Direct Measurement of Neutron-Neutron Scattering
E. I. Sharapov , C. D. Bowman† , B. E. Crawford , W. I. Furman , C. R. Howell‡ ,
B. G. Levakov§ , V. I. Litvin§ , W. I. Lychagin , A. E. Lyzhin§ , E. P. Magda§ ,
G. E. Mitchell¶ , G. V. Muzichka , G. V. Nekhaev , Yu. V. Safronov ,
V. N. Shvetsov , S. L. Stephenson , A. V. Strelkov and W. Tornow‡
Joint Institute for Nuclear Research, 141980 Dubna, Russia
ADNA
Corporation, 1045 Los Pueblos, Los Alamos NM, USA 87544
Gettysburg College, Box 405, Gettysburg PA, USA 17325
‡
Duke University and Triangle Universities Nuclear Laboratory, Durham NC, USA 27708-0308
§
Russian Federal Nuclear Center All-Russian Research Institute of Technical Physics,
P.O. Box 245, 456770 Snezhinsk, Russia
¶
North Carolina State University, Raleigh NC, USA 27695-8202 and
Triangle Universities Nuclear Laboratory, Durham NC, USA 27708-0308
†
Abstract. In order to resolve long-standing discrepancies in indirect measurements of the neutron-neutron scattering length
ann and contribute to solving the problem of the charge symmetry of the nuclear force, the collaboration DIANNA (Direct
Investigation of ann Association) plans to measure the neutron-neutron scattering cross section σnn . The key issue of our
approach is the use of the through-channel in the Russia reactor YAGUAR with a peak neutron flux of 1018 /cm2 /s. The
proposed experimental setup is described. Results of calculations are presented to connect σnn with the nn-collision detector
count rate and the neutron flux density in the reactor channel. Measurements of the thermal neutron fields inside polyethylene
converters show excellent prospects for the realization of the direct nn-experiment.
INTRODUCTION
The densities of such neutron targets are extremely small,
e.g., 1010 /cm3 for a flux density of 2 5 10 15 /cm2 s at the
best steady-state reactors. The situation can be much better at pulsed neutron sources, where the thermal neutron
flux density is 1 10 17 /cm2 s or higher. Increasing the
flux improves dramatically the ratio of the nn-effect to
background, and nn-measurements become feasible.
Here we describe the DIANNA approach to the direct
nn-scattering measurement which is proposed [10] to be
performed at the Russian pulsed reactor YAGUAR.
An attractive way to solve the fundamental problem of
charge symmetry of the nuclear force is comparison of
the values for the neutron-neutron a nn and proton-proton
a pp scattering lengths. While the length a pp has the well
established value of 17 3 0 005 stat 0 4 syst fm
obtained in the pp-scattering experiments, determination
of the length a nn has encountered difficulties. Recent
10% discrepancies [1, 2] in the results of indirect
measurements of a nn , which prevent comparison with the
quark approach [3] to the symmetry breaking, provide an
additional motivation for direct measurements of a nn .
Direct measurements have been proposed for pulsed
reactors [4, 5, 6], for accelerators [7], for steady-state reactors [8], and even for underground nuclear explosions
[9]. However, no experiment has been performed. The
main idea was to use neutron collisions in a powerful
beam and to detect the scattered neutrons externally. The
“target” and the “beam” then are neutrons produced by
the same neutron source, and therefore the nn-scattering
intensity is proportional to the square of the neutron flux
density, while the background due to scattering on walls
or on residual gas depends linearly on the flux density.
DIRECT MEASUREMENT OF THE
NN-SCATTERING LENGTH
The nn-cross section and scattering length
In effective-range theory, the singlet spin scattering cross
section σs is defined by the scattering length a nn , the
effective range r 0 , and the neutron wave number k as
σs 4π
1 ann k2 r0 2 2 k2
4π a2nn at k 0
(1)
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
261
For thermal neutrons (with typical energy of 0.025 eV),
the r0 0 approximation works well. The cross section
σnn measured with unpolarized neutrons is a statistical
sum of the singlet σ s and triplet σt cross sections1 :
σnn 1 3
σs
σ 4
4 t
1
σs π a2nn 4
(2)
Since the Pauli exclusion principle for identical particles
forbids the interaction of two neutrons in the triplet state,
σt is expected to be zero, and the measured cross section σnn is equal to one fourth of the “theoretical” singlet
cross section σs . Eq. (2) determines directly the scattering length a nn from the measured σ nn . The relative uncertainty for a nn is one half of that for σ nn .
