Slope unconstrained by data Adding R
N eliminate the dispersion in plot.
from 208 Pb will
Heavy nuclei are expected to have a neutron skin structure. Both relativistic and nonrelativistic mean-field models suggest that the thickness of the neutron skin ( and proton ( r p
) root-mean-square (rms) radii (
 r np
≡ r n
 r
− r np p
), defined as the difference between the neutron ( r precise measurement of the skin thickness of 208 Pb is very important for studying the radius, composition, and cooling system of neutron stars .
n
)
), depends on the balance among the various nuclear matter properties. In particular, the neutron skin thickness of 208 Pb is strongly correlated with the nuclear symmetry energy or the pressure coefficients of the equation of states (EOS) in neutron matter. Moreover a

•
• Proton-Nucleus Elastic Scattering
• Pion, alpha, d Scattering
• Pion Photoproduction
• Heavy ion collisions
• Rare Isotopes (dripline)
• Magnetic scattering
• PREX (weak interaction)
Involve strong probes
Most spins couple to zero.
Theory
MFT fit mostly by data other than neutron densities

With high-energy polarized protons the Relativistic Impulse Approximation (RIA) with free nucleon-nucleon interactions can be applied for analyzing the data. Elaborate analysis of the experimental data.
Hadronic probes exhibit uncertainties in the reaction mechanism, which is mainly caused by an incomplete knowledge of the nucleon-nucleon (NN) scattering amplitude inside the nuclear medium. To extract precise information about the neutron density distribution an appropriate probe and an effective NN interaction must be carefully chosen. Model ambiguity is an unavoidable problem in describing hadronic reactions.
Information about the nuclear interior is masked by the strong absorption.
Differential cross sections and analyzing powers for elastic scattering from 58 Ni and 204 , 206 , 208 Pb at Ep =
295MeV, whereas the lines are due to Murdock and
Horowitz (solid) and the global Dirac optical potential
(dashed). The dash-dotted lines show the MH model calculations for 58 Ni with the realistic nucleon density by an unfolding charge density
Calibration of medium-effect parameters by fitting to the experimental data for 58 Ni. The solid line is the mediummodified RIA calculation with best-fit parameters The dashed and dash-dotted lines are from the original MH model with DH and realistic nucleon densities.
RCNP, Osaka University
Best-fit results for neutron density distributions in 204 , 206 , 208 Pb are shown as solid lines. The original MH and medium-modified RIA calculations with the DH nucleon density are also shown by dashed and dash-dotted lines.
Results of fitting to the experimental data and extracted neutron density of 208 Pb with its standard error envelope (solid lines). The dashed and dashdotted lines are medium-modified RIA calculations, but using the DH nucleon densities and the 3pG neutron density by Ray [ 9 ], respectively
J. Zenihiro et al., Phys. Rev. C 82 (2010) 044611

The cross section of

elastic scattering on the nucleon is relatively large in the

(1332) resonance region and is about three times larger for neutrons than for protons. This makes  elastic scattering a promising tool for studying the neutron distribution of nuclei. Unfortunately, a strong absorption occurs at the nuclear surface, making this method very sensitive to the tail of the distributions. The method was successfully used only for studying the neutron distributions of light stable nuclei.
R. R. Johnson et al., PHYS REV LETT 43, 844 (1979)
TRIUMF
Π of 29.
2-and 49.
5-MeV average energy

0
Mainz Microtron MAMI photon beam derived from the production of Bremsstrahlung photons during the passage of the MAMI electron beam through a thin radiator.
Crystal Ball Detector

Simple Correction for distortion
For first preliminary assessment
1) Carry out simple correction of q shift using the theory
2) Analyse corrected minima - fit with Bessel fn.

