Neutron Billiards: Direct measurement of the neutron-neutron scattering length at the YAGUAR reactor Bret Crawford March 21, 2007

Direct neutron-neutron scattering measurement of a nn (neutron-neutron scattering length) Experimental Goal –Make the first direct measurement of a nn (~strength of attraction between two neutrons) to a precision of 3% Motivation –Current indirect results for a nn are in conflict –Current lack of precision in a nn does not constrain theory

Scattering Length Defined in terms of the phase shift,  o, or the low-energy cross section Total cross section is combination of states but Pauli Exclusion prevents triplet state, so

pp vs. nn Is the strength of the strong interaction between two protons the same as between two neutrons? Experiment says No. How different are they? Can we test different theories by measuring this effect? p-pn-n

pp vs. nn: Charge Symmetry Breaking a pp = (-17.3 ± 0.8) fm a nn = (-18.5 ± 0.3) fm (  -d capture, n-d breakup) a nn = ( ± 0.40) fm (n-d breakup)  a CSB = (a pp – a nn ) Use  a CSB to test theory. But the magnitude and sign of  a CSB are uncertain! We need a direct measurement of a nn. Nagels et al. NUCL. PHY B 147 (1979) 189. Howell et al. PHYS LETT B 444 (1998) 252. González Trotter et al. PHYS REV LETT 83 (1999) Huhn et al. PHYS REV C 63 (2001)

Neutron Scattering – a way to investigate the strong force Many processes depend on the nature of the strong force Elastic scattering (deflection angle) Inelastic scattering (deflection angle, energy loss) Neutron capture (gamma ray emission) Fission (fission products) Reactions (reaction products) Target nuclei Neutron beam

Cross section We measure cross sections and then relate the cross section to more fundamental parameters (like scattering length) Units of area, like cross sectional area Represents probability of a particular process happening

pp vs. nn: Charge Symmetry Breaking a pp = (-17.3 ± 0.8) fm a nn = (-18.5 ± 0.3) fm (  -d capture, n-d breakup) a nn = ( ± 0.40) fm (n-d breakup)  a CSB = (a pp – a nn ) Use  a CSB to test theory. But the magnitude and sign of  a CSB are uncertain! We need a direct measurement of a nn. But there are NO neutron targets!! Nagels et al. NUCL. PHY B 147 (1979) 189. Howell et al. PHYS LETT B 444 (1998) 252. González Trotter et al. PHYS REV LETT 83 (1999) Huhn et al. PHYS REV C 63 (2001)

No Beam on Target so Beam on Beam Chances of collision are very small unless we have very, very intense beams (flux~10 18 neutrons/cm 2 /s).

Where can you find lots of free neutrons?

Where can you find lots of free neutrons? …how about a secret city in Russia? Snezhinsk (Chelyabinsk-70) has got ‘em!

YAGUAR Reactor All-Russian Research Institute of Technical Physics Snezhinsk, Russia

ISINN International Seminar on Interactions of Neutrons with Nuclei Frank Laboratory of Neutron Physics Joint Institute for Nuclear Research Dubna, Russia Experiment at YAGUAR first proposed at ISINN-8 (2000)

YAGUAR Reactor Pulsed reactor with high instantaneous flux Annular design with open through-channel (nn-cavity) 90% enriched 235 U-salt/water solution Energy per pulse – 30 MJ Pulse duration – 680  s Fluency – 1.7x10 15 /cm 2 Flux – 1x10 18 /cm 2 /s Neutron density – 1x10 13 /cm 3

The Experiment Polyethylene moderator inserted in to through channel (thermal neutrons) a nn can be found by relating the number of collisions to the number of neutrons in the cavity during the pulse Goal – count the number of n-n collisions by counting ONLY scattered neutrons All other neutrons MUST be stopped before the detector –Collimators, absorbers, sheilding Shielding detector absorber Reactor with Moderator sleeve

