Measurement of natZr (n,2n) Reaction Cross Section from the Angle-Correlated Neutron
Spectrum with Pencil-beam DT Neutron Source
K. Shiken, S. Takaki, K. Kondo, M. Matsunaka H. Miyamaru, I. Murata,K.Ochiai* C.konno*T. Nishitani*
Department of Electric, Information Systems and Energy Engineering
Graduate School of Engineering, Osaka University, Suita, Japan*Japan Atomic Energy Agency, Tokai-mura, Ibaraki, Japane-mail: shiken@ef.eie.eng.osaka-u.ac.jp

natAngle-correlated differential cross-section for Zr (n,2n) reaction has been measured with thecoincidence detection technique and a pencil-beam DT neutron source at FNS, JAEA. Energy spectra of
two emitted neutrons were obtained for azimuthal and polar direction independently.
Introduction
The (n,2n) reaction is a neutron multiplication reaction, the cross-section data of which are
crucial information to design a fusion reactor. The natZr (n,2n) reaction cross-section is very importantbecause Li2ZrO3 is one of the fusion blanket candidate materials. However, in the previous benchmark
studies it was pointed out that agreement between experiment and evaluation was not acceptable as shownin Figs.1 and 2. In the case of natZr (n,2n) reaction cross section measurement, the conventional foil
activation method cannot be applied, because suitable radioisotopes cannot be produced by the reaction. In
the present study, two neutrons simultaneously emitted by the (n,2n) reaction were detected directly by twodetectors.
Flux (n/cm2/source/lethargy)

1.

EXP
JENDL-3.2
JENDL-fusion file
ENDF/B-VI
FENDL/E-1.0
FENDL/E-2.0

10-8

10-9

10-10

Li2ZrO3Thickness = 25.4 cm
θs= 0 deg.

C/E10-11210

JENDL-3.2
JENDL fusion file
ENDF/B-VI
FENDL/E-1.0
FENDL/E-2.0
10-1100101

Neutron energy (MeV)

Fig.1 Comparison of measured and calculated leakage
neutron spectra at 0°for 25.4 cm thick Li2ZrO3
assembly
I. Murata et al. Fus. Eng. Des., 51-52(2000) p.821.

Fig.2 Measured and calculated neutron leakage spectrafrom the Zr pile
C. Ichihara et al. J. Nucl. Sci. Tech., 40 (2003) p.417.

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2. Experimental procedure
In present experiment, we used a pencil-beam DT neutron source of Fusion Neutronics Source(FNS) in Japan Atomic Energy Agency (JAEA). It is the only existing pencil-beam DT neutron source inthe world, which supplies an excellent experimental condition, i.e., 105 n/cm2/sec inside the beam and very
low neutron flux of several hundred n/cm2/sec outside the beam.
The schematic experimental arrangement around detectors is shown in Fig.3. The distance
between the neutron source and a zirconium sample (2.4cm in diameter, 2cm long) was 550cm. Twospherical NE213 (4cm in diameter) detectors to detect neutrons emitted simultaneously by the (n,2n)reaction were located at 18.8cm from the zirconium sample. An 238U fission chamber was set up on thebeam line behind the sample to monitor the neutron flux. As shown in Fig.4, three angle parameter (θ 0 ,θ ,φ) with respect to the detector position were defined in which θ0 and θ are the polar angles of emitted twoneutrons andφis the azimuthal angle of detector 2 from detector 1. Measurement points weredetermined by the combination of these angle parameters.
polyethyleneCdPbFePre-collimator

200cm

T target

Sample2cmφneutron beam
200cm
150cm
concreteFig.3 Schematic experimental arrangement

Fig.4 Arrangement around sample and detectors

Because two detectors are positioned very close with each other, there exists a neutron, which canbe detected in both detectors by passing through them in turn. This is a troublesome background called“inter-detector scattering” in this paper. A polyethylene shielding brick up to 10.16cm in thickness was thus
arranged between two detectors to prevent the inter-detector scattering components.
Because NE213 detectors are sensitive also to gamma ray, n/γ discrimination was carried out by
the pulse shape discrimination technique. Two amplifiers with different gains were used to cover a wider
measurable energy range from 800 kev to around 10 MeV. Time difference spectrum of anode signals of thetwo detectors was used to extract the coincidence signals. The region including the peak was gated anddefined as Foreground (FG), and the flat region of time-independent signals was defined as Background(BG). Eight pulse height spectra were measured for one case considering two detectors (1/2), two gains(high/low) and FG and BG. Details of the electric circuit of the measurement is described in Ref.[1].

