) from the target (r) under irradiation by a proton beam with energy INSTRUMENTS AND EXPERIMENTAL TECHNIQUES
R max
Φ ( r, W, E ) =
∫
(0) dE p
∫ dR ∫ dW g ( E p
(0) p )ξ ( R )
0 (0)
× σ pn ( E p, W p
(4)
(0)
E, W )E p ( E p , R )ψ ( W p, E p , R ), (0)
where R is the ion range in the target materials, g( E p ) is the energy distribution of ions incident on the target (0) (0) surface, Ep( E p , R) and ψ(Wp, E p , R) are the energy and angular distributions of ions at depth R, ξ(R) is the concentration of tritium or deuterium nuclei at depth R from the target surface, and σpn is the cross section of the (p, n) reaction. However, the absence of information on distribution ξ(R) makes it impossible to obtain accurate values of the absolute neutron flux from Eq. (4). The method we used for determining the neutron flux is based on an experimental procedure in which a sample enclosed in the tube of the pneumatic system is placed between two thin-walled fission chambers containing fissile layers with known numbers of fissile nuclei (237Np and 239Pu, respectively, for threshold and nonthreshold fissile nuclides under investigation). In this geometry of measurements, the fission chambers provide quantitative information on the flux, which is subsequently used for the absolutization of the neutron flux from the accelerator, calculated with allowance for the known effects of interaction between the ions and the target material [10]. The layout of the sample under investigation, the fission chambers, and the neutron target of the accelerator is shown in Fig. 1. The use of two fission chambers for the absolutization of the neutron flux improves the reliability of the Vol. 49
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Ch +0.2 kV
ChD
A
PS
CFC I
FC1
PA1
SV1 SPS1
SPS2 SV2 PAD1 PAD2
FC2 BC
PAD3 +0.2 kV
–0.65 kV
PS
PS
+0.65 kV
PS
PA2
PA4
ADC1
AU
ADC2
C1
SCC
G
MCC
CAMAC crate
C2
CU
ë3
CAMAC bus
Crate controller
Fig. 2. Block diagram of the experimental setup: (PAD) preamplifier, amplifier, and discriminator; (AU) adder unit; (PA) preamplifier and amplifier; (SV) electromagnetic valve; (SPS) sample position sensor; (CU) controlled unit; (CFC) current-to-frequency converter; (ADC) analog-to-digital converter; (SCC) software-controlled counter; (MCC) multichannel counter; (G) quartz generator of pulses; (PS) power source; (Ch) chopper; (ChD) magnetic chopper drive; (A) ion guide aperture; (T) accelerator target; (FC) fission chamber; (BC) boron counter of neutrons; (C1) counter with a preset exposure time; (C2) counter of total counts from the CFC and BC; and (C3) counter of the CFC and BC counts within preset time intervals.
method considerably, since the data obtained thereby reflect variations of the neutron flux near the sample more adequately. These variations are subsequently taken into account when calculating the rate of fission reactions in the analyzed samples during neutron field simulation [10]. A SETUP FOR STUDYING THE ENERGY DEPENDENCE OF THE DELAYED NEUTRON CHARACTERISTICS AND A MEASURING PROCEDURE The schematic diagram of the experimental setup is shown in Fig. 2. The setup is located on the ion guide of the äÉ-2.5 electrostatic accelerator. It comprises a 4π neutron detector, monitors of the neutron flux and the ion current delivered to the target, a pneumatic system for sample transportation with starting electromagnetic valves (SV1 and SV2) and sample position sensors (SPS1 and SPS2), an ion beam chopping system, and an electronic system for data acquisition.
