nuclear physics with electromagnetic probes · 2012-06-11 · 2 course outline • introduction to...
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Nuclear Physics with Electromagnetic Probes
Lawrence Weinstein Old Dominion University
Norfolk, VA
Lecture 2 Hampton University Graduate School
2012
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Course Outline • Introduction to EM probes.
– Electron and photon interactions with nuclei. – Beams and detectors.
• Nuclear Physics with electrons and photons. • Elastic electron-nucleus scattering. – Charge, matter and momentum distributions. – Single nucleons – Correlated nucleon pairs. – Nucleon modification in nuclei – Hadronization in nuclei – Nuclear transparency
HUGS 2012 Nuclear Physics Weinstein
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Why use electrons and photons?
• Probe structure understood (point particles) • Electromagnetic interaction understood (QED) • Interaction is weak (α = 1/137)
– Perturbation theory works! • First Born Approx / one photon exchange
– Probe interacts only once – Study the entire nuclear volume
BUT: • Cross sections are small • Electrons radiate
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It’s all photons! • An electron interacts with a nucleus by
exchanging a single* virtual photon.
Incident e-
Scattered e-
Virtual photon Real photon
Real photon: Momentum q = energy ν Mass = Q2 = |q|2 - ν2 = 0
Virtual photon: Momentum q > energy ν Q2 = - qμqμ = |q|2 - ν2 > 0 Virtual photon has mass!
(ν and ω are both used for energy transfer) HUGS 2012 Nuclear Physics Weinstein
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(e,e’) spectrum
Generic Electron Scattering at fixed momentum transfer
d!d"
d!d"
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Experimental goals:
• Elastic scattering – structure of the nucleus
• Form factors, charge distributions, spin dependent FF
• Quasielastic (QE) scattering – Shell structure
• Momentum distributions • Occupancies
– Short Range Correlated nucleon pairs – Nuclear transparency and color transparency
• Deep Inelastic Scattering (DIS) – The EMC Effect and Nucleon modification in nuclei – Quark hadronization in nuclei
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Program central to all of nuclear science
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Energy vs length
Three cases: • Low q
– Photon wavelength λ larger than the nucleon size (Rp) • Medium q: 0.2 < q < 1 GeV/c
– λ ~ Rp – Nucleons resolvable
• High q: q > 1 GeV/c – λ < Rp – Nucleon structure resolvable
Select spatial resolution and excitation energy independently • Photon energy ν determines excitation energy • Photon momentum q determines spatial resolution: ! !
!
q
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Types of photon Polarisation
• Both real and virtual photons can have polarisation – Real photons: transverse pol only – Virtual photons: longitudinal or transverse
• Determining azimuthal distribution of reaction products around these polarisation directions gives powerful information (see later)
Linear polarisation (Electric field vector oscillates in a plane)
Circular polarisation (Electric field rotates
clockwise or anticlockwise)
Virtual photons can also have a longitudinal
polarisation component - related to coulomb (charge)
scattering
Virtual photon
Longitudinal polarisation
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Real and virtual photon coupling
JµAµ
ρΦ (e/m)(pxA) sx(qxA)
Coulomb Convection spin
Longitudinal Virtual photon
only
Transverse Real and Virtual
Photons
Photon-nucleus EM interaction: Photon EM field 4-vector potential couples to the nuclear charge and current
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Inclusive electron scattering (e,e’)
Invariants:
Lab frame kinematics
(not detected)
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Formalism • Inclusive scattering:
– measure scattering angle θe and energy E’e (ω = Ee – E’e) and the cross section
• One photon exchange:
Lμν and Hμν are the lepton and hadron tensors
d! / d"ed#
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More Formalism Lepton tensor known (QED):
Spin dependent
Hadron tensor unknown:
Nuclear current operators Two approaches: 1. Calculate Jμ from models or 2. Create most general hadron tensor from tensors
(bilinear Lorentz vectors) Aiμν = aμbν and Lorentz
scalers Si = aμbμ : Hμν = ΣAiμνFi(S1,S2,…)
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Most general hadron tensor: EM current conservation parity conservation
Time reversal symmetry Available independent four vectors for (e,e’): • target momentum pμ • photon momentum qμ • target polarization Sμ
Four independent structure functions • Spin independent: F1(Q2,x) and F2(Q2,x) • Spin dependent: g1(Q2,x) and g2(Q2,x) (arguments also written as (Q2,ω) or (Q2,ν))
x =Q2
2p !q=
Q2
2M"
Spin dependent
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Elastic cross section (p’2 = m2) Recoil factor Form factors
F1, F2: Dirac and Pauli form factors GE, GM: Sachs form factors (electric and magnetic)
GE(Q2) = F1(Q2) - τκF2(Q2) GM(Q2) = F1(Q2) + κF2(Q2)
RL, RT: Longitudinal and transverse response fn
τ = Q2/4M2
κ = anomalous magnetic moment
Mott cross section
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Electron-nucleus interactions
I II
III
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Electrons as Waves
ph=!