Scheme of the nn-experiment at YAGUAR
FIGURE 1.
The reactor YAGUAR (VNIITF, Snezhinsk, Russia) [11],
can produce two bursts per day with an energy release of
up to 33 MJ per burst. During the pulse duration T =0.90
ms (FWHM for the case of an inserted thermal neutron
converter), about 10 18 fast neutrons with an average energy of 0.9 MeV are generated in a V =40-liter volume of
the liquid active core. The solute contains 465 g per liter
of uranium (90% 235 U) and 5 g per liter of cadmium. The
critical height is about 39 cm. The body of the reactor has
a cylindrical space of 12-cm diameter for the experimental channel.
After collisions in the reactor channel, neutrons will
reach the detector placed at about 12 m from the channel
central plane, and will be measured by the time-of-flight
(TOF) method. At this flight path the detector effective
solid angle Ωe f f is about 5x10 6 . The detector counts
ND per pulse (integrated over the thermal part of the TOF
spectrum) are related to σ nn and neutron flux density Φ av
by
ND 2cav
Φ2av
σnn TV Ωe f f counts pulse vo
Setup for the nn-scattering experiment.
1 reduces the neutron scattering from the back wall into
the detector, while the time-of-flight measurement additionally separates (due to the difference in flight paths)
the remaining back-wall background from the nn signal.
The shields 2 serve to screen the detector from epithermal and fast neutrons.
Analytical and Monte Carlo calculations
If the geometry of the nn-cavity is fixed and the neutron
field and velocities are known at each point of the cavity, then the Eq. (3) constants c av and v0 can be calculated. We consider the cylindrical nn-cavity surface as
a source of thermal neutrons with characteristics provided by Monte-Carlo modeling of the reactor and moderator. We assume that the neutron speeds are purely
Maxwellian, then v o is the most probable velocity. Since
the YAGUAR pulse is much longer than the neutron
moderation time, we neglect a possible small correction
due to a non-stationary stage of the neutron moderation
process.
The nn-cavity is an evacuated volume inside the neutron moderator in the through-channel. Fig. 2 shows the
geometry of the nn-cavity with two source points Q 1 and
Q2 at distances d1 and d2 from the cavity point P, respectively, where two neutrons collide. Due to the cylindrical symmetry of the problem, it is suffficient to consider
the cavity points on the y-axis. The density of neutrons
at the point P produced by the surface element at Q 1 is
proportional to the surface element ds 1 Rdφ1 dz, to the
density of neutrons at the surface, and to the probability
of neutron emission from the moderator surface with an
angle δ1 to the normal. The source density varies with
(3)
This relation is discussed in the next subsection.
One possible arrangement for the experiment is shown
schematically in Fig. 1. The reactor active core 3 is
placed at 2 m above the floor level. The polyethylene
moderator 4 is inserted in the reactor channel. An evacuated tube contains a collimation system 5 that is designed to screen the neutron source from the detector and
to eliminate background due to neutrons scattered from
the walls. The neutron detector 6 is placed at about 12 m
from the above the center of the moderator. An absorber
To the best of our knowledge, this distinction between σnn and σs
was not made in all earlier proposals, where σnn 4π a2nn was used.
1
262
height and radius of the nn cavity for different A values.
The characteristic cos 2 π z L of the nn-production has
less than 10% dependence on A in the range of A values
considered. For the YAGUAR
case of A 0, the calcu
lated value is cav 0 83 0 01 and ND 170 counts per
pulse.
z
P
r
d1
δ1
y
z
Q1
φ1
FIRST EXPERIMENTAL RESULTS
z1
x
z2
d2
δ2
Q2
Neutron activation measurements were performed [14]
to study the neutron fluxes formed by polyethylene converters inside the through-channel. The converters were
fabricated as hollow cylinders of 40-cm length and 12.0cm outer diameter, while the thickness was varied. The
activation detectors for the absolute flux measurements
were Au- and Cu-foils placed at the central plane.