A Source of Monoenergetic Neutrons Nuclear reactions induced in solid-state tritium and deuterium targets by proton and deuteron beams from the äÉ-2.5 electrostatic accelerator are used in the experiment as a source of monoenergetic neutrons. The reaction T(p, n)3He is a source of monoenergetic neutrons in the energy range of 0.37–1.1 MeV. Monoenergetic neutrons with energies of 3.25–4.72 MeV are generated by the reaction D(d, n)3He. A neutron source based on the reaction T(d, n)4He is used in measurements at energies of 14.23–17.98 MeV. An epithermal neutron flux was obtained by placing a polyethylene cube with a side of ~20 cm near the accelerator target. The layout of the target assembly and a sample enclosed in the moderator is shown in Fig. 3. Fast neutron spectra ϕ(En) corresponding to neutrons from the reactions T(p, n)3He and D(d, n)3He (Figs. 4 and 5, respectively) were calculated using the Monte Carlo method and averaged over the volume of the fissile sample. The neutron distribution averaged over the sample volume at the center of the polyethyl-
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1 6 cm
2
4
1
2 2
3
0 19.5 cm
4 3
6
5.2 cm
0.4
0.8
1.2 En, MeV
Fig. 4. Energy distribution of neutrons from the reaction T(p, n)3He, averaged over the fissile sample: (1–4) energy spectra of neutrons from the reaction T(p, n), generated by protons with energies of 1.318, 1.550, 1.777, and 1.974 MeV, respectively.
21 cm
∅3 cm
769
which is comparable to the half-life of the most shortlived delayed neutron group. Information on the sample position arrives from the LEDs. The light signal is transmitted to the LEDs via a fiber-optic cable attached to the pneumatic pipeline at the sample location near the neutron target and in the neutron detector. A 4π Neutron Detector
21 cm
Fig. 3. Neutron source (the accelerator target) and sample positions in experiments at low energies: (1) target assembly, (2) pipe of the sample transportation system, and (3) fissile sample.
ene cube is shown in Fig. 6. The mean neutron energy in the moderator, averaged over the sample volume, was 2.85 eV. A System for Fissile Sample Transportation A pneumatic device is used to transport a sample from the irradiation position to the neutron detector. A pneumatic pipeline is a thin-walled (0.3-mm-thick) stainless steel tube with an outer diameter of 10 mm. Samples of fissile materials are packed in hermetically sealed stainless steel capsules, which are then enclosed in a titanium container. The average mass of fissile samples is ~1 g, which allows us to avoid introducing high corrections for the neutron multiplication. Transportation of a sample in the desired direction is controlled by means of two electromagnetic valves SV1 and SV2. The sample transportation time is ~150 ms, INSTRUMENTS AND EXPERIMENTAL TECHNIQUES
A CHM-11 boron counter having a low γ-ray sensitivity is the main detecting element of the neutron detector, which is an assembly of 30 counters distributed inside a polyethylene moderator along three concentric circles with radii of 53, 80, and 110 mm. The inner circle contains six boron counters; each of the middle and outer circles has 12 counters. The outer diameter of the moderator is 400 mm, and its length is 300 mm. The counters are operated in a proportional mode at a voltage of 650 V. At the center of the detector is a 36-mm-diameter channel into which an analyzed sample is inserted. The moderator block is shielded by boron carbide, cadmium, and borated polyethylene layers. The design of the neutron detector is shown in Fig. 7. Signals from each of the three sections of boron counters are amplified by a preamplifier and fed into the adder unit that performs discrimination of background and shaping of pulses. The dead time of the neutron detector is 2.3 ± 0.2 µs. The energy dependence of neutron detector efficiency εn(En) varies smoothly at energies in the range of 0–1.5 MeV, which are characteristic of the overwhelming majority of delayed neutrons. The stable performance of the neutron detector and the electronic channels of the data acquisition system is checked using standard Am–Li and Pu–Li neutron sources. Vol. 49
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ϕ, arb. units 1012
4 3
6
108 2
4
104 2
1
0 2.5
3.0
3.5
4.0
4.5
100 10–8
5.0 5.5 En, MeV
Fig. 5. Energy distribution of neutrons from the reaction D(d, n)3He, averaged over the volume of the fissile sample: (1–4) energy spectra of neutrons from the reaction D(d, n), generated by deuterons with energies of 0.493, 0.888, 1.283, and 1.777 MeV, respectively.
10–6
10–4
10–2
100
102 En, MeV
Fig. 6. Distribution of the neutron energy in the low-energy experiment, averaged over the fissile sample. The mean energy of moderated neutrons (averaged over the sample volume) was 2.85 eV.
εn, % 10
1 2 3
1 2
9 8 7 6
8 7 6
5
4
Fig. 7. Design of the 4π neutron detector: (1) cadmium shielding, (2) boron carbide powder, (3) borated polyethylene, (4) boron counters (of the CHM-11 type), (5) polyethylene, (6) lead shielding, (7) channel for moving a sample, and (8) container with fissile material.
