Direct Measurement of Neutron-Neutron Scattering

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 An attractive way to solve the fundamental problem of best steady-state reactors. The situation can be much bet- charge symmetry of the nuclear force is comparison of ter at pulsed neutron sources, where the thermal neutron the values for the neutron-neutron a nn and proton-proton flux density is  1  10 17 /cm2 s or higher. Increasing the a pp scattering lengths. While the length a pp has the well flux improves dramatically the ratio of the nn-effect to   established value of  17  3 0  005  stat 0  4  syst fm background, and nn-measurements become feasible. obtained in the pp-scattering experiments, determination Here we describe the DIANNA approach to the direct of the length a nn has encountered difficulties. Recent nn-scattering measurement which is proposed [10] to be 10% discrepancies [1, 2] in the results of indirect performed at the Russian pulsed reactor YAGUAR. 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 MEASUREMENT OF THE Direct measurements have been proposed for pulsed NN-SCATTERING LENGTH reactors [4, 5, 6], for accelerators [7], for steady-state re- actors [8], and even for underground nuclear explosions [9]. However, no experiment has been performed. The The nn-cross section and scattering length main idea was to use neutron collisions in a powerful beam and to detect the scattered neutrons externally. The In effective-range theory, the singlet spin scattering cross “target” and the “beam” then are neutrons produced by section σs is defined by the scattering length a nn , the the same neutron source, and therefore the nn-scattering effective range r 0 , and the neutron wave number k as intensity is proportional to the square of the neutron flux 4π density, while the background due to scattering on walls σs 4π a2nn at k  0 (1)  1  ann  k2 r0  2 2  k2 or on residual gas depends linearly on the flux density. 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 : 1  3 1 σnn σs σ σs π a2nn  (2) 4 4 t 4 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 sec- tion σnn is equal to one fourth of the “theoretical” singlet cross section σs . Eq. (2) determines directly the scatter- ing length a nn from the measured σ nn . The relative un- certainty for a nn is one half of that for σ nn . Scheme of the nn-experiment at YAGUAR FIGURE 1. Setup for the nn-scattering experiment. 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 1 reduces the neutron scattering from the back wall into ms (FWHM for the case of an inserted thermal neutron the detector, while the time-of-flight measurement addi- converter), about 10 18 fast neutrons with an average en- tionally separates (due to the difference in flight paths) ergy of 0.9 MeV are generated in a V =40-liter volume of the remaining back-wall background from the nn signal. the liquid active core. The solute contains 465 g per liter The shields 2 serve to screen the detector from epither- of uranium (90% 235 U) and 5 g per liter of cadmium. The mal and fast neutrons. critical height is about 39 cm. The body of the reactor has a cylindrical space of 12-cm diameter for the experimen- tal channel. Analytical and Monte Carlo calculations After collisions in the reactor channel, neutrons will reach the detector placed at about 12 m from the channel If the geometry of the nn-cavity is fixed and the neutron central plane, and will be measured by the time-of-flight field and velocities are known at each point of the cav- (TOF) method. At this flight path the detector effective ity, then the Eq. (3) constants c av and v0 can be calcu- solid angle Ωe f f is about 5x10 6 . The detector counts lated. We consider the cylindrical nn-cavity surface as ND per pulse (integrated over the thermal part of the TOF a source of thermal neutrons with characteristics pro- spectrum) are related to σ nn and neutron flux density Φ av vided by Monte-Carlo modeling of the reactor and mod- by erator. We assume that the neutron speeds are purely Maxwellian, then v o is the most probable velocity. Since Φ2av the YAGUAR pulse is much longer than the neutron ND 2cav σnn TV Ωe f f  counts  pulse  (3) moderation time, we neglect a possible small correction vo due to a non-stationary stage of the neutron moderation This relation is discussed in the next subsection. process. One possible arrangement for the experiment is shown The nn-cavity is an evacuated volume inside the neu- schematically in Fig. 1. The reactor active core 3 is tron moderator in the through-channel. Fig. 2 shows the placed at 2 m above the floor level. The polyethylene geometry of the nn-cavity with two source points Q 1 and moderator 4 is inserted in the reactor channel. An evac- Q2 at distances d1 and d2 from the cavity point P, respec- uated tube contains a collimation system 5 that is de- tively, where two neutrons collide. Due to the cylindri- signed to screen the neutron source from the detector and cal symmetry of the problem, it is suffficient to consider to eliminate background due to neutrons scattered from the cavity points on the y-axis. The density of neutrons the walls. The neutron detector 6 is placed at about 12 m at the point P produced by the surface element at Q 1 is from the above the center of the moderator. An absorber 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 1To the best of our knowledge, this distinction between σnn and σs angle δ1 to the normal. The source density varies with was not made in all earlier proposals, where σnn 4π a2nn was used.
