Neutron Billiards: Direct measurement of the neutron-neutron scatteringlength at the YAGUAR reactor

Bret Crawford

March 21, 2007

Direct neutron-neutron scattering measurement of ann (neutron-neutron

scattering length)

• Experimental Goal– Make the first direct measurement of ann (~strength of

attraction between two neutrons) to a precision of 3%

• Motivation– Current indirect results for ann are in conflict

– Current lack of precision in ann does not constrain theory

Scattering Length

2

04lim nns

ka

ka o

knn

sinlim

0

0Defined 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

stsnn 4

1

4

3

4

1

2nnnn a

pp vs. nn

• Is the strength of the strong interaction between two protons the same as between two neutrons?

Experiment says No.Experiment says No.

• How different are they? • Can we test different theories by measuring this effect?

p-p n-n

pp vs. nn: Charge Symmetry Breaking

app = (-17.3 ± 0.8) fm

ann = (-18.5 ± 0.3) fm (-d capture, n-d breakup)

ann = (-16.27 ± 0.40) fm (n-d breakup)

aCSB = (app – ann)

Use aCSB to test theory. But the magnitude and sign of aCSB are uncertain!

We need a direct measurement of aWe need a direct measurement of annnn . .Nagels et al. Nagels et al. NUCL. PHY BNUCL. PHY B 147147 (1979) 189. (1979) 189.

Howell et al. Howell et al. PHYS LETT BPHYS LETT B 444444 (1998) 252. (1998) 252.

GonzGonzáález Trotter et al. lez Trotter et al. PHYS REV LETT PHYS REV LETT 8383 (1999) 3788. (1999) 3788.

Huhn et al. Huhn et al. PHYS REV C PHYS REV C 6363 (2001) 014003. (2001) 014003.

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 nucleiNeutron 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

224 cm1010barn10~ nn

pp vs. nn: Charge Symmetry Breaking

app = (-17.3 ± 0.8) fm

ann = (-18.5 ± 0.3) fm (-d capture, n-d breakup)

ann = (-16.27 ± 0.40) fm (n-d breakup)

aCSB = (app – ann)

Use aCSB to test theory. But the magnitude and sign of aCSB are uncertain!

We need a direct measurement of aWe need a direct measurement of annnn . .

But there are NO neutron targets!!But there are NO neutron targets!!Nagels et al. Nagels et al. NUCL. PHY BNUCL. PHY B 147147 (1979) 189. (1979) 189.

Howell et al. Howell et al. PHYS LETT BPHYS LETT B 444444 (1998) 252. (1998) 252.

GonzGonzáález Trotter et al. lez Trotter et al. PHYS REV LETT PHYS REV LETT 8383 (1999) 3788. (1999) 3788.

Huhn et al. Huhn et al. PHYS REV C PHYS REV C 6363 (2001) 014003. (2001) 014003.

No Beam on Targetso

Beam on Beam

Chances of collision are very small unless we have very, very intense beams

(flux~1018 neutrons/cm2/s).

Where can you find lots of free neutrons?

Where can you find lots of free neutrons?

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 ReactorAll-Russian Research Institute of Technical Physics

Snezhinsk, Russia

ISINNInternational 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 235U-salt/water solution

• Energy per pulse – 30 MJ• Pulse duration – 680s• Fluency – 1.7x1015 /cm2

• Flux – 1x1018 /cm2/s• Neutron density – 1x1013 /cm3

 

The Experiment• Polyethylene moderator

inserted in to through channel (thermal neutrons)

• ann 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

2n

nnnn

n

Na

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

TVvfnN relannD2

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, 10B 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 gas P(H2)~10-7 <1

P(N2)~10-6 <1

Total 20—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 (3He ionization detectors)

• Fast neutron flux also agrees with modeling

Thermal Neutron vs. depth

Open circles = measuredClosed circles = modeled

Fast Neutrons vs. depth

Open circles = measuredClosed 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 modelingSpatial, angular, energy, time distributions

TVvfnN relannD2

n

af

relv

modeled & measured modeledmodeledmodeled & measured

eff

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

235U solution

Polyethylenemoderator

Side view

Top view

MCNP Modeling of Neutron Field

Spatial Distribution Angular Distribution*

cos( z/La) cos() + A cos2(); A=0

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

1 - cos (delta)

Norm

alized tally/particle

y = 2 cos (delta)

*Amaldi and Fermi, PHYS REV 50 (1936) 899-928.

0 < < 3

MCNP Modeling of Neutron Field

Energy Distribution

Maxwellian (E0=26 meV) with epithermal tail (1/E)

Geometry for Analytic Calculations

• Neutrons from source points Q1 and Q2 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

21

21

22

02

21

21

12

01

02

01

2

000 L

zdd

L

zdddvdvddsinrdrR

R

col

22

21

212211

2

23

6oo vv

orelvv

o evv)cos,v,v(vevvAR

LS

LzcosRd

cosAcosLzcos

Rd

cosAcos22

2

2212

1

11 11

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

t (ms)

rD nn(t

)/ nn

(105 /s

/cm

2 /ms)

dete

ctor

coun

ts/m

s

0 2 4 6 8 100

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

0

10

20

30

40

50

60

70MT detMT 4 scaled

•~1012 simulated collisions

•4 spectrum scaled by eff

•Very little effect from scattering anisotropy

Modeling Results

• Anisotropy factor

• Effective Solid Angle

of 4

oorel v1.60vv

22• Average Relative Velocity

•Ideal Max., isotropic gas

•YAGUAR pure Max.

•YAGUAR Max.+Tail

orel v.v 731

orel 1.84vv

980.fa

610474 .eff

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 Q1 and Q2 collide at point field point P

• Calculate neutron density, collision rate, detector count rate

Time-of-Flight SpectrumPure Maxwellian flux vs. realistic flux (Maxwellian plus epithermal tail)

before and after scattering

t (ms)

r nn(t

)/ nn

(1010

/s/c

m2 /m

s)

dete

ctor

coun

ts/m

s

0 2 4 6 8 100

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

0

10

20

30

40

50

60

70

MT afterM afterMT beforeM before

Duke/TUNLNCSU/TUNLGettysburg College

JINR (Dubna)

ARRITP (Snezhinsk)

Direct Investigation

Of ann

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 (~10-30 kg, negative charge) in orbits far from nucleus

Nucleus contains protons (~10-27 kg, positive charge) and neutrons (~10-27 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

224 cm1010barn10~ nn

xno

toteNxN )(x

target

n = target # density (1/cm3) = cross section (cm2)x = distance (cm)