W. M. SnowPhysics DepartmentIndiana UniversityNPSS, Bar Harbor
Neutron Physics
5 lectures:
1. Physics/Technology of Cold and Ultracold Neutrons2. Electroweak Standard Model Tests [neutron beta decay]3. Nuclear physics/QCD [weak interaction between nucleons]4. Physics Beyond the Standard Model [EDM/T violation, B]5. Other interesting stuff that neutrons can do [NNN interaction, searches for extra dimensions,…]
Other Interesting Physics
1. Neutron Gravitational Bound States2. Precision Few-Nucleon Physics: n-A scattering lengths3. T violation in Polarized Neutron/Polarized Target Transmission4. Bell’s Inequalities and Entangled QM States
Thanks for slides to: Hartmut Abele (Heidelberg), Valery Nezvishevsky (ILL), Muhammad Arif (NIST), Tim Black (UNC/Wilmington), Yuji Hasegawa (Atominstitut, Wein)
Classical and QM Point of ViewClassical and QM Point of View
Neutron Neutron Probability Distributions Above the Probability Distributions Above the MirrorMirror
Experimental ApparatusExperimental Apparatus
Observation of neutron gravitational Observation of neutron gravitational quantum statesquantum states
Comparison to TheoryComparison to Theory
Large extra dimensions?Large extra dimensions?
Neutron, Newtonian
Non-Newtonian Interaction
Neutron, Non-Newtonian
Ratio
TeV scale Quantum Gravity:
2)4(
2)4(
++= n
nPln
nPl MrM 2)4(
2)4(
++= n
nPln
nPl MrM 2)4(
2)4(
)4(2
24 ~1~
M
M
Mrg n
nnn
+
+2
)4(
2)4(
)4(2
24 ~1~
M
M
Mrg n
nnn
+
+
g = 9.85 ± 0.7 m/s2
Previous Previous LimitsLimits
Limits for alpha and lambdaLimits for alpha and lambda
H. A. et al., Lecture Notes in Physics, Springer, 2003
01.11.04 V.V.Nesvizhevsky
- Search for extra fundamental forces at short distances of 1 nm - 10 µm
-Verification of electrical neutrality of neutrons
Perturbation frequency, Hz
Transition probability
induced by
vibrating mass
eVE 18min 10−≈δ
6
12
min 10−≈− EE
Eδ
ijji wEE ⋅=− h
Hz26021 ≈ν
Quantum trap
Resonance transitions
Potential Applications in fundamental physics
Neutron Interferometer and Optics Facility (NIOF) at NIST
How a neutron interferometer works
Neutron
beam
Interferometer
O-beam
H-beam
Phaseshifter
Sample
∆ε
δ
Phase Shifter Angle (deg)
1000
500
0-2 -1 0 21
Visibility
∆φ
Outgoing
wave front
Incident
wave front
optV
∆φ
Sample
λ λλ/ n
λ λλ
D
Only neutron optics devicewhich can directly measurethe phase shift.
Visibility > 90%
Sample
Top View
Neutron wave functioncoherently split byBragg diffraction.
∆φ = − λΝbD
Coherent Neutron scattering lengths 1 cm n - beam
phase shifterSi (111)
vacuum cell
cell out
Temp B
3He detectors
Temp A
cell in
gas cell
quartzalignment
flag
Two n-A scattering lengths b± for I±1/2
Coherent scattering amplitude bcoh=sum over those amplitudes which do not change the QM state of the target
Phase shift proportional to bcoh
1950 1960 1970 1980 1990 20006.4
6.5
6.6
6.7
6.8
Year
Many MethodsBragg DiffractionChristiansen filterGravity reflectometryTotal reflectionInterferometryTransmission
D2 scattering length measurement
bnd = (6.6727 ± 0.0045) fm
Theoretical calculations of the coherent scattering length compared with the experimental value. The central dark band is the 1σ confidence band and the lighter band is the 2σ confidence band. Only 2 of the theories fall within 2σ.
Precision measurements in 3-body systems can see effectsof nuclear 3-body forces. No one knows what the nuclear 3-body force should look like.