Measuring the absolute efficiency of the neutron detector. Absolute efficiency of the neutron detector εn(En) was measured by two independent methods [11]. The first of these is based on the use of the reaction 51V(p, n)51Cr as a monoenergetic neutron source, the intensity of which is measured according to the activation technique. The other method utilizes the wellknown energy distribution of neutrons from spontaneous fission of 252Cf isotope and involves calculation of the absolute detector efficiency by the Monte Carlo method. The results for both cases of the neutron detector’s absolute efficiency calibration are shown in Fig. 8. The values of the neutron detector efficiency at 430 keV obtained using two independent methods agree within
5
0
0.5
1.0
1.5 En, MeV
Fig. 8. Energy dependence of the absolute efficiency εn(En) of the 4π neutron detector, obtained using (1) a 252Cf source and (2) reaction 51V(p, n)51Cr.
the limits of errors. The error of the efficiency measured with a 252Cf source is 2.1–3.5% in the energy range of 0.01–10.5 MeV and does not exceed 2.14% in the energy range corresponding to the delayed neutron spectrum. The efficiency obtained using the activation method has an error of 3.64%. Neutron Flux Monitors Increased requirements are specified in our method to the stability of the primary neutron flux characteristics in the course of time, as is the case in any activation measurements. The stability of the neutron flux was controlled with the help of a neutron flux monitor and
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771
N, 103 counts/channel 7 6 5
(a)
(b)
4 3 2 1 0
50
100
150
200
250 0 Channel no.
50
100
150
200
250
Fig. 9. Pulse-height distribution for fission fragments in fission ionization chambers with (a) 237Np and (b) 239Pu layers. The chambers were located ahead of and past the sample along the ion beam incident on the target. The energy of primary neutrons was 5 MeV.
an ion current integrator. A long counter produced on the basis of a CHM-11 boron counter served the functions of the main monitor. The ratio of the long counter readings to the readings of the current integrator, which is proportional to the neutron yield from the accelerator target, was used to control the physical conditions of the accelerator target. Supplementary information on the neutron flux can be obtained from the fission chambers located in the immediate proximity to the fissile sample.
Determining the masses of the 237Np and 239Pu fissile layers in the fission chambers. Two methods are conventionally used to measure the mass of the fissile layer in a fission chamber. The first involves the absolute counting of α particles inside the fission ionization chamber at a high gas pressure, and the other consists in counting of α particles within small solid angles by surface-barrier detectors located at different distances from the fissile layer. The spectrum of α particles in the chamber with a 237Np layer, measured in a 2π geometry, is presented in Fig. 10 as an illustration.
Fission chambers and mass of the fissile layers. The fission chambers were made of stainless steel. The fissile material backings and the electrodes of the fission chambers were made of aluminum 0.2 mm thick and 20 mm in diameter. Layers of neptunium and plutonium dioxides with a thickness of ~100 µg/cm2 were used as fissile materials. To reduce the scattering and absorption of neutrons incident on the sample and the fission chambers, the mass of the structural materials was minimized. The electronic cables and the pipes for the delivery of the working gas to the fission chambers were connected through flange joints located 30 cm away from the chambers. The working gas was a mixture of ëé2 (10%) and Ar (90%). The pulse height distributions of fission fragments in the chambers with 237Np and 239Pu layers, irradiated by 5-MeV neutron beams, are shown in Figs. 9a and 9b.
The vast majority of counts correspond to the 237Np decay, and 1.25% is associated with the decays of 238Pu and/or 241Am impurity nuclides. The pulse-height distribution of α particles also contains a low-energy region that accounts for 0.43 and 0.37% of the total
Efficient discrimination between the pulse height distributions of fission fragments and α particles has made it possible to obtain high detection efficiency for fission fragments at a relatively high α activity of the fissile layers in the fission chambers. The detection efficiency was 98%, on average. The error of the efficiency is governed by the extrapolation of the pulse height distribution of fission fragments to a zero pulse height. The mechanical strength of the fissile layers was checked by counting α particles before and after the experiment. INSTRUMENTS AND EXPERIMENTAL TECHNIQUES
N, 104 counts/channel 4 3 2 1 0 0
50
100
150
200 250 Channel no.