KVI
α of 196 MeV provided by the super-conducting cyclotron
AGOR bombarded the enriched (99.0 %), self-supporting
208 Pb target with a thickness of
20 mg/cm 2 .
The energy and the scattering angle of the
α particles were measured with the Big-Bite
Spectrometer . The emittd γ rays were detected by a large 10x14 NaI(Tl) crystal
The cross section for excitation of the GDR was calculated connecting the oscillations of the proton and neutron density distributions with the oscillations of the associated optical potential. DWBA cross sections were calculated using the code ECIS with the optical-model parameters determined by Goldberg et al. for 208 Pb. In the derivation of the coupling potentials, which are the most crucial quantities in the calculations, the prescription of Satchler was used. For the density oscillations both the Goldhaber-Teller (GT) and the Jensen-Steinwedel (JS) macroscopic models were adopted. Coulomb excitation was included in both calculations by adding the usual Coulomb transition potential. The cross sections σ
αα’
( E) were calculated as a function of excitation energy by assuming 100% exhaustion of the TRK EWSR. The results were then folded with the photonuclear strength distribution σ
γ
E)
A. Krasznahorkay et al., Nuclear Physics A 731, 224 (2004)

RCNP, Osaka
3 He ++ of 90.1 MeV accelerated with the AVF cyclotron wer injected into the K 400 MeV ring cyclotron, and further accelerated to 450 MeV.
The beam extracted from the ring cyclotron was achromatically transported to the 114 Sn, 116 Sn, 118 Sn,
120 Sn, 122 Sn, and 124 Sn targets with thicknesses of 3.7 - 9.2 mg/cm 2 .
The energy of tritons was measured with the magnetic spectrometer
“Grand Raiden”. The ejectile tritons were detected with two multiwire drift chambers (MWDC’s)
Krasznahorkay et al., Phys Rev Lett 82, 3216 (1999)

SIS-18 synchrotron at GSI
Beam of 238 U ions of 550 MeV/nucleon
Secondary radioactive ions were produced by fission in a Be target
Fission products with a mass-to-charge ratio around that of 132 Sn passed through a 238 Pb target
Dipole-strength distributions have been measured . A sizable fraction of “pygmy”
Dipole strength, energetically located below the giant dipole resonance, was observed in all of these nuclei.
A series of fully self-consistent RHB model plus RQRPA calculations of ground-state properties and dipole strength distributions was carried out. A set of density-dependent meson-exchange (DD-ME) effective interactions has been used, for which the parameter a4 is systematically varied in the interval 30 MeV < a4 < 38 MeV in steps of 2 MeV, while the remaining parameters are adjusted to accurately reproduce nuclear matter properties (the binding energy, the saturation density, the compression modulus, and the volume asymmetry) and the binding energies and charge radii of a standard set of spherical nuclei. For open-shell nuclei, pairing correlations are also included in the RHB+RQRPA framework and described by the pairing part of the Gogny force. The consistent calculation of ground state properties and dipole strength distributions, using the same effective interaction, provides a direct relation between symmetry energy parameters and the predicted size of the neutron skin and the pygmy strength such as shown for 130,132 Sn
A. Klimkiewicz et al. PHYSICAL REVIEW C 76 , 051603(R) (2007)

208
209
Low Energy Antiproton Ring (LEAR)
CERN
Antiprotons of momentum 106 MeV/c.
The antiprotonic x rays emitted during the antiproton cascade were measured by three high-purity germanium
(HPGe) detectors.
A slow antiproton can be captured into an atom like an electron. Since its mass is about 1800 times larger than that of the electron the radius of atomic orbits becomes extremely small. This means that antiproton reaches the surface of the nucleus already at n=9,10.
The strong interaction between antiproton and nucleus causes a sizable change of the energy of the last x-ray transition from its purely electromagnetic value. The nuclear absorption reduces the lifetime of the lowest accessible atomic state [ the “lower level,” which for lead is the ( n, l = 9 , 8) state] and hence this x-ray line is broadened . The widths and shifts of the levels due to the strong interaction are sensitive to the interaction potential which contains, in its simplest form, a term depending on the sum of the neutron and proton densities. Using modern antiproton-nucleus optical potentials, the neutron densities in the nuclear periphery are deduced. Assuming two-parameter Fermi distributions (2pF) describing the proton and neutron densities, the neutron rms radii are deduced
B. Kłos et al., PHYSICAL REVIEW C 76, 014311 (2007)