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3. Data processing
Obtained pulse height spectra were transformed into light output spectra. Examples of measured
pulse height spectra are shown in Fig.5. The position of Compton edge made by 1.275MeV gamma ray
emitted from 22Na and 0.834MeV gamma ray emitted from 54Mn was used in the light unit calibration. TheBG spectrum ( y BG ) was subtracted from the FG spectrum ( y FG ) to derive the net FG spectrum by thefollowing equation.

y = y FG − αy BG(1)where α is the ratio of the gate widths between FG and BG spectra.

counts / light unit104
θ0=55[deg.]
θ=90[deg.]
φ=110[deg.]
Detector 2

103
102
101
100 -210High gain, FG
Low gain, FG
High gain, BG
Low gain, BG

10-1
100
Light output [light unit]

101

Fig.5 Measured light output spectra.
The net light output spectra were unfolded using FORIST[2] unfolding code. Necessary response
function was calculated with SCINFUL[3]. And the energy and angle differential cross sections wereobtained by the following equations,y (θ 0 ,θ , φ , E ) = R ⋅ x(θ 0 ,θ , φ , E )σ i (θ 0 ,θ , φ , E ) =xi (θ 0 ,θ , φ , E )N ⋅ FC ⋅ C ⋅ dΩ i ⋅ dΩ j ⋅ f j

(2)
(3)

where subscripts in Eq.(3) represent either detector 1 or detector 2 , R is the response matrix of theNE213 detector, xi is the unfolded spectrum, σ i is the obtained energy and angle differential crosssection, N is the number of nuclei of the sample, FC is the integrated counts of the fission chamber,

C is the conversion factor of FC into the neutron flux at the sample, dΩ i , dΩ j is the solid angle ofeach detector, f j is the efficiency of detector j . The efficiency of the other detector was considered in
the response matrix. The conversion factor C was determined by the activation method using aluminum
foil. As for the correction of the inter-detector scattering, the detection rate of inter-detector scattering wasestimated by Monte Carlo calculation with MCNP[4] taking into account precise model of eachexperimental arrangement.

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4. Results and discussion
Figure 6 shows the obtained energy spectra. This is a triple-differential cross section, i.e.,
double-angle and single energy differential cross section, called TDX. Hence, there are no evaluated data,
which can be compared with the present measured data. The spectra seem to be an evaporation spectrum.
Estimated error contains statistical error and unfolding process error evaluated by FORIST. Figure 7 showsthe detection ratio between the inter-detector scattering component of a neutron and the coincident signalof two neutrons emitted from (n,2n) reaction calculated by MCNP.

The results were used to evaluate

correction factors. The ratio increases as the distance between two detectors becomes closer. A 10 cm
polyethylene shield, arranged between the detectors, effectively suppressed the inter-detector scattering.

1010

θ0=55[deg.]

109 φ=110[deg.]

1614107

12610Ratio ( % )TDX[mb/sr/sr/MeV]108

θ=125[deg.]
θ=90[deg.]
θ=55[deg.]

105
104

10864103

21020101

θ0 55 55 55 55

100

12 3 4 5Energy [MeV]

6Fig.6 Measured energy spectra at each angle.

55 90 90 134 90

909055 90 125 134 90 134 125 9090

90

55,4055,5555,9055,12555,13490,9090,1313 44,1290 5,90
90 ,6090 ,90,1,90,1 40
80
00
00

θ

40

φ 110 110 110 110 110 110 110 110 60

140 180

Fig.7 Ratio of inter-detector scattering component at each angle.

By integrating TDX over energy, two kind of angular distributions named ADDX are obtained,i.e., one is as a function of azimuthal angle (Fig. 8) and the other is for polar angle (Fig. 9). It seems noangular dependence azimuthally within the error bar as shown in Fig. 8. A gentle forward oriented polar
distribution was observed for axial ADDX as in Fig. 9. The ADX is obtained by integrating ADDX overangle. It shows also a slight forward peaked distribution. The obtained total cross-section (TOX) over theminimum measurable energy of 800 keV was fairly larger than the one evaluated in JENDL-3.3 as
described in Table 1. Unexpectedly, the result shows an opposite trend to the suggestion pointed out by theprevious benchmark studies.