Fig. 10. Pulse height distribution of α particles in the fission chamber with a 237Np layer. Vol. 49
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counts for the layers of the first and second chambers, respectively. The half-lives of 237Np and 238Pu were assumed to be (2.14 ± 0.01) × 105 yr [12] and 87.74 ± 0.05 yr [13], respectively. Upon integrating the α-particle spectra and applying corrections for the impurity nuclide decays and the random summation of pulses (0.63 and 0.52% for the first and second fission chambers, respectively), we obtained that the first and second chambers contained 7.593 × 1017 and 6.304 × 1017 237Np atoms, respectively. Measuring the rate of the fission reaction in a sample. In this study, we developed a method for determining the rates of fission reactions in samples irradiated by monoenergetic neutrons from the reactions T(p, n)3He, D(d, n)3He, and T(d, n)4He. Generally, calculation of fission reaction rate Rs(En) in a sample is a rather complicated problem. It includes finding a solution to the neutron transport kinetic equation with allowance for the multiple neutron scattering in a sample and structural materials of the experimental setup. Moreover, the complex polyenergetic character of the accelerator-based neutron source must be taken into account. A portion of the primary ion energy is lost in the target material; as a result, the angular kinematic characteristics of the neutron spectrum broaden. In addition, the geometry of the experiment falls into the category of “close geometries,” in which the analyzed sample is located very close to the neutron source. Along with thick (0.6–2.0 mg/cm2) targets used to obtain highintensity neutron fluxes, this geometry is also responsible for a spread in the neutron energies. As a result, the spectrum of neutrons escaping from the target becomes much wider (by as much as 10–15% with respect to En) and an asymmetry is observed. The other cause for the spread in the neutron energies is attributable to the secondary neutrons produced in the processes of neutron moderation in a layer (0.4 mm) of water used to cool the target and multiple neutron scattering in the sample and constructional materials of the experimental setup. These processes are responsible for the appearance of the low-energy tail in neutron spectrum ϕ(En), averaged over the volume of the analyzed sample (see Fig. 4). Rate of the fission reaction in a sample Rs may be presented in a simplified form by the expression Rs = N s
∫ ∫ kϕ ( E , θ, φ )σ ( E ) dE dV , n
s
n
n
s
(5)
where Ns is the number of nuclei in the sample; ϕ(En, θ, φ) is the energy distribution of neutrons emitted from the target in direction (θ, φ) with allowance for the effects of multiple neutron scattering; dVs is the elementary volume in the sample; En is the neutron energy; σs is the fission cross section; and k is the normalization factor introduced for the absolutization of relative neutron flux from the target Φ(r, W, E) (see Eq. (4)). It should be noted that expression (5) does not reflect the processes of multiple neutron scattering by the setup components and inside the sample itself; it ignores both the finite size of the neutron target and
interactions between the charged particles and the target material. Information on normalization factor k can be obtained from fission reaction rate Rch in the fission chamber. Taking into account the chamber efficiency, the fission rate is equal to the ratio of total counting in the fission chamber ΣNc to irradiation time tirr:
∑
Nc R ch = ------------ε ch t irr = N ch
∫ ∫ kϕ [ E ( θ, φ ) ]σ n
(6)
ch ( E n ) dE n dV ch ,
where Nch is the number of 237Np or 239Pu nuclei in the layers of fissile materials in fission chambers, dVch is the volume element of the fissile materials in fission chambers, σch is the fission cross section, and εch is the efficiency of the fission chamber. The resulting expression for Rs is
∑ ∫∫ ∫∫
N s N c ϕ ( E n, θ, φ )σ s ( E n ) dE n dV s R s = ---------------------------------------------------------------------------------------------N ch ε ch t irr ϕ ( E n, θ, φ )σ ch ( E n ) dE n dV ch
(7)
N s 〈 σϕ〉 s -. = R ch -----------------------N ch 〈 σϕ〉 ch