P
R
Ex
: PREX
Elastic Scattering Parity Violating Asymmetry
E = 1 GeV ,
 
5
0 electrons on lead
Spokespersons
• Krishna Kumar
• Robert Michaels
• Kent Pascke
• Paul Souder
• Guido Maria Urciuoli
208 Pb
Hall A Collaboration Experiment

Electron - Nucleus Potential
V
ˆ
( r )

V ( r )
 
5
A ( r ) electromagnetic
V ( r )
  d
3 r
/
Z

( r
/
) | r
 r
/
| d
 d

 d
 d

Mott
| F
P
( Q
2
) |
2 axial
A ( r )

2
G
F
2

( 1

4 sin
2

W
) Z

P
( r )

N

N
( r )

A ( r ) is small, best observed by parity violation
1

4 sin
2

W

1 neutron weak charge >> proton weak charge
Proton form factor
F
P
( Q
2
)

1
4

 d
3 r j
0
( qr )

P
( r )
Parity Violating Asymmetry
A






 d
 d
 


R d
 d
 


R







 d
 d
 


L d
 d
 


L

Neutron form factor
F
N
( Q
2
)

1
4

 d
3 r j
0
( qr )

N
( r )
G
F
Q
2
2

2 


1

4 sin
2

W

0

F
N
( Q
2
)
F
P
( Q
2
) 



G.M. Urciuoli
Atomic
Parity
Violation
Measured Asymmetry
Correct for Coulomb
Distortions
Weak Density at one Q
2
Small Corrections for n
G
E
G
E s
MEC
Neutron Density at one Q
2
Assume Surface Thickness
Good to 25% (MFT)
Mean Field
& Other
Models
Heavy
I ons
Neutron
Stars
R n

HAPPEX: 2 MHz
PREX: 850 MHz
G.M. Urciuoli

Consolidated techniques from the previous Hall A parity violating electron scatttering experiments (HAPPEX)
Polarized Source P I T A Effect
( P olarization I nduced T ransport A symmetry)
Beam Asymmetries
Intensity Feedback
G.M. Urciuoli

Upgraded Polarimetry
(Sirish Nanda et al.)
Compton Polarimeter ( 1 % Polarimetry)
Laser  Green Laser
Upgrades:
Moller Polarimeter (< 1 % Polarimetry)
Upgrades:
Magnet  Superconducting Magnet from Hall C
Target  Saturated Iron Foil Targets
DAQ  FADC
G.M. Urciuoli

Systematic Errors
Error Source
Polarization (1)
Absolute
(ppm)
0.0071
Relative
( % )
1.1
Beam Asymmetries
Detector Linearity
BCM Linearity
Rescattering
(2) 0.0072
0.0071
0.0010
0.0001
0.0012
1.1
1.1
0.2
0
0.2 Transverse Polarization
Q 2 (1)
Target Thickness
12 C Asymmetry (2)
Inelastic States
TOTAL
0.0028
0.0005
0.0025
0
0.4
0.1
0.4
0
0.0130
2.0
(1) Normalization Correction applied
R
N
(2) Nonzero correction (the rest assumed zero)
= 5.78 + 0.16 - 0.18 fm
Neutron Skin = R
N
- R
P
= 0.33 + 0.16 - 0.18 fm
A


0 .
656 ppm
0 .
060 ( stat )

0 .
0140 ( syst )
 Statistics limited ( 9% )
 Systematic error goal achieved ! (2%)
R
N

6 .
156

1 .
675

A

3 .
420

A
2

G.M. Urciuoli
Approved by PAC (Aug 2011)
“A” Rating 35 days run in 2013 / 2014

CREX
PARITY-VIOLATING MEASUREMENT of the WEAK CHARGE DISTRIBUTION of 48 Ca to 0.02 fm ACCURACY
PREX II and CREX together will constrain isovector contributions to the nuclear EDF.
If PREX II and CREX results agree with DFT expectations, this provides confidence in theoretical predictions of isovector properties all across the periodic table..
If PREX II and CREX results disagree with DFT expectations, this will demonstrate that present parameterizations of the isovector part of energy functionals are incomplete.

