Measurement of the neutronskin of heavy nuclei

G. M. Urciuoli

INFN Sezione di Roma

Why do we measure the neutron skin of heavy nuclei?

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 (rnp), defined as the difference between the neutron (rn) and proton (rp) root-mean-square (rms) radii (rnp ≡ rn − rp), depends on the balance among the various nuclear matter properties. In particular, the neutron skin thickness of 208Pb is strongly correlated with the nuclear symmetry energy or the pressure coefficients of the equation of states (EOS) in neutron matter. Moreover a precise measurement of the skin thickness of 208Pb is very important for studying the radius, composition, and cooling system of neutron stars .

Slope unconstrained by data Adding RN from 208Pb will eliminate the dispersion in plot.

How do we measure the neutron skin of heavy nuclei?

• Proton-Nucleus Elastic Scattering

• Pion, alpha, d Scattering

• Pion Photoproduction

• Heavy ion collisions

• Rare Isotopes (dripline)

• Magnetic scattering

• PREX (weak interaction)

• TheoryMFT fit mostly by data other than neutron densities

Involve strong probes

Most spins couple to zero.

Proton-Nucleus Elastic ScatteringWith 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.

J. Zenihiro et al., Phys. Rev. C 82 (2010) 044611RCNP, Osaka University

Differential cross sections and analyzing powers for

elastic scattering from 58Ni and 204,206,208Pb 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 58Ni with the realistic nucleon density by an unfolding charge density

Calibration of medium-effect parameters by fitting to the

experimental data for 58Ni. The solid line is the medium-

modified RIA calculation with best-fit parameters The

dashed and dash-dotted lines are from the original MH

model with DH and realistic nucleon densities.

Best-fit results for neutron density distributions

in 204,206,208Pb 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 208Pb with its standard

error envelope (solid lines). The dashed and dash-

dotted lines are medium-modified RIA calculations,

but using the DH nucleon densities and the 3pG neutron density by Ray [9], respectively

Pion-Nucleus Elastic ScatteringThe 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

Coherent π0 photoproduction

photon beam derived from the

production of Bremsstrahlung

photons during the

passage of the MAMI electron

beam through a thin radiator.

Crystal Ball Detector

Mainz Microtron MAMI

For first preliminary assessment

1) Carry out simple correction of q shift using the theory

2) Analyse corrected minima - fit with Bessel fn.

Simple Correction for distortion

GDR KVI

α of 196 MeV provided by the super-conducting cyclotronAGOR bombarded the enriched (99.0 %), self-supporting 208Pb target with a thickness of 20 mg/cm2.

The energy and the scattering angle of the α particles were measured with the Big-BiteSpectrometer . The emittd γ rays weredetected by a large 10x14 NaI(Tl) crystal

A. Krasznahorkay et al., Nuclear Physics A 731, 224 (2004)

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 208Pb. 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 σαα’( E)

were calculated as a function of excitation energy by assuming 100% exhaustion of the TRK EWSR. The results were then folded with the photo-

nuclear strength distribution σγE)

SDR

Krasznahorkay et al., Phys Rev Lett 82, 3216 (1999)

RCNP, Osaka

3He++ of 90.1 MeV acceleratedwith 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 114Sn, 116Sn, 118Sn, 120Sn, 122Sn, and 124Sn targets with thicknesses of 3.7 - 9.2 mg/cm2.The energy of tritons was measured with the magnetic spectrometer“Grand Raiden”. The ejectile tritons were detected with two multiwiredrift chambers (MWDC’s)

PDR

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 130,132Sn

A. Klimkiewicz et al. PHYSICAL REVIEW C 76, 051603(R) (2007)

SIS-18 synchrotron at GSI

Beam of 238U 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 132Sn passed through a 238Pb 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.