Measurement of the n-3He coherent scattering length
3.5 × 10-48.250 × 1019 cm-3N1.0 × 10-43.380 × 105 PaP2.3 × 10-423.237 °CT1.0 × 10-41.0016 cmDcell
2.0 × 10-50.271207 nmλ
1.45 × 10-3-1.379 rad∆φcell
6.6 × 10-42.69 rad∆φnD
Relative σV / VValue VParameter
fm )007.0857.5(3 ±=Henbnew measurement
previous world average fm )041.0733.5(3 ±=Hen
b
fm )007.0854.5(3 ±=Hen
bnew world average
•P. R. Huffman, D. L. Jacobson, K. Schoen, M. Arif, T. C. Black, W. M. Snow, and S. A. Werner, A precision neutron interferometric measurement of the n-3He coherent neutron scattering length submitted to Phys. Rev. C.
5 .8
5 .8 5
5 .9
5 .9 5
6
6 .0 5
6 .1
-2 .5 -2 .4 5 - 2 .4 - 2 .3 5
C o m p a r is o n o f t h e o r y a n d e x p e r im e n t fo r c o h e r e n t a n d
in c o h e r e n t b o u n d n + 3 H e s c a t t e r in g le n g th s
b coh [
fm]
bi [ fm ]
A V 1 8
A V 1 8 + U I X E x p e r im e n t
A V 1 8 + U I X + V3
*
Comparisons with RGM calculations using modern NN potentials with 3N Forces*
*H. M. Hoffman and G. M. Hale, Phys. Rev. C 68, 021002(R) (2003).
TT--violation experiments in violation experiments in Polarized Neutron TransmissionPolarized Neutron Transmission
through Polarized Targets through Polarized Targets
H0nuclearspin, I
sn
π/2 flip
orMeissner
sheet
nkn
T-odd correlation in total cross section: (kn×I) · sn
nanalyzer
npolarizer
first step for Tfirst step for T--violation experiment violation experiment measurement of measurement of Xe Xe pseudomagnetismpseudomagnetism
TwoTwo--particle vs. twoparticle vs. two--space entanglemenspace entanglemen
2-Particle Bell-State Ψ = 1
2↑ I⊗ ↓ II + ↓ I⊗ ↑ II
I, II represent 2-Particles
Measurement on each particle A
Ia = +1 ⋅P a;+1
I+ –1 ⋅P a;–1
I
BII
b = +1 ⋅P b;+1
II+ –1 ⋅P b;–1
II
where P ξ;±1 = 1
2↑ ± eiξ ↓ ↑ ± e–iξ ↓
Then, AI, B
II= 0
2-Space Bell-State Ψ = 1
2↑ s⊗ I p + ↓ s⊗ II p
s, p represent 2-Spaces, e.g., spin &
Measurement on each property A
sα = +1 ⋅P α
s+ –1 ⋅P α+π
s
Bp
χ = +1 ⋅P χp
+ –1 ⋅P χ+πp
where P φ = 1
2ϕ + eiφ ϕ ϕ + e–iφ ϕ
Then, As, B
p= 0
==>> (Non-)Contextuality(In)Dependent Results for commuting Observables
Non-Locality: rI≠ rII for
PI(rI) & P
II(rII)
Schematic view of the experimentSchematic view of the experiment
Top ViewTop View
Manipulation of twoManipulation of two--subspacessubspaces(a) Path(a) Path (b) Spin(b) Spin
Oscillations with various spinOscillations with various spin--analysesanalyses
E' α=0, χ = 0.79π= N' 0,0.79π + N' π,1.79π
– N' 0,1.79π – N' π,0.79π÷ N' 0,0.79π + N' π,1.79π
+ N' 0,1.79π + N' π,0.79π= 0.542
In thesamemanner,
E' α=0, χ = 1.29πE' α=0.5π, χ = 0.79πE' α=0.5π, χ = 1.29π
weredetermined.
Violation of the BellViolation of the Bell--like inequalitylike inequality
E' α,χ =
N'+ + α,χ + N'+ + α+π,χ+π – N'+ + α,χ+π – N'+ + α+π,χN'+ + α,χ + N'+ + α+π,χ+π + N'+ + α,χ+π + N'+ + α+π,χ
where N'+ + α,χ = Ψ P α
s⋅P χ
pΨ
E' α1,χ1 = 0.542 ± 0.007E' α1,χ2 = 0.488 ± 0.012E' α2,χ1 = – 0.538 ± 0.006E' α2,χ2 = 0.483 ± 0.012
where
α1 = 0α2 = 0.50πχ1 = 0.79πχ2 = 1.29π
===>>> S' ≡ E' α1,χ1 + E' α1,χ2 – E' α2,χ1 + E' α2,χ2
= 2.051 ± 0.019 > 2
Cf. Max. violaion: SCf. Max. violaion: S’’=2.81>2=2.81>2confidence: 99.6%confidence: 99.6%