Lead (
208
Pb) Radius Experiment :
E = 850 MeV,   6 0
electrons on lead
PREX
Elastic Scattering Parity
Violating Asymmetry
0
Z of Weak Interaction :
Clean Probe Couples Mainly to Neutrons
( T.W. Donnelly, J. Dubach, I Sick )
In PWIA (to illustrate) :
 d 
 d 
2

 

F
(
Q
) 
2
n
GF Q 
 d  R  d  L
2
A 

 1  4 sin  W 

2
F
(
Q
)
2

2
d

d





P



 

 d  R  d  L
0
208Pb
w/ Coulomb distortions (C. J. Horowitz) :
dA
 3% 
A
PREX
PAVI06
May 2006
dRn
 1%
Rn
R. Michaels
Jefferson Lab
Impact on Nuclear Physics:
What is the size of a
nucleus ?
Is the size of a heavy nucleus
determined by neutrons or by protons ?
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Reminder: Electromagnetic Scattering determines
 r 
(charge distribution)
208
Pb
 r 
d  mb 


d  str 
1
PREX
PAVI06
2
q
May 2006
 fm1
3
R. Michaels
Jefferson Lab
0
Z of weak interaction : sees the
neutrons
Analysis is clean, like electromagnetic scattering:
1. Probes the entire nuclear volume
2. Perturbation theory applies
PREX
PAVI06
proton
neutron
Electric charge
1
0
Weak charge
0.08
1
May 2006
R. Michaels
Jefferson Lab
Neutron Densities
• Proton-Nucleus Elastic
Involve strong probes
• Pion, alpha, d Scattering
• Pion Photoproduction
Most spins couple to zero.
• Magnetic scattering
• Theory Predictions
Fit mostly by data other than
neutron densities
Therefore, PREX is a powerful
check of nuclear theory.
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Electron - Nucleus Potential
Vˆ (r )  V (r )   5 A(r )
axial
electromagnetic
/
V (r )   d r Z  (r ) | r  r |
3
/
/
A(r ) 
FP (Q 2 ) 
1
4
3
d
 r j0 (qr )  P (r )
2 2
(1  4 sin
2
 W ) Z  P (r )  N  N (r )
A(r ) is small, best observed
by parity violation
d d

| FP (Q 2 ) | 2
d d Mott
Proton form factor
GF
1  4 sin 2  W  1 neutron weak
charge >> proton weak charge
Neutron form factor
FN (Q 2 ) 
1
4
3
d
 r j0 (qr )  N (r )
Parity Violating Asymmetry
 d 
 d 

 

GF Q 2
d


 R  d  L
A 

2 2
 d 
 d 

 

 d  R  d  L
PREX
PAVI06
May 2006

FN (Q 2 ) 
2
 1  4 sin  W 

FP (Q 2 ) 

0
R. Michaels
Jefferson Lab
PREX:
2
Measurement at one Q is sufficient to measure R
N
( R.J. Furnstahl )
Why only one
parameter ?
(next slide…)
PREX
error bar (1 )
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
PREX: pins down the symmetry energy
E
 N Z 
  av  a 4 