The ratio of the fission rates in the sample and the fission chamber 〈σϕ〉s/〈σϕ〉ch is calculated using the Monte Carlo method in view of the multiple neutron scattering by the structural materials of the setup and the sample itself [10]. The double-differential cross sections of neutron generation in the T(p, n)3He, D(d, n)3He, and T(d, n)4He reactions were presented in [14, 15]. Information on number of fissile nuclei Nch in the fission chambers was obtained in a separate experiment. Configuration of the measuring channel in the data acquisition system. The schematic diagram of the data acquisition system was presented in Fig. 2. The system is used to measure the pulse height distribution of the fission-fragment signals from two fission chambers and the time dependences of the neutron flux incident on the sample, as well as the ion currents and the delayed neutron activities after irradiation is complete. The system is controlled by a personal computer via an FK-4410 crate controller and an interface computer card. Apart from data acquisition, the data acquisition system exercises control of the accelerator beam chopping and sample transportation systems and monitors the stability of the experimental conditions. The system alternately performs measurements in the two modes that involve irradiation of the sample and time analysis of the delayed neutron intensity measured by the 4π neutron detector. In the irradiation mode, the relative neutron flux from the accelerator target is measured using long counter BC, and the current of ions incident on the target is determined by means of current-to-frequency converter CFC. In this
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A METHOD AND SETUP FOR STUDYING THE ENERGY DEPENDENCE 〈σϕ〉ch/〈σϕ〉s 45 40 35 30 25 20 15 10 5 0 0 1
〈σϕ〉ch/〈σϕ〉s 8
(‡)
1 2
773
(b)
7 6 1 2
5 4 3 2 2
3
4
5 En, MeV
1
0
1
2
3
4
5 En, MeV
Fig. 11. Ratio of the fission reaction rates in (a) 237Np and (b) 239Pu layers (1) of the first and (2) second fission chambers to the reaction rate in a 239Pu sample. Curves were drawn to guide the eye.
case, 32-bit counter C2 records the integral counting of detector BC and converter CFC during the whole irradiation time. The constancy of the neutron flux and the ion current on the accelerator target in the course of the experiment is monitored using 16-bit counter C3. Its interrogation time is selected by means of counter C1 with a preset exposure time, at the inputs of which the signals from quartz generator G arrive at frequencies of 0.1 and 1 Hz. The LAM requests of counter C3, formed using counter C1, are continuously interrogated in the process of irradiation. The arrival of LAM requests causes the contents of the data register in counter C3 to be read out and stored. This helps form histograms of counts from neutron detector BC and converter CFC within preselected time intervals. To ensure stability of irradiation, the average intensity of the neutron flux is calculated in the course of measurements from the preset number of interrogation signals. The number of channels for averaging and the relative acceptable variation of the neutron flux are selected prior to beginning the experiment. Should the monitor counts over the interrogation time deviate from the average neutron flux intensity by a significant value, irradiation is ceased, and an alarm message is displayed on the computer monitor. The systems for sample transportation and ion beam chopping are controlled by controlled unit CU. According to the program of measurements, the CU generates control signals that initiate both motion of the Faraday cup shutting off the ion guide of the accelerator and opening of valve SV1 or SV2, depending on the mode of measurements (irradiation or detection of delayed neutrons). The signal from sample position sensor SPS1 or SPS2 arrives at controller unit CU, which in turn generates a signal to close valve SV1 or SV2. To analyze the time dependence of pulses from the 4π neutron detector, the resultant signal from adder unit AU is fed into software-controlled counter SCC with preset number of groups in a time spectrum of neutrons INSTRUMENTS AND EXPERIMENTAL TECHNIQUES
and channel width in each group (see Fig. 12). The data register of the counter is read in response to an LAM request. The values read out of it are added to the data array element corresponding to an appropriate time channel in the current time group. Two recording counters in the SCC are triggered in turn, which reduces the probability of losing a neutron count. Experimental results are salved to two files: (1) a file of a particular measurement with recorded time spectra of delayed neutrons, histograms of the current (Fig. 13) and the neutron flux (Fig. 14), and pulse-height spectra of fission fragments from both chambers, and (2) a protocol file with the experimental conditions. RESULTS Background Conditions of Measurements To illustrate the background conditions that may exist in actual experiments, Fig. 15 shows the delayed N, counts/channel 104 200 0.1-s-wide 200 1-s-wide channels channels 50 10-s-wide channels 150 0.02-s-wide channels
103
150 0.01-s-wide channels
102 100
200
300
400
500
600 700 Channel no.