pcEe !
Scattering process is quantum mechanical
De broglie wavelength:
Electron energy:
λ resolving “scale”: ! =2" (197 MeV # fm)
Ee
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Analogy between elastic electron scattering and
diffraction
k!
k!!
q!
θ
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Classical Fraunhofer Diffraction
Amplitude of wave at screen:
( ) drrdibra
!!"
# #$%0
2
0
cosexp
Simple analogy for elastic electron scattering….
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Classical Fraunhofer Diffraction
( )( ) 212
sinsin/2
!"#$
%&'(
))*+aJ
!"
sin22.12 #a
Intensity:
Minima occur at zeroes of Bessel function. 1st zero: x = 3.8317
Hence
…some algebra…
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Excursion: Babinet’s principle
Screen with apertures
Complementary screen
Patterns appear the same
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qeff (fm-1) 1 2 3 4
σ/σ m
ott
10-1
1 10
1 Example: 30Si(e,e’)
1st minimum = 1.3 fm-1
θ = 32.8o
Electron energy = 454.3 MeV λ = 2.73 fm
Calculated radius = 3.07 fm
(1 fm-1 = 197 MeV/c)
Measured rms radius = 3.19 fm (from fit to entire curve)
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I. Elastic Electron Scattering from Nuclei (done formally)
Fermi’s Golden Rule
Plane wave approximation for incoming and outgoing electronsBorn approximation (interact only once)
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I. Elastic Electron Scattering from (spin-0) Nuclei Form Factor and Charge Distribution Using Coulomb potential from a charge distribution, ρ(x),
Charge form factor F(q) is the Fourrier transform
of the charge distribution ρ(x) HUGS 2012 Nuclear Physics Weinstein
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I. Elastic Electron Scattering from (spin-0) Nuclei
qeff (fm-1) 1 2 3 4
σ/σ m
ott
10-1
1 10
1
F=1 for point particle
1 fm-1 = 197 MeV/c
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I. Elastic (e,e’) Scattering ⇒ charge distributions
Elastic electron scattering measured for many nuclei over a wide range of Q2(mainly at Saclay in the 1970s) Measured charge distributions agree well with mean field theory calculations.