A
 A 
( R.J. Furnstahl )
2
 as / A
1/ 3
 ...
(1 parameter)
energy cost for unequal #
protons & neutrons
PREX
error
bar
(1 )
208
Pb
PREX
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Nuclear Structure: Neutron density is a fundamental
observable that remains elusive.
Reflects poor understanding of
symmetry energy of nuclear
matter = the energy cost of N  Z
E (n, x)  E (n, x  1 / 2)  S (n) (1  2 x 2 )
n  n.m. density
x  ratio
proton/neutrons
• Slope unconstrained by data
208
• Adding R N from
Pb
will eliminate the
dispersion in plot.
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Impact on
Neutron Stars
What is the nature of extremely dense matter ?
Do collapsed stars form “exotic” phases of matter ?
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
PREX & Neutron Stars
( C.J. Horowitz, J. Piekarweicz )
R N calibrates EOS of
Neutron Rich Matter
Crust Thickness
Explain Glitches in Pulsar Frequency ?
Combine PREX R N with
Obs. Neutron Star Radii
Phase Transition to “Exotic” Core ?
Strange star ? Quark Star ?
Some Neutron Stars
seem too Cold
Cooling by neutrino emission (URCA)
Crab Pulsar
PREX
PAVI06
May 2006
Rn  R p  0.2 fm
URCA probable, else not
R. Michaels
Jefferson Lab
Neutron EOS and Neutron Star Crust
Liquid/Solid Transition Density
Liquid
FP
Solid
Fig. from
PREX
PAVI06
J.M. Lattimer & M. Prakash,
Science 304 (2004) 536.
May 2006
TM1
• Thicker neutron skin in Pb means
energy rises rapidly with density 
Quickly favors uniform phase.
• Thick skin in Pb  low transition
density in star.
R. Michaels
Jefferson Lab
Pb Radius vs Neutron Star Radius
( C.J. Horowitz, J. Piekarweicz )
• The 208Pb radius constrains the pressure of neutron
matter at subnuclear densities.
• The NS radius depends on the pressure at nuclear
density and above.
• Most interested in density dependence of equation of
state (EOS) from a possible phase transition.
• Important to have both low density and high density
measurements to constrain density dependence of EOS.
– If Pb radius is relatively large: EOS at low density is stiff with
high P. If NS radius is small than high density EOS soft.
– This softening of EOS with density could strongly suggest a
transition to an exotic high density phase such as quark matter,
strange matter, color superconductor, kaon condensate…
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
PREX Constrains Rapid Direct
URCA Cooling of Neutron Stars
( C.J. Horowitz, J. Piekarweicz )
• Proton fraction Yp for matter in
beta equilibrium depends on
symmetry energy S(n).
• Rn in Pb determines density
dependence of S(n).
• The larger Rn in Pb the lower
the threshold mass for direct
URCA cooling.
• If Rn-Rp<0.2 fm all EOS models
do not have direct URCA in
1.4 M¯ stars.
• If Rn-Rp>0.25 fm all models do
have URCA in 1.4 M¯ stars.
Rn-Rp in 208Pb
If Yp > red line NS cools quickly via
direct URCA reaction n p+e+
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Impact on Atomic Parity
Measures atomic overlap with weak charge.
Neutrons carry most weak charge
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Atomic Parity Violation
2
• Low Q test of Standard Model
Isotope Chain Experiments
e.g. Berkeley Yb
• Needs R N to make further progress.
H PNC 
 N

2
GF
2
 N (r )  Z (1  4 sin 2  W )  P (r )  e/  5  e d 3 r


0
APV
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
PREX
Physics
Impact
Measured Asymmetry
Correct for Coulomb
Distortions
Weak Density at one Q 2
Mean Field
& Other
Models
Small Corrections for
Atomic
Parity
Violation
G
n
E
s
GE
MEC
2
Neutron Density at one Q
Assume Surface Thickness
Good to 25% (MFT)
Heavy
Ions
Neutron
Stars
Rn
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Corrections to the Asymmetry are
Mostly Negligible
• Coulomb Distortions ~20% = the biggest correction.
• Transverse Asymmetry (to be measured)
• Strangeness
• Electric Form Factor of Neutron
• Parity Admixtures
• Dispersion Corrections
• Meson Exchange Currents
• Shape Dependence
Horowitz, et.al. PRC 63 025501
• Isospin Corrections
• Radiative Corrections
• Excited States
• Target Impurities
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
PREX: Experimental Issues
Spokespersons:
P.A. Souder, G.M. Urciuoli, R. Michaels
Hall A Collaboration Experiment
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
PREX in Hall A at JLab
Spectometers
Lead Foil
Target
Pol. Source
Hall A
CEBAF
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Hall A at Jefferson Lab
Polarized eSource
PREX
PAVI06
May 2006
Hall A
R. Michaels
Jefferson Lab
High Resolution Spectrometers
Spectrometer Concept:
Resolve Elastic
Elastic
detector
Inelastic
Left-Right symmetry to
control transverse
polarization systematic
Quad
target
Dipole
PREX
PAVI06
Q Q
May 2006
R. Michaels
Jefferson Lab
Integrating Detection
• Integrate in 30 msec helicity period.
• Deadtime free.
• 18 bit ADC with < 10
•
-4
But must separate backgrounds & inelastics (
PMT
May 2006
HRS).
Integrator
Calorimeter (for lead, fits in palm of hand)
PREX
PAVI06
nonlinearity.
ADC
R. Michaels
Jefferson Lab
Optimum Kinematics for Lead Parity:
<A> = 0.5 ppm.
E = 850 MeV,
Accuracy in Asy 3%
Fig. of merit
Min. error in Rn
maximize:
1 month run
1% in R n
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Optimization for Barium
-- of possible direct use for Atomic PV
1 GeV optimum
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Beam Asymmetries
Araw = Adet - AQ + E+ ixi
Slopes from
PREX
PAVI06
May 2006
•natural beam jitter (regression)
•beam modulation (dithering)
R. Michaels
Jefferson Lab
Helicity Correlated Differences: Position, Angle, Energy
Scale +/- 10 nm
BPM X1
slug
Spectacular results
from HAPPEX-H
show we can do
BPM X2
PREX.
Position Diffs
average to ~ 1 nm
• Good model for
controlling laser systematics
at source
• Accelerator setup
(betatron matching, phase
advance)
PREX
PAVI06
May 2006
slug
BPM Y1
slug
BPM Y2
slug
“Energy”
BPM
“slug” = ~1 day running
R. Michaels
Jefferson Lab
Redundant Position Measurements at the ~1 nm level
Y (cavity)
X (cavity)
nm
nm
(Helicity – correlated differences averaged over ~1 day)
X (stripline)
PREX
PAVI06
May 2006
nm
Y (stripline)
nm
R. Michaels
Jefferson Lab
Lead Target
208
Pb
Successful ly tested at 80 A
Liquid Helium
Coolant
12
beam
C
Diamond Backing:
• High Thermal Conductivity
• Negligible Systematics
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Num. events
208
Pb Elastic
Detector
1st Excited State
(2.6 MeV)
Momentum (MeV)
Data taken Nov 2005
•
Check rates
•
Backgrounds (HRS is clean)
•
Sensitivity to beam
parameters
•
Width of asymmetry
A  1
Num. events
PREX
PAVI06
Lead Target Tests
May 2006
•
HRS resolution
•
Detector resolution
I
R. Michaels
Jefferson Lab
Polarimetry
Møller : dPe/Pe ~ 3 %
(limit: foil polarization)
(a high field target ala Hall C being considered)
Compton
2 analyses based
on either electron
or photon detection
e 
:
2% syst. at present
PREX:
1 % desirable
2 % required
Electron only
Photon only
Superlattice:
Pe=86% !
PREX
PAVI06
May 2006
Preliminary: 2.5% syst ( only)
R. Michaels
Jefferson Lab
Upgrade of Compton Polarimeter
in ~ 1.5 years
(Nanda, Lhuillier)