Fig. 12. Delayed neutron activity, measured after single irradiation of a 233U sample by 4.25-MeV neutrons. Vol. 49
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I, µA
N, 103 counts/channel 12
60 45
9
30
6
15
3
0 0 0
25
50
75 100 Channel no.
0
25
50
75
100 Channel no.
Fig. 13. Time dependence of the proton current on the accelerator target during irradiation of a sample. The channel width was 2 s.
Fig. 14. Time dependence of the neutron flux from the reaction T(p, n)3He, measured by the long counter in the course of irradiation. The channel width was 2 s.
neutron activity decay curves measured during fastneutron-induced fission of 232Th, 233U, 239Pu, and 241Am nuclei. From Fig. 15, it is apparent that the background conditions of experiments with different samples differ widely. The neutron background levels in different time intervals after the end of irradiation are presented in the table. These values were obtained during measurements of the delayed neutron activity using D(d, n)3He and T(p, n)3He reactions as neutron sources. The table shows that the background conditions for 232Th, 233U, 239Pu, and 241Am samples differ, which can be attributed to spontaneous fission of impurities in the 239Pu sample and the (α, n) reaction on oxygen in the 241Am sample. The neutron background in the experiment with the 241Am sample exceeded the background measured in the experiment with 232Th by three orders of magnitude. Therefore, the time parameters of each particular experiment should be optimized to achieve the best results.
accuracy achieved in our method for thermal neutrons is considerably higher than the accuracy of recommended data in [3, 4]. The average half-lives 〈T〉 in the range 3.25–4.72 MeV are much smaller than those obtained in [5]. In addition, a significant spread in the data in [5] leads to an ambiguous inference about the energy dependence of the average half-life of delayed neutron precursors 〈T(En)〉. In [16], it was shown that, at neutron energies below the threshold of emissive fission reaction (n, n'f), the average half-life of delayed neutrons decreases as the excitation energy of a 240Pu* nucleus increases. Therefore, taking into account the agreement between our results and the recommended data, we suppose that the data in [5] for the range of 4– 6 MeV were significantly overestimated.
Energy Dependence of the Relative Yields of Delayed Neutrons and the Half-Lives of Their Precursors from the 239Pu Fission Induced by Neutrons with Energies of 2.85 eV–18 MeV The energy dependence of the delayed neutron group parameters (ai , Ti) for neutron-induced fission of 239Pu nuclei was measured in the range of 2.85 eV– 18 MeV. In Fig. 16, our results are compared to similar data from other authors in terms of average half-life 〈T〉 of delayed neutron precursors [16]: 6
〈 T〉 =
∑
The observed increase in the average half-life of precursors in the energy range of 15–17.9 MeV is associated with the opening of the emissive fission reaction N, counts/s 103 241Am
102 239Pu
101
233U
100 232Th
10–1 100
101
ai T i .
102 Time, s
i=1
Figure 16 demonstrates a good agreement between our data and the recommended data for thermal [4] and fast [3] neutrons. In this case, it should be noted that the
Fig. 15. Delayed neutron activity, measured after the 232Th, 233U, 239Pu, and 241Am samples were irradiated by fast neutrons.