R
N
Surface thickness
Shape Dependence ?
Parity Violating Electron Scattering
Measurements of Neutron Densities
Shufang Ban, C.J. Horowitz, R. Michaels arXiv:1010.3246 [nucl-th]
G.M. Urciuoli
R
N
Surface thickness

Polarized e -
Source
Hall A
G.M. Urciuoli

G.M. Urciuoli
Pol. Source

G.M. Urciuoli
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
• Adding R from Pb will eliminate the dispersion in plot.

( C.J. Horowitz, J. Piekarweicz )
Neutron Rich Matter
Crust Thickness
Explain Glitches in Pulsar Frequency ?
 Thicker neutron skin in Pb means energy rises rapidly with density  Quickly favors uniform phase.
Thick skin in Pb  low transition density in star.
Neutron Star Radii
Phase Transition to “Exotic” Core ?
Strange star ?
Quark Star ?

The 208 Pb radius constrains the pressure of neutron matter at subnuclear densities.
The NS radius depends on the pressure at nuclear density and above..
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…
Some Neutron Stars seem too Cold
G.M. Urciuoli

Proton fraction Y p for matter in beta equilibrium depends on symmetry energy S(n).
R n in Pb determines density dependence of S(n).
The larger R n cooling.
in Pb the lower the threshold mass for direct URCA
If R n
1.4 M
-R p
¯
<0.2 fm all EOS models do not have direct URCA in stars.
If R n
-R p
>0.25 fm all models do have URCA in 1.4 M
¯ stars.

G.M. Urciuoli
• Low Q test of Standard Model
• Needs R to make further progress.
Isotope Chain Experiments e.g. Berkeley Yb
H
PNC

2
G
F
2



N

N
( r

)

Z ( 1

4 sin
2

W
)

P
( r

)


/ e

5
 e d
3 r

0
APV

sufficient to measure R
N
Pins down the symmetry energy (1 parameter)
G.M. Urciuoli
( R.J. Furnstahl )

G.M. Urciuoli
Neutron Skin and Heavy – Ion Collisions ( Alex Brown)
E/N
Skx-s15

N
Skx-s20

N
E/N
Skx-s25

N
E/N

Spectrometer Concept:
Resolve Elastic
Inelastic
Elastic detector
Left-Right symmetry to control transverse polarization systematic target
Dipole
Quad
Q Q
G.M. Urciuoli

An electromagnetic probe, due to its simple reaction mechanism, can extract precise information about the density deep inside a nucleus

Average with signs = what exp’t feels
Points: Not sign corrected
Helicity
– Correlated
Position Differences
Wien Flips helped !

X
R

X
L
 for helicity L , R
Units: microns
Slug # ( ~ 1 day)
G.M. Urciuoli

ppm
(P e x A)
G.M. Urciuoli
Slug ~ 1 day

Crossed E & B fields to rotate the spin
• Two Wien Spin Manipulators in series
• Solenoid rotates spin +/-90 degrees (spin rotation as B but focus as B 2 ).
Flips spin without moving the beam !
Electron
Beam
SPIN
G.M. Urciuoli
Joe Grames, et. al.