Shielding detector absorber Reactor with Moderator sleeve Count = 1

Shielding detector absorber Reactor with Moderator sleeve Count = 0

Shielding detector absorber Reactor with Moderator sleeve Count = 0

Shielding detector absorber Reactor with Moderator sleeve Count = 1

Shielding detector absorber Reactor with Moderator sleeve Count = 1

Shielding detector absorber Reactor with Moderator sleeve Count = 1

Shielding detector absorber Reactor with Moderator sleeve Count = 1

Shielding detector absorber Reactor with Moderator sleeve Count = 1

Shielding detector absorber Reactor with Moderator sleeve Count = 1

Shielding detector absorber Reactor with Moderator sleeve Count = 1

Shielding detector absorber Reactor with Moderator sleeve Count = 2

Shielding detector absorber Reactor with Moderator sleeve Count = 3

Shielding detector absorber Reactor with Moderator sleeve Count = 3

Shielding detector absorber Reactor with Moderator sleeve Count = 3

Shielding detector absorber Reactor with Moderator sleeve Count = 3

Shielding detector absorber Reactor with Moderator sleeve Count = 4

Shielding detector absorber Reactor with Moderator sleeve Count = 4

Shielding detector absorber Reactor with Moderator sleeve Count = 4

Shielding detector absorber Reactor with Moderator sleeve Count = 5

Shielding detector absorber Reactor with Moderator sleeve Count = 5

Shielding detector absorber Reactor with Moderator sleeve Count = 5

Shielding detector absorber Reactor with Moderator sleeve Count = 5

Shielding detector absorber Reactor with Moderator sleeve Count = 6

Shielding detector absorber Reactor with Moderator sleeve Count = 6

Shielding detector absorber Reactor with Moderator sleeve Count = 6

Shielding detector absorber Reactor with Moderator sleeve Count = 7

Shielding detector absorber Reactor with Moderator sleeve Count = 7

Shielding detector absorber Reactor with Moderator sleeve Count = 7

Shielding detector absorber Reactor with Moderator sleeve Count = 7

Shielding detector absorber Reactor with Moderator sleeve Count = 8

Shielding detector absorber Reactor with Moderator sleeve Count = 8

Shielding detector absorber Reactor with Moderator sleeve Count = 8

Shielding detector absorber Reactor with Moderator sleeve Count = 9

Shielding detector absorber Reactor with Moderator sleeve Count = 9

Shielding detector absorber Reactor with Moderator sleeve Count = 10

The Experiment Neutron collisions take place in reactor through-channel Neutrons are detected 12 m below reactor Time of flight determines neutron energy  nn determined from detector counts and measured average neutron density Expect ~150 counts/pulse ~30 days of pulses should achieve required statistics

To Do… Vacuum system, shielding, collimation (JINR, ARRITP, TUNL) Neutron detectors (JINR) Data acquisition electronics (JINR, ARRITP, TUNL) Computer modeling –Characteristics of neutron field (GC) –Detector count rate sensitivity to neutron field characteristics (GC) –Neutron background (JINR, ARRITP) Background Test Experiment (JINR, ARRITP)

Neutron Background Sources of background Thermals direct from moderator sleeve –Collimation, neutron absorbers Wall scattered thermals –Collimation, neutron absorbers Backscattered neutrons –Long reverse flight path, 10 B absorber Scattering from residual gas –Pressure <10 -6 Torr Initial fast neutrons –TOF and thick shielding Delayed fast neutrons –Thick Shielding

Fast vs. Thermal TOF spectra

“Back Wall” Background

MCNP modeling of neutron background Neutron speed Source of background Number of neutrons per pulse Fast (>0.5eV) Initial and delayed ~10 Thermal (<0.5eV) Back wall~10 Collimators/walls<10 Residual gasP(H 2 )~10 -7 <1 P(N 2 )~10 -6 <1 Total20—40 A. Yu. Muzichka, et al., NIM-A 2007 (accepted for publication).