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Background conditions in different experiments (t is the acquisition time for delayed neutrons, B is the neutron background intensity, and ΣB/ΣNd is the ratio of the background-to-delayed neutron counts over the respective acquisition time (724.5, 224.5, or 100 s)) 232Th
Parameter t, s ΣB/ΣNd, % B, counts/s
233U
724.5 224.5 1.10–1.84 0.35–0.58 0.16
724.5 5.95
23239Pu
224.5 2.69
724.5 30
0.73
241Am
224.5 12
229.5 95.2
224.5 95.1 129.9
11.58
channel (n, 2nf), with the result that three compound nuclei—240Pu*, 239Pu*, and 238Pu*—participate in the fission process. As a matter of fact, the average half-life of precursors in the fission of different isotopes of the same element is exponentially dependent on parameter (A – 3Z), where A and Z are the mass number and the atomic number of a fissioning compound nucleus, respectively [16]. Therefore, as the cross section of emissive fission grows, the fraction of fissions proceeding via the 239Pu* and 238Pu* compound nuclei increases. The average half-lives of the precursors produced during fission of these nuclei are ~11.8 and 10.3 s, respectively [16]. Finally, this causes the value of 〈T〉 to increase, which is observed in the experiment. The spread in 〈T〉 at energies of >15 MeV in [5] is considerably greater than the errors of the data, thus pointing to a complex structure of energy dependence 〈T(En)〉. However, physical effects in nuclear fission that could be responsible for such a behavior of 〈T(En)〉 have not yet been seen. It is most likely that the structure observed in dependence 〈T(En)〉 in [5] was brought about by the experimental errors, which were difficult to reveal in the course of the experiment, because there had been no reliable criteria for comparing the relative yields and half-lives of delayed neutron precursors before the procedure of data analysis in terms of the average half-life was introduced in [18]. Taking into
100 41.5
account the aforesaid, we draw the inference that the measured relative yields and half-lives of delayed neutrons make it possible to considerably reduce the existing uncertainties in these data and to reveal thereby the tendency in the behavior of the energy dependence of the delayed neutron temporary parameters over a wide range of neutron energies. Energy Dependence of the Absolute Total Delayed Neutron Yield from Neutron-Induced Fission of 233U and 239Pu The method described in this paper and the setup developed on its basis were used to study the energy dependence of the total delayed neutron yield from neutron-induced fission of 233U and 239Pu nuclei in the energy range of 0.37–4.72 MeV. The results of our study were compared to data from other authors in Figs. 17 and 18, respectively. It is apparent that energy dependence νd(En) for 233U is in good agreement with the data obtained by the “prompt burst” method [20]. However, the data uncertainties achieved using our method was 5%, which is considerably better than the uncertainties in [20]. Dependence νd(En) in [20] is seen to be shifted along the energy axis with respect to our data. A possible cause for this shift is that the geometry of the experi-
〈T〉, s 13
1 2 3 4 5 6
12 11 10 9 8
0
2
4
6
8 En, MeV
16
18
20
22 En, MeV
Fig. 16. Energy dependence of the average half-life of delayed neutron precursors in neutron-induced fission of 239Pu in the energy ranges of 0–5 and 15.8–18 MeV. These data are compared to data from other authors following Spriggs’ compilation [17]: (1) this paper, (2) Keepin (1957), (3) Waldo (1981), (4) Rose (1957), (5) Besant (1977), and (6) Maksyutenko (1963, 1967, 1971). INSTRUMENTS AND EXPERIMENTAL TECHNIQUES
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νd, neutrons/100 fissions
νd, neutrons/100 fissions 1.0 11 0.9
0.9
1 2 3 4 5
0.8 0.8 0.7
0.7 1 2 3 4
0.6 0.5 0.4
12
6 7 8 9 10
0
1
2
5 6 7 8 3
0.6 0.5 4
5
6 7 En, MeV
Fig. 17. Energy dependence of the absolute total delayed neutron yield in neutron-induced fission of 233U nuclei. These data are compared to data from other authors in [19]: (1) this paper, (2) Krick (1970), (3) Keepin (1957), (4) Rose (1957), (5) Masters (1969), (6) Notea (1969), (7) Branson (1955), and (8) Conant (1970).
ment in [20] was such that a sample intercepted a large solid angle relative to the neutron source. This caused the energy spectrum of neutrons incident on the sample to broaden and, as a consequence, the mean neutron energy to decrease, which was not evidently taken into account in the final results in [20]. The νd value for fast neutron energies is greater by 4% than the respective value in [4] and coincides with the recommended value (0.073 neutron/fission) [21]. The energy dependence νd(En) obtained when studying the 239Pu fission at neutron energies corresponding to the reaction T(p, n) is in good agreement both with the evaluated data and with the data measured using the “prompt burst” method [20]. However, the accuracy of our data, as was the case with 233U fission, exceeds the accuracy obtained by the other methods. Data νd(En) at energies of >1 MeV, being consistent (within the limits of errors) with the data in [22], obviously indicates that the total yield of delayed neutrons is energy-dependent. The value of νd grows right up to an energy of ~3.5 MeV and then decreases. Generally, the behavior of energy dependence νd(En) for 233U and 239Pu is the same and agrees with the prediction in [21]. In the energy range of