HUGS 2012 Nuclear Physics Weinstein
Char
ge d
ensi
ty
Radius (fm) 6 0
Pb
40Ca
12C 4He
Cros
s Se
ctio
n
10-26
10-36
q (fm-1) 3 1
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Lead 208Pb Radius Experiment : PREX
208Pb
Pb(e,e’) Elastic Scattering Parity Violating Asymmetry
Spokespersons
• Paul Souder
• Krishna Kumar
• Guido Urciuoli
• Robert Michaels
Ebeam = 1 GeV θe = 5o
Ibeam = 60 μA
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Slides courtesy of R. Michaels
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Parity Violating Asymmetry 610~ −
+−
=LR
LRPVA σσ
σσ
γ 0Z−e −e
+
2
≈σ
Applications of PV at Jefferson Lab
• Nucleon Structure (strangeness) -- HAPPEX / G0
• Standard Model Tests ( ) -- e.g. Qweak
• Nuclear Structure (neutron density) : PREX Wθ
2sin
Applications of PV at Jefferson Lab
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⎥⎦
⎤⎢⎣
⎡−−=
⎟⎠⎞⎜
⎝⎛
Ω+⎟
⎠⎞⎜
⎝⎛
Ω
⎟⎠⎞⎜
⎝⎛
Ω−⎟
⎠⎞⎜
⎝⎛
Ω=)(
sin4122 2
22
QFQG
dd
dd
dd
dd
AP
WF
LR
LR θπασσ
σσ
%1%3 =→=n
n
RdR
AdA
Lead 208Pb Radius Experiment : PREX Z0 of Weak Interaction: Clean Probe Couples Mainly to Neutrons
(T.W. Donnelly, J. Dubach, I Sick)
(C. Horowitz)
Left-Right Cross section asymmetry (simplified):
w/ Coulomb distortions:
0≈
FW(Q
2)
Rn = neutron matter radius
HUGS 2012 Nuclear Physics Weinstein 29
Fp(Q2): 208Pb Charge Form Factor
proton neutron
Electric charge 1 0
Weak charge 0.08 1
Clean Probe Couples Mainly to Neutrons
FW(Q2): 208Pb Weak Form Factor
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PREX & Neutron Stars
Crab Pulsar
( C.J. Horowitz, J. Piekarewicz )
Rn calibrates EOS of Neutron Rich Matter
Combine PREX Rn with Obs. Neutron Star Radii
Some Neutron Stars seem too Cold
Crust Thickness Explain Glitches in Pulsar Frequency ?
Strange star ? Quark Star ?
Cooling by neutrino emission (URCA)
0.2 fm URCA probable, else not >− pn RR
Phase Transition to “Exotic” Core ?
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PREX in Hall A at JLab
CEBAF Hall A
Pol. Source
Lead Foil Target
Spectrometers
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High Resolution Spectrometers
Elastic
Inelastic
detector
Q Q
Dipole
Quad
Spectrometer Concept: Resolve Elastic
target
Pb 1st excited state at 2.6 MeV
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Lead Target – melts easily
Liquid Helium Coolant
Pb
C
208
12
Diamond Backing:
• High Thermal Conductivity • Negligible Systematics
Beam, rastered 4 x 4 mm
beam
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Target Assembly
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PRex Results
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APV = 656 ± 60 (stat) ± 14 (syst) ppb
5.4 5.5 5.6 5.7 5.8 5.9 6R
n (fm)
0.6
0.65
0.7
0.75
0.8
AP
b
PV
(p
pm
)
SI
NL3p06
SLY4
SIIIFSU
NL3
NL3m05
Rp
PREX-I
PREX-II
Rn=R
p
Look for PRex II, coming soon to a lab near you!
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Deuteron Elastic Scattering • Only bound 2 nucleon system • Prime testing ground for models: where is the limit
for the description in terms of nucleons and mesons
• Questions: – How does the photon interact with a BOUND nucleon? – Effects of meson interactions? – Final State Interactions? – Deuteron wave function at small distance? – Where do quarks come in?
6/11/12 36
Review Articles: • M.Garcon and J.W. van Orden Adv.Nucl.Phys.26(2001)293 • R. Gilman and F. Gross, J. Phys. G: Nucl. Part. Phys. 28 (2002) R37–R116 • R.J.Holt and R. Gilman http://arxiv.org/abs/1205.5827v1
Deuteron slides from W. Boeglin (Florida International U)
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Elastic D(e,e’)
6/11/12 37
dσ
dΩ= σMott
A(Q2) +B(Q2) tan2(θ/2)
A = G2C +
2
3ηG2
M +8
9η2G2
Q
B =4
3η(1 + η)G2
M
η = Q2/4M2D
T20 = −89η
2G2Q + 8
3ηGCGQ + 23ηG
2M
12 + (1 + η) tan2(θ/2)
√2A+B tan2(θ/2)
.
GQ Quadrupole form factor
GM Magnetic form factor
GC Charge form factor
Note: A and B are linear combinations of F1 and F2 or of RL and RT.