L/2
φ2
R
FIGURE 2. The cylindrical nn-cavity geometry.
4
3.5
height z along the moderator as S cos π z L , where S
is the source density at the midpoint of the cylinder, and
the parameter L 48 5 cm is found from Monte-Carlo
simulation of the neutron transport in the reactor core
and moderator. The angular distribution of neutron emission from the moderator is the Fermi angular distribution
3 for an
2 1 2A 3 cos δ 1 Acos δ , where A external surface of a slab moderator. However, from the
MCNP-4b code [12] modeling we find for our internal
surface that the same neutron is re-emitted from the surface multiple times leading to A 0. In analytical calculations, we leave A as a free parameter and study the
sensitivity of our results to its value and to the geometrical parameters L and R.
We find the total production rate in the z- direction as
3
2.5
F
2
1.5
ND
σnn T Ωe f f
1
2 rel
1
1
rdr
dz
0
0
1
2
3
4
5
t
FIGURE 3.
Experimental and calculated flux results.
Fig. 3 [14] shows the thermal neutron fluency F
(1013 /cm2 /MJ) versus the polyethylene converter thick-
2π
0
2
12
1
2
1 2
dφ1
0
1
1
2
2
1 2A 3
0.5
z z
d
dφ
d
L
L
dv
dv v v v cos θ M v v M v v ψ γ θ cos δ 1 A cos δ cos δ 1 Acos δ cos π z L cos π z L (4)
d R
d R
L R 2 S2
1
2π
1
1 2
0
2
12
0
2
1 2
2
2
1 2
2
1
2
2
2
ness t (cm). The fluency is defined as the number of neutrons per cm2 , per 1-MJ pulse. The points with error bars
are the experimental results, while the circles represent
our Monte-Carlo calculations. We conclude that the 3-cm
thick converter provides for the 30-MJ pulse an instantaneous value of 1 1 10 18 /cm2 s for the thermal neutron
flux density in the central plane. The measured height
distribution of the activation behaves as cos π z L , and
yields L 48 0 cm, which agrees with the calculations.
From the Monte Carlo modeling, the neutron velocity
spectrum is expected to be predominantly Maxwellian
where M v vo is a normalized Maxwellian distribution,
and where the transformation from the CM to the LAB
system is accomplished through the Jacobian ψ γ θ12
[6]. Here γ is the angle between the CM velocity vector and the direction to the detector, θ 12 is the angle between the velocity vectors of two colliding neutrons, and
vrel v1 v2 cos θ12 is the relative speed of the colliding
neutrons. Calculating Φ av [13] in a similar manner and
applying Eq.(3), one determines the constant c av .
Monte-Carlo integration was used to obtain the neutron density and production rate as functions of the
263
REFERENCES
1
1.
F(E), eV -1
0.1
2.
3.
0.01
0.001
4.
0.0001
0.001
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E, eV
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10
FIGURE 4. Energy spectrum normalized to the peak value.
5.
6.
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7.
8.
9.
10.
CONCLUSION
The goal of the planned experiment is a study of the
charge symmetry of nuclear forces by performing a direct measurement of the nn-scattering length using the
pulsed reactor YAGUAR. Analytical calculations and
Monte-Carlo modeling show that a nn can be measured
with a total accuracy of 3%. This first nn-experiment
will be crucial for evaluating the prospects of obtaining
even better accuracy in direct measurements of a nn .
In the preliminary experiments at YAGUAR aimed at
optimizing the thermal neutron field inside the throughchannel, an instantaneous value of 1 1 10 18 /cm2 s was
obtained for the thermal neutron flux density. This suggests excellent prospects for the realization of the first
direct measurement of a nn .
11.
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ACKNOWLEDGMENTS
This work was supported in part by the Russia Foundation for Basic Research under grant No. 01-02-17181,
by the US Department of Energy, Office of High Energy and Nuclear Physics under grants Nos. DE-FG0297-ER41042 and DE-FG02-97-ER41033, and by the US
National Science Foundation through an International
Research Fellow Award No. 0107263.
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