Background Modeling Tests Neutron flux measured as a function of depth in underground channel. Neutron flux modeled with MCNP Thermal neutron flux agrees with model ( 3 He ionization detectors) Fast neutron flux also agrees with modeling

Thermal Neutron vs. depth Open circles = measured Closed circles = modeled

Fast Neutrons vs. depth Open circles = measured Closed circles = modeled

Detector Count Rates and the Need for Modeling Detector Counts avg density anisotropy factor avg relative velocity effective solid angle MCNP and Analytic modeling Spatial, angular, energy, time distributions modeled & measured modeled modeled & measured

MCNP Modeling of Neutron Field Model YAGUAR reactor core with moderator sleeve Determine Neutron Field Distributions in through-channel Reactor geometry for MCNP Iron vessel 235 U solution Polyethylene moderator Side view Top view

MCNP Modeling of Neutron Field Spatial DistributionAngular Distribution* cos(  z/L a ) cos(  ) + A cos 2 (  ); A=0 *Amaldi and Fermi, PHYS REV 50 (1936) <  <  3

MCNP Modeling of Neutron Field Energy Distribution Maxwellian (E 0 =26 meV) with epithermal tail (1/E)

Geometry for Analytic Calculations Neutrons from source points Q 1 and Q 2 collide at point field point P Calculate neutron density, collision rate, detector count rate

Collision Rate Expression Nine-dimensional integral that depends on geometry and velocity distribution of neutrons No analytic solution…numerically integrate on computer.

Numerical Calculation – PZSIM.f90 Choose collision point, source points, velocities Calculate differential collision rate (big integral) Simulate isotropic scattering in CM frame Transform neutron velocities back to LAB frame Follow neutron trajectories Sum differential collision rate for 4  and detected neutrons Sum differential collision rate in velocity and time bins to create spectra

Collision Rate vs. position

Velocity Spectrum How does velocity spectrum change after collisions?

Detector Time-of-Flight Spectrum ~10 12 simulated collisions 4  spectrum scaled by  eff Very little effect from scattering anisotropy

Modeling Results Anisotropy factor Effective Solid Angle of 4  Average Relative Velocity Ideal Max., isotropic gas YAGUAR pure Max. YAGUAR Max.+Tail

Status Shaft holes in floor and ceiling completed Vacuum pipes tested Building collimation system Preparing for run this calendar year

Vacuum testing of upper section of neutron channel.

Summary nn-scattering experiment at the YAGUAR reactor is in final construction phase. Background modeling indicates possibility of keeping background from all sources to ~20%. Measurements of neutrons in the underground channel confirm models for thermal neutron background. Modeling of neutron field and nn-scattering kinematics allows accurate extraction of scattering cross section from detector counts. Time dependence of nn-scattering kinematics has been studied already in more detail this summer.

Geometry for Analytic Calculations Neutrons from source points Q 1 and Q 2 collide at point field point P Calculate neutron density, collision rate, detector count rate

Time-of-Flight Spectrum Pure Maxwellian flux vs. realistic flux (Maxwellian plus epithermal tail) before and after scattering

Duke/TUNL NCSU/TUNL Gettysburg College JINR (Dubna) ARRITP (Snezhinsk) Direct Investigation Of a nn Association (DIANNA)

The Atom Electrostatic attraction between electrons and protons holds electrons in orbit Electrostatic repulsion between protons tries to push apart nucleus (several pounds of force!!) Nuclear Strong Force binds protons and neutrons to form stable nucleus Electrons (~ kg, negative charge) in orbits far from nucleus Nucleus contains protons (~ kg, positive charge) and neutrons (~ kg, no charge)

Cross section We measure cross sections and then relate the cross section to more fundamental parameters (like scattering length) Units of area, like cross sectional area Represents probability of a particular process happening Example: Attenuation of beam through target material x target n = target # density (1/cm 3 )  = cross section (cm 2 ) x = distance (cm)