To reach 1% accuracy:
• Green Laser
(increased sensitivity at low E)
 laser on-hand, being tested
• Integrating Method
(removes some systematics of
analyzing power)
 developed during HAPPEX & in 2006
• New Photon Detector
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
PREX : Summary
• Fundamental Nuclear Physics with
many applications
• HAPPEX & test runs have
demonstrated technical aspects
• Polarimetry Upgrade needed
• Will run 1 month, perhaps in 2008
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Neutron Skin and Heavy – Ion Collisions
• Impact on Heavy - Ion physics: constraints and predictions
• Imprint of the EOS left in the flow and fragmentation distribution.
Danielewicz, Lacey, and Lynch, Science 298 (2002) 1592.
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Example : Recent Pion Photoproduction
B. Krusche
arXiv:nucl-ex/0509003
Sept 2005
This paper obtains
RN
RP !!
Proton – Nucleus Elastic:
0.083  RN  RP  0.111 fm
Mean Field Theory
0.05  RN  RP  0.35 fm
PREX accuracy
d RN   0.05 fm
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Transverse Polarization
Part I: Left/Right Asymmetry
Transverse Asymmetry
AT  AT0 PT sin 
Systematic Error for Parity

Theory est. (Afanasev)
A  5  1 ppm
0
T
Transverse polarization
PT  P sin 
 3o

HRS-Left

P

d A  d AT0  PT 
“Error in”
 
Left-right apparatus
asymmetry
Control  w/ slow feedback on
polarized source solenoids.
d AT0   1 ppm
HRS-Right
Need
 PT << 10 3  10 3
correction
PREX
PAVI06
May 2006
measure in ~ 1 hr
(+ 8 hr setup)
syst. err.
R. Michaels
Jefferson Lab
Transverse Polarization
Part II: Up/Down Asymmetry
Vertical misalignment
 cos    0
Systematic Error for Parity
d A  d AT0 PT  cos   

Horizontal polarization
e.g. from (g-2)
• Measured in situ using
2-piece detector.
PT  P sin 
up/down
misalignment
HRS-Left

P
PREX
PAVI06
• Study alignment with
tracking & M.C.
• Wien angle feedback (

Need
HRS-Right
PT  cos   << 10 3  10 3

( Note, beam width is very tiny
May 2006
)
~ 100  m )
R. Michaels
Jefferson Lab
Noise
•
Need 100 ppm per window pair
•
Position noise already good enough
•
New 18-bit ADCs
 Will improve BCM noise.
•
Careful about cable runs, PMTs, grounds.
 Will improve detector noise.
•
Plan: Tests with Luminosity Monitor
to demonstrate capability.
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
Warm Septum
Existing superconducting septum won’t work at high L
Warm low energy (1 GeV) magnet designed.
Grant proposal in preparation (~100 k$) [Syracuse / Smith College]
TOSCA design
P resolution ok
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab
2
Measurement at one Q is
sufficient to measure R N
Pins down the symmetry
energy (1 parameter)
PREX
accuracy
PREX
accuracy
( R.J. Furnstahl )
PREX
PAVI06
May 2006
R. Michaels
Jefferson Lab