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8

θ0= 90[deg.]
θ= 90[deg.]

3ADDX[mb/sr/sr]

ADDX[mb/sr/sr]

4

2

1

θ0=55[deg.]
φ=110[deg.]

Legendre fitting

64
20060

120

Azimuthal angle φ[deg.]

180-1-0.5
00.5
Polar angle θ (cosθ）

1Fig.8 The azimuthal distribution of natZr (n,2n) Fig.9 Example of the polar distribution of natZr(n,2n) reaction cross-section.

reaction cross-section.

Table.1 Comparison of the obtained total cross-section (TOX) of natZr (n,2n) reaction

ADX at 55 deg. [mb/sr](En＞800 keV )TOX. [mb](En＞800 keV )Present Exp.

64±3

745±23JENDL-3.3

44.9

538.2

Next, to discuss the unexpected discrepancy of the total (n,2n) reaction cross section mentioned
above, extrapolation of spectrum for energies below 800 keV was carried out with an evaporation spectrum.
The nuclear temperature preferred is 1 MeV in the present study, because the evaporation spectrum for 1
MeV would fit our spectrum very smoothly. The value is the same as the one evaluated in RIPL-2. Nuclear
temperatures stored in JENDL-3.3 and ENDF/B-VI are also used as references. The results are summarizedin Table 2 below.
Table.2 Comparison of total cross-sections for natZr(n,2n) reaction, estimated by extrapolation of themeasured energy spectrum below 800 keV with different evaporation spectra for several nuclear
temperatures.
Nuclear temperature [MeV]Preliminary TOX [mb]0.65

1.01.73(assumed in JENDL(used also in(assumed in ENDF

evaluation)

RIPL-2 library)evaluation)1095±30997±27919±26

The result shows the agreement with JENDL-3.3 is acceptable for the total cross-section of natZr(n,2n) reaction obtained by extrapolating the measured energy spectrum down to zero energy. Ourestimation agrees very well with the only existing measured data of Frehaut et. al., (946±67 mb at En=14.3
MeV). As a result, it is suggested that the discrepancy seen in the previous benchmark studies may be caused,
not by the problem of absolute value, but by the problem of energy spectrum shape determined by the nuclear
temperature. For JENDL-3.3, the absolute value is more or less acceptable, but the nuclear temperature used52006 Symposium on Nuclear Data

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may be a little small, meaning a little underestimation is seen in larger energy region and overestimation inlower energy region. For ENDF/B-VI, a slight underestimation is seen as a whole. However, from thepresent result and the previous benchmark study, the nuclear temperature used may be a little too high. The
above results suggest examination of nuclear temperature used in the nuclear data library is worth being
carried out.

5.

conclusion
Using the pencil-beam DT neutron source and the coincidence detection technique,angle-correlated energy differential cross-section for natZr (n,2n) reaction was measured successfully. The
obtained total cross-section above the emitted neutron energy of 800 keV was fairly larger than the one
evaluated in JENDL-3.3. The total cross-section of natZr (n,2n) reaction was estimated by extrapolating thespectrum down to zero energy taking into account the nuclear temperature. The estimated value wasbetween those of JENDL- 3.3 and ENDF/B-VI. It is suggested that the disagreement pointed out in theprevious benchmark studies may be due to inappropriate nuclear temperature used in the evaluation of natZr(n,2n) reaction cross section.

References[1]

I. Murata et al., J. Nucl. Sci. Technol., Sup. 2, p. 433-436 (2002)[2]

R. H. Johnson: ‘FORIST:Neutron Spectrum UnfoldingCode - Iterative Smoothing Technique’,PSR-92, ORNL/RSIC (1975).

[3]

J. K. Dickens: ‘A Monte Carlo Based Computer Program to Determine a Scintillator Full Energy
Response to Neutron Detector for En Between 0.1 and 80 MeV:User's Manual and FORTRAN
Program Listing’, ORNL-6462 (1988).

[4]

J. F. Briesmeister, Ed.: “MCNP – A General Monte Carlo N-Particle Transport Code, Version 4C”,
LA-13709-M (2000).

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