Antiprotonic 208Pb and 209Bi atoms

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)

Lead ( Pb) Radius Experiment : PREX208

208Pb

05

Elastic Scattering Parity Violating Asymmetry

Spokespersons

• Krishna Kumar

• Robert Michaels

• Kent Pascke

• Paul Souder

• Guido Maria Urciuoli

Hall A Collaboration Experiment

E = 1 GeV, electrons on lead

neutron weak charge >> proton weak charge

is small, best observed by parity violation

)()()(ˆ 5 rArVrV

||)()(/

//3 rrrZrdrV )()()sin41(22

)( 2 rNrZG

rA NPWF

22 |)(| QFd

d

d

dP

Mott

)()(4

1)( 0

32 rqrjrdQF PP )()(

4

1)( 0

32 rqrjrdQF NN

)(

)(sin41

222

22

2

QF

QFQG

d

d

d

d

d

d

d

d

AP

NW

F

LR

LR

Electron - Nucleus Potential

electromagnetic axial

Neutron form factor

Parity Violating Asymmetry

)(rA

1sin41 2 W

Proton form factor

0

G.M. Urciuoli

Measured Asymmetry

Weak Density at one Q 2

Neutron Density at one Q2

Correct for CoulombDistortions

Small Corrections for

GnE G

s

E MEC

Assume Surface Thickness Good to 25% (MFT)

Atomic Parity Violation

Mean Field

& Other

Models

Neutron

Stars

Rn

PREX Physics Impact

Heavy

Ions

Experimental Method

Flux Integration Technique:HAPPEX: 2 MHz

PREX: 850 MHz

G.M. Urciuoli

Consolidated techniques from the previous Hall A parity violating electron scatttering experiments (HAPPEX)

G.M. Urciuoli

Polarized Source P I T A Effect

(Polarization Induced Transport Asymmetry)

Intensity Feedback Beam Asymmetries

G.M. Urciuoli

Moller Polarimeter (< 1 % Polarimetry)

Upgrades:

Magnet Superconducting Magnet from Hall C

Target Saturated Iron Foil Targets

DAQ FADC

Compton Polarimeter (1 % Polarimetry)

Upgrades:

Laser Green Laser

Upgraded Polarimetry(Sirish Nanda et al.)

Error Source Absolute(ppm)

Relative ( % )

Polarization (1) 0.0071 1.1

Beam Asymmetries (2) 0.0072 1.1

Detector Linearity 0.0071 1.1

BCM Linearity 0.0010 0.2

Rescattering 0.0001 0

Transverse Polarization 0.0012 0.2

Q2 (1) 0.0028 0.4

Target Thickness 0.0005 0.1

12C Asymmetry (2) 0.0025 0.4

Inelastic States 0 0

TOTAL 0.0130 2.0

Systematic Errors

(1) Normalization Correction applied

(2) Nonzero correction (the rest assumed zero)

)(0140.0)(060.0

656.0

syststat

ppmA

Statistics limited ( 9% )

Systematic error goal achieved ! (2%)

2420.3675.1156.6 AARN

PREX Result

RN = 5.78 + 0.16 - 0.18 fm

Neutron Skin = RN - RP = 0.33 + 0.16 - 0.18 fm

PREX-II Approved by PAC (Aug 2011)

“A” Rating 35 days run in 2013 / 2014

G.M. Urciuoli

CREXPARITY-VIOLATING MEASUREMENT of the WEAK CHARGE DISTRIBUTION of 48Ca 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.

Spare

Other Nuclei

Shape Dependence ?

RN

RN

Surface thickness

Surface thickness

arXiv:1010.3246 [nucl-th]

Parity Violating Electron Scattering Measurements of Neutron Densities Shufang Ban, C.J. Horowitz, R. Michaels

G.M. Urciuoli

Measurement of the neutron skin in the past

G.M. Urciuoli

Hall A at Jefferson Lab

Polarized e-

SourceHall A

G.M. Urciuoli

PREX in Hall A at JLab

CEBAF

Hall A

Pol. Source

Lead Foil Target

Spectometers

G.M. Urciuoli

Nuclear Structure: Neutron density is a fundamental

observable that remains elusive.

ZN

Reflects poor understanding of symmetry energy of nuclear matter = the energy cost of

xn

)21()()2/1,(),( 2xnSxnExnE

n.m. densityratio proton/neutrons

• Slope unconstrained by data

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

N

208

G.M. Urciuoli

PREX & Neutron Stars( C.J. Horowitz, J. Piekarweicz )

R calibrates EOS of Neutron Rich Matter

Combine PREX R with Obs. Neutron Star Radii

Some Neutron Stars seem too Cold

N

N

Crust Thickness

Explain Glitches in Pulsar Frequency ?

Strange star ? Quark Star ?

Phase Transition to “Exotic” Core ?

- Thicker neutron skin in Pb means energy rises rapidly with density Quickly favors uniform phase.

