!"##$%&!'

( )

* '&+ , - .+ , / ))01 02)!))))20 !3)!0!4 5 !* )%) ))0)&)!)2&!- 6 27 &) !08 )24 0&)27 !92

))+ : , - !)&7 )0&003!)2 )* ) )!&&);"$29)))0'* )!* &)2)!&0)!<02)!<-#7 * 9!* * !2! = <)>8 )+ .02- &))!7 '24 = <&8 &>20 &)2

23!)))!&))))+ ,#928 0?))!! !7 * 0)0)0!!&2

?

Neutron Interferometry

1964 – Perfect crystal interferometer co-invented by Bonse and Hart for x-rays.1974 – First demonstration of a working neutron interferometer Rauch, Treimer and Bonse.1975 – Gravitationally induced quantum interferference by Collela, Overhauser and Werner.1975-2005 – Many experiments at Missouri University Research Reactor, ILL Grenoble, France, MIT, Atominstitut Vienna, Austria, and Hahn Meitner Institute, Berlin, and NIST.

Neutron Interferometer and Optics Facility

Vibration Isolation = 10-7g

Translation = Less than a µm

Rotation = Less than a mrad

Temperature = 0.1 C

Cold Neutron Guide Hall

Weak Interaction Physics

Neutron Interferometry

Gravitationally Induced Quantum Interference

Interferometer

Neutron

Beam

Sample

Phase Shifter

Detectors

H-beam

O-beam

δ

Sample

Top View

Neutron wave functioncoherently split byBragg diffraction.

3Hedetectors

δ

Phase Shifter

∆ε

H-beam

O-beampath I

path II

Perfect Crystal Interferometer

Cut from a single ingot of > 17 MΩ silicon.Three to four blades are machined and left attached to a common silicon base to maintain the perfect registry of all atoms in the crystal.The NIST crystals are cut such that the silicon (111) lattice planes are are perpendicular to the surfaces of the blades.Each crystal blade acts as a beam splitter in the transmission Laue-Bragg reflection geometry.

Selected Neutron Interferometry and Optics Experiments

• Precision measuremet of Si-scattering length: bSi=(4.1507±0.0002)fm–(HMI, NIST, NPI of CAS, Missouri, LANL)

• Double slit interference experiment – (University of Vienna, NIST)

• Phase Contrast Imaging ––(University of Melbourne, NIST, Missouri)

• Quantum entanglement in H2O/D2O mixtures–(Missouri, NIST, LANL, HMI-Berlin)

• 4 rotation symmetry –(HMI-Berlin, Missouri, NIST, LANL)

• n-D, n-p, n-3He scattering lengths–(Missouri, NIST, N. Carolina-Wilmington, Indiana, LANL)

• Reciprocal Space Imaging–(MIT, NIST)

• n-e scattering - neutron charge radius –(Tulane ,Missouri, NIST, N. Carolina-Wilmington)

• Neutron Fourier spectroscopy –(NIST, Indiana, Vienna, MIT)

• Spin-dependent neutron-3He scattering amplitude –(Tulane ,Indiana, NIST, N. Carolina-Wilmington)

• Tests of decoherence for quantum information –(MIT, NIST)

• Gravity experiment with floating interferometer–(Indiana, NIST, Tulane)

P recision Neut ron Int er feromet r ic Mea su rement of the ndCohere nt Neut ro n Scat ter ingLeng th and Con sequences for Models of T hree-Nucleon For ces

T. C. Black , P. R. Huffman, D. L. Jacobson , W. M. Snow, K. Schoen, M. Arif, H. Kaiser,S. K. Lamoreau x, and S. A. Werner

Un iversity of Nor th Ca rolina at Wilmington, Wilmington, Nor th Ca rolina 28403-3297Nationa l Institute of Standa rds a nd Technolog y, Ga ithersburg, Ma r yla nd 20899-8461

Indiana University/ IUCF, Bloomington, India na 47408Universit y of Missour i–Colu mbia , Colu mbia , Missour i 65211

Los Ala mos Nationa l Labor at ory, Los Ala mos, New Mexico 87545(Received 19 November 2002; published 16 May 2003)

P H YS ICA L R E VI E W L E T T E RS week end ing16 MAY 2003VOLU ME 90, NUMBER 19

Precision neutr on interfer ometric measur ement of the n-3He coher ent neutr on scattering length

P. R. Huffman,1,2 D. L. Jacobson,2 K. Schoen,3 M. Arif,2 T. C. Black,4 W. M. Snow,5 and S. A. Werner3,2

1North Carolina State University, Raleigh, North Carolina 27695, USA2National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8461, USA

3University of Missouri-Columbia, Columbia, Missouri 65211, USA4University of North Carolina at Wilmington, Wilmington, North Carolina 28403-3297, USA

5Indiana University/IUCF, Bloomington, Indiana 47408, USA(Received 10 March 2004; published 15 July 2004)

PHYSICAL REVIEW C 70, 014004 (2004)

Pr ecision neutr on interfer ometric measur ements and updated evaluationsof the n -p and n -d coher ent neutr on scattering lengths

K. SchoenUniversity of Missouri-Columbia, Columbia, Missouri 65211

D. L. Jacobson, M. Arif, and P. R. HuffmanNational Institute of Standards and Technology, Gaithersburg, Maryland 20899-8461

T. C. BlackUniversity of North Carolina at Wilmington, Wilmington, North Carolina 28403-3297

W. M. SnowIndiana University/IUCF, Bloomington, Indiana 47408

S. K. LamoreauxLos Alamos National Laboratory, Los Alamos, New Mexico87545

H. KaiserUniversity of Missouri-Columbia, Columbia, Missouri 65211

S. A. WernerUniversity of Missouri-Columbia, Columbia, Missouri 65211

and National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8461~Received 10 December 2002; published 29 April 2003!