G.M. Urciuoli
Diamond
• Three bays
• Lead (0.5 mm) sandwiched by diamond (0.15 mm)
• Liquid He cooling (30 Watts)
LEAD melted
NOT melted melted

target
5 0 Septum magnet
(augments the High Resolution Spectrometers)
(Increased Figure of Merit)
HRS-L collimator collimator
HRS-R

Integrating Detection
Deadtime free, 18 bit ADC with < 10 -4 nonlinearity
.
DETECTORS
New HRS optics tune focuses elastic events both in x & y at the PREx detector location
.
The x, y dimensions of the quartz determined from beam test data and
MC (HAMC) simulations.
Quartz thickness optimized with MC.
120 Hz pair windows asymmetry distribution.
No Gaussian tails up to 5 standard deviations.

A
T
 i.e. spin transverse to scattering plane
 
 
  
  


S e

(
 k e

 k ' e
) x
Possible systematic if small transverse spin component k

y
S

A
T
> 0 means z
+ -
208
Pb : A
T
 
0 .
13

0 .
19

0 .
36 ppm
12
C : A
T
 
6 .
52

0 .
36

0 .
35 ppm
• Small A
T for 208 Pb is a big (but pleasant) surprise.
• A
T for 12 C qualitatively consistent with 4 He and available calculations (1) Afanasev ; (2) Gorchtein & Horowitz
G.M. Urciuoli

G.M. Urciuoli
208

Measured Asymmetry
Correct for Coulomb
Distorsion
Fourier Transform of the
Weak Charge Density at q = 0.475 ± 0.003 fm -1
Small Corrections for
G n
E
G
E s
MEC
Assume Surface Thickness
Good to 25% (MFT)
R
N

A
W

0 .
656


1


0 e
 r
 a
R
0 .
060 ( stat )

0 .
014 ( syst ) ppm
F
W
( q )

1
Q
W
 d
3 r sin( qr )
 w
( r ) qr
F
W
( q )

0 .
204

0 .
028 (exp)

0 .
001 (mod)
R
W
Helm Model

5 .
826

0 .
181 (exp)

0 .
027 (mod) fm
R n
2 
Q w q n
N
R w
2  q p
Z q n
N
2
R ch
 r p
2 
Z
N r n
2 
Z

N q n
N r s
2
R n
2 
0 .
9525

R w
2 
1 .
671
 r s
2 
0 .
7450 fm
2
R n

5 .
751

0 .
175 (exp)

0 .
026 (mod)

0 .
005 ( str ) fm
(To be compared with R
N
= 5.78 + 0.16 - 0.18 fm)
G.M. Urciuoli

Asymmetry leads to R
N
A

0 .
656

0 .
060 ( stat )

0 .
014 ( syst ) ppm
PREX data
G.M. Urciuoli
R
N

6 .
156

1 .
675

A

3 .
420

A
2

G.M. Urciuoli

DATA
DATA r
N
= r
P theory: P. Ring
Atomic Number, A
cont.
0 .
.
656

0 .
.
060 ( ( ) ) 0 0 .
.
014 ( ( syst ) )
R
N
= 5.78 + 0.16 - 0.18 fm
R
N
= 5.78 + 0.16 - 0.18 fm
Neutron Skin = R
N fm
- R
P
= 0.33 + 0.16 - 0.18
Establishing a neutron skin at ~92 % CL
G.M. Urciuoli

target
PREX Region After Target
Tungsten
Collimator &
Shielding
Improvements for PREX-II
HRS-L
Q1
Q1
HRS-R
Former O-Ring location which failed & caused time loss during PREX-I
 PREX-II to use all-metal seals
Collimators

Strategy
• Tungsten ( W ) plug
0 .
7 0   
3 0
• Shield the W
• x 10 reduction in
0.2 to 10 MeV neutrons scattering chamber
J. Mammei, L. Zana
PREX-II shielding strategies shielding
Number of Neutrons per incident Electron
0 - 1 MeV beamline
1 - 10
MeV
Energy (MeV)
--- PREX-I
--- PREX-II, no shield
--- PREX-II, shielded
10 - 1200
MeV
Energy (MeV)
Energy (MeV)
26

(runs in 2013 or 2014) 
G.M. Urciuoli