To measure the tensor polarization T20, use: !d(e,e ')d
d(e,e '!d )
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Calculation: H.Arenhövel et al. PRC 61, 034002
10−5
10−4
10−3
10−2
0.5 1.0 1.5 2.0Q2 (GeV/c)2
−1.5
−1.0
−0.5
0.0
0.5
10−8
10−7
10−6
10−5
10−4
10−3
A
t20~
GC=0
B
Figure 13: Elastic ed scattering observables calculated with the v/c expan-sion [123]: NRIA with the Bonn OBEPQ-B potential (dotted curve); same plusall relativistic corrections to leading order (dashed); all of the former plus the!"# exchange current (solid). NEMFF: Galster.
33
Hall A data
Hall C data
Hall C data
NRIA NRIA + RC
NRIA + RC + !"#
Experiments: • Hall A : L.C.Alexa et al. PRL 82 (1999) 1374 • Hall C: D.Abbott et al. PRL 82 (1999) 1379 • Hall C: D.Abbott et al. PRL 84 (2000) 5053
d d
Photon couples to nucleon
π
Meson Exchange Current
ρ π
ρπγ Meson Exchange Current
A
B
T20
Q2
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Transition between nuclear and quark-gluon descriptions of hadrons and light nuclei21
)2 (GeV2Q0 2 4 6
A
-1010
-810
-610
-410
-210
1 BuchananEliasBenaksasArnoldPlatchkovGalsterCramerSimonAbbottAlexaBerardAkimov
IMIIIM+E II
f/g=0!"#
f/g=6.1!"#
)2 (GeV2Q0 1 2 3 4
B
-1010
-810
-610
-410
BostedCramerAuffretSimonBuchanan
IMIIIM+E II
f/g=0!"#
f/g=6.1!"#
)-1Q (fm0.0 0.5 1.0 1.5 2.0
20T
-2
-1
0
1
DmitrievVoitsekhovskiiFerro-LuzziSchulzeBowhuisGilmanBodenGarconAbbottNikolenkoZhang
IMIIIM+E II
f/g=0!"#
f/g=6.1!"#
Figure 12. World data for A(Q2), B(Q2), and t20 = T20 in e-d elastic scatteringcompared to recent meson-nucleon calculations. Shown are a Hamiltoniandynamics calculation [197] without (“IMII”) and with (“IM+EII”) MEC, anda propagator dynamics calculation [199] (“!"#”) with two choices (solid: f/g=0,dash: f/g=6.1) for the tensor strength of the !NN interaction used in the !"#exchange current. The best overall description of the data is with the “IM+EII”calculation.
5.2. Quark-gluon approaches to the N-N interaction and the deuteron
The issue of quark-gluon vs. hadronic degrees of freedom was discussed in Sec. 2.In this section we focus on the high-momentum transfer NN interaction, and thehigh-momentum structure of the deuteron. It is generally accepted for these reactionsthat only the leading qqq Fock state of the nucleon needs to be considered. As shownin [10], high energy hadron-hadron reactions which can proceed via quark exchangehave cross sections an order of magnitude larger than reactions which proceed viagluon exchange or quark-antiquark annihilation. This leads to the conclusion that thehigh-energy NN reaction is dominated by quark interchange diagrams, such as that
no MEC contributions
with MEC
Rel. Calculations in Hamiltonian dynamics: IMII and IM+EII Y.Huang and W.N.Polyzou PRC80 (2009) 025503
Rel. Calculations in propagator dynamics: Need ρπγ diagram – not well constrained D.R.Phillips et al. PRC72 (2005) 014006)
A B
T20
0
-1
MEC
No MEC
Q2 (GeV2)d
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Deuteron Elastic Scattering Summary:
• Non-Relativistic models fail at the highest Q2 • Relativistic models successfully describe Deuteron
form factors • MEC contributions are very important • ρπγ exchange current important and not well
constrained
d d
Photon couples to nucleon
π
Meson Exchange Current
ρ π
ρπγ Meson Exchange Current
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Elastic Scattering Summary • Beautiful measurements of the nuclear charge distribution
• And first measurements of the nuclear matter radius
• Beautiful measurements of the deuteron • A, B and Tensor polarization • Allows separation of charge, magnetic and quadrupole form factors
HUGS 2012 Nuclear Physics Weinstein
m=0 m=±1