PHYSICAL REVIEW C 67, 044005 ~2003!

∆φ = 2π (1−n)λ

D

Phase ShiftOutgoingwave front

Incidentwave front

optV

∆φ

Sample

λ λλ/n

λ λλ

D

Re

Ψ

Re

Ψ

path I

path II

Phase shifts are measured by rotating a quartz plate called a phase flag tracing out an interfereogram

D → D(δ) so that ∆φ ∝ δThe data is fitted to a sinusoid allowing the phase shift due to the sample to be determined. This is done back to back within a 40 minute period to allow the systematic overall time dependent phase drift to be removed.

λNbD=

Sample

Top View

3Hedetectors

δ

Phase Flag

H-beam

O-beampath I

path II

∆φ

∆φ

n-d scattering length

doublet

quartet

neutron (s=1/2) deuteron (I=1)

If both the sample and the neutron are unpolarized.

Gas Phase Shift Cell

-3 -2 -1 0 1 2 30

100

200

300

400

500

600

700

800cell outcell in + D2gas

δ (deg)

-6.28 -3.14 0.00 3.14 6.28

∆φ (rad)

∆φ

Neutron Deuteron Scattering Length Measurements

1950 1960 1970 1980 1990 20006.4

6.5

6.6

6.7

6.8

4.3

4.4

4.5

Year of Measurement

Many MethodsBragg DiffractionChristiansen filterTransmissionGravity reflectometryInterferometryCurrent weighted average1st standard uncertainty

D2

b nd

(fm

)

a nd

(fm

)

Measured at NIST

bnd = 6.6649+/- 0.0040 fm

New World Average

bnd = 6.6683+/- 0.0030 fm

bdoublet = (0.96 ± 0.02) fm

Theory deuteron

0.939AV18+UR3BF

0.863AV14+BR3NF

6.6649.5570.879AV14+TM3NF

6.9749.5691.7835AV14

6.9789.571.794AV14

6.7939.6631.053MTI-III

6.799.6451.065MTI-III

6.609.4050.984Yamaguchi

6.679.570.855AV14+BR3NF

6.639.450.99RSC+TM3NF

6.3799.5670.0015AF14+BR3NF

6.9729.5581.8AV14

6.5059.4620.5895RSC+TM3NF

7.0629.4532.28RSC

0.9RSC-5

7.079.6151.98SSCC

7.0559.572.025AV14

2.64RSC-5

6.799.661.05MT I-II

3.249.66-9.6Exponential

5.349.585-3.15Yukawa

b(fm)

b(quartet)

b(doublet)

Potential Model

b = (1/3) bdoublet + (2/3)bquartet

bquartet(theory) = (9.52 ± 0.01) fm

b(exp) = (6.665 ± 0.004) fm

bdoublet = (0.96 ± 0.02) fm

Combining theory with experiment gives:

Neutron Proton Scattering Length Measurement

Year of Measurement1950 1960 1970 1980 1990 2000

-3.80

-3.76

-3.72

-3.68

-3.64

-1.90

-1.88

-1.86

-1.84

-1.82

TransmissionTotal reflectionGravity reflectometryInterferometryCurrent weighted average1st standard uncertainty

b np

(fm

)

a np

(fm

)

H2

Measured at NIST

bnp = -3.7384+/-0.0020 fm

New World Average

bnp = -3.7405+/-0.0009 fm

Neutron Helium-3 Scattering Length Measurements

Measured at NIST

b = 5.8572+/- 0.0072 fm

New World Average

b = 5.8530+/- 0.0070 fm

1970 1980 1990 20005.0

5.5

6.0

6.5

7.0

4.0

4.5

5.0

3He

b(f

m)

Year of Measurement

Total ReflectionInterferometryTransmissionWeighted Average

a(f

m)

Prior to Measurement at NIST

b = 5.74 +/- 0.04 fm

Lowered uncertainty by a factor of 6

It is interesting to combine this result with the recent measurement by Zimmer, et al* of the bound

incoherent scattering length:

fm )020.0365.2( ±−=ib

fm )007.0854.5( ±=cohb

to extract the singlet and triplet values of the bound scattering lengths

fm )017.0488.4(

fm )027.0949.9(

1

0

±=±=

b

b

corresponding to free nuclear scattering lengths of

fm )013.0363.3(

fm )020.0456.7(

1

0

±=±=

a

a

*O. Zimmer, G. Ehlers, B. Farago, H. Humboldt, W. Ketter, and R. Scherm, EPJdirect A1, 1 (2002).

Summary

Thanks to ...

PostdocsWangchun Chen (Indiana)Brian Fisher (Tulane)Dan Hussey (NIST/NRC)H. Pieter Mumm (NIST/NRC)

Graduate StudentsChris Bass (Indiana)Rob Cooper (Michigan)MikeHuber (Tulane)Da Luo (Indiana)Dmitri Pushin (MIT)Carroll Trull (Tulane)Liang Yang (Harvard)

Neutron Interaction and Dosimetry Scientific StaffMuhammad Arif (group leader)Scott DeweyTom GentileDavid GilliamCraig HeimbachDavid JacobsonJeff NicoAlan Thompson

• The work is supported by NIST Physics Lab, NCNR, and DOE. Experiments funded by NSF, DOE, and NIST.

• More than 30 students from undergraduate institutions and local high schools

• 13 former thesis students; 7 current thesis students

There is an active and growing program in fundamental neutron physics based at NIST. It is possible through strong national and international collaborations.