262  height and radius of the nn cavity for different A values. The characteristic cos 2  π z  L of the nn-production has z 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 P r pulse. d1 z y δ1 Q1 φ1 z1 x FIRST EXPERIMENTAL RESULTS z2 d2 Neutron activation measurements were performed [14] δ2 φ2 L/2 to study the neutron fluxes formed by polyethylene con- R Q2 verters inside the through-channel. The converters were fabricated as hollow cylinders of 40-cm length and 12.0- cm 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. FIGURE 2. The cylindrical nn-cavity geometry. 4 3.5 height z along the moderator as S cos  π z  L , where S 3 is the source density at the midpoint of the cylinder, and 2.5 the parameter L 48  5 cm is found from Monte-Carlo 2 F simulation of the neutron transport in the reactor core 1.5 and moderator. The angular distribution of neutron emis- sion from the moderator is the Fermi angular distribution  2   1  2A  3 cos δ  1  Acos δ , where A 3 for an
0.5 1 external surface of a slab moderator. However, from the 0 0 1 2 3 4 5 MCNP-4b code [12] modeling we find for our internal t surface that the same neutron is re-emitted from the sur- face multiple times leading to A 0. In analytical cal- FIGURE 3. Experimental and calculated flux results. culations, we leave A as a free parameter and study the sensitivity of our results to its value and to the geometri- cal parameters L and R. Fig. 3 [14] shows the thermal neutron fluency F We find the total production rate in the z- direction as (1013 /cm2 /MJ) versus the polyethylene converter thick-    z     z   d d ND 2 2 2π 1 2 2π 1 2  L  R 2 S2   L dφ  L dφ1 1 2 rdr dz σnn T Ωe f f 1  2A  3   2 0 1 2 0 1 2  dv dv v  v  v  cos θ M  v  v M  v  v ψ γ  θ 1 2 rel 1 2 12 1 0 2 0 12  cos π z  L   cos π z  L   (4) cos δ  1  A cos δ 1 cos δ  1  Acos δ 1 2 2 1 2  d  R 1 2  d  R 2 2  where M  v vo is a normalized Maxwellian distribution, ness t (cm). The fluency is defined as the number of neu- trons per cm2 , per 1-MJ pulse. The points with error bars  and where the transformation from the CM to the LAB system is accomplished through the Jacobian ψ γ θ12 are the experimental results, while the circles represent [6]. Here γ is the angle between the CM velocity vec- our Monte-Carlo calculations. We conclude that the 3-cm tor and the direction to the detector, θ 12 is the angle be- thick converter provides for the 30-MJ pulse an instan- tween the velocity vectors of two colliding neutrons, and taneous value of 1  1  10 18 /cm2 s for the thermal neutron   vrel  v1 v2 cos θ12 is the relative speed of the colliding neutrons. Calculating Φ av [13] in a similar manner and flux density in the central plane. The measured height distribution of the activation behaves as cos  π z  L , and applying Eq.(3), one determines the constant c av . yields L 48  0 cm, which agrees with the calculations. 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