- Thick skin in Pb low transition density in star.

- The 208Pb 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…

- 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.

G.M. Urciuoli

Atomic Parity Violation

• Low Q test of Standard Model

• Needs R to make further progress.

2

N

rdrZrNG

H eePWNF

PNC

35/2 )()sin41()(22

0

APV

Isotope Chain Experiments e.g. Berkeley Yb

G.M. Urciuoli

( R.J. Furnstahl )

Measurement at one Q is sufficient to measure R

2

N

Pins down the symmetry energy (1 parameter)

G.M. Urciuoli

Skx-s25

Skx-s20

Skx-s15

E/N

N

E/N

N

E/N

Neutron Skin and Heavy – Ion Collisions (Alex Brown)

N

G.M. Urciuoli

High Resolution Spectrometers

Elastic

Inelastic

detector

Q Q

Dipole

Quad

Spectrometer Concept:

Resolve Elastic

target

Left-Right symmetry to control transverse polarization systematic

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

Slug # ( ~ 1 day)

Units: microns

RLhelicityforXX LR ,

Average with signs = what exp’t feels

Points: Not sign corrected

Parity Quality

Beam !

Helicity – Correlated

Position Differences

< ~ 3 nm

Wien Flips helped !

G.M. Urciuoli

PREX Asymmetry (Pe x A)

ppm

Slug ~ 1 day

G.M. Urciuoli

• Two Wien Spin Manipulators in series• Solenoid rotates spin +/-90 degrees (spin rotation as B but focus as B2).

Flips spin without moving the beam !

Double Wien FilterCrossed E & B fields to rotate the spin

Electron Beam

SPIN

Joe Grames, et. al.

G.M. Urciuoli

Lead Target

G.M. Urciuoli

Diamond

LEAD

• Three bays

• Lead (0.5 mm) sandwiched by diamond (0.15 mm)

• Liquid He cooling (30 Watts)

melted

melted

NOT melted

target

HRS-L

HRS-R

collimator

collimator

50 Septum magnet

(augments the High Resolution Spectrometers)

(Increased Figure of Merit)

DETECTORS

Integrating Detection

The x, y dimensions of the quartz determined from beam test data and MC (HAMC) simulations.Quartz thickness optimized with MC..

New HRS optics tune focuses elastic events both in x & y at the PREx detector location

Deadtime free, 18 bit ADC with < 10-4 nonlinearity.

120 Hz pair windows asymmetry distribution.

No Gaussian tails up to 5 standard deviations.

y

z

xS

k

+ -

AT > 0 means

)'( eeeT kkSA

Beam-Normal Asymmetry in elastic electron scattering

i.e. spin transverse to scattering plane

Possible systematic if small transverse spin component

New results PREX

ppmAC T 35.036.052.6:12

ppmAPb T 36.019.013.0:208

• Small AT for 208Pb is a big (but pleasant) surprise.

• AT for 12C qualitatively consistent with 4He and available

calculations (1) Afanasev ; (2) Gorchtein & Horowitz

G.M. Urciuoli

208Pb Radius from the Weak Charge Form Factor

G.M. Urciuoli

G.M. Urciuoli

Measured Asymmetry

Fourier Transform of the Weak Charge Density at

Correct for Coulomb

Small Corrections for

G n

E

s

E MEC

Assume Surface Thickness Good to 25% (MFT)

Distorsion

ppmsyststatA )(014.0)(060.0656.0

RN

(mod)001.0(exp)028.0204.0)( qFW

aRr

eW

1

0

Helm Model

fmRW (mod)027.0(exp)181.0826.5

)()sin(1

)( 3 rqr

qrrd

QqF w

W

W

q= 0.475 ± 0.003 fm-1

222222

s

n

npch

n

p

w

n

wn r

Nq

NZr

N

ZrR

Nq

ZqR

Nq

QR

G

2222 7450.0671.19525.0 fmrRR swn

fmstrRn )(005.0(mod)026.0(exp)175.0751.5

(To be compared with RN = 5.78 + 0.16 - 0.18 fm)

Asymmetry leads to RN

PREX data

G.M. Urciuoli

ppmsyststatA )(014.0)(060.0656.0

2420.3675.1156.6 AARN

Future: PREX-II

G.M. Urciuoli

PREX Result, cont.

ppmsyststatA )(014.0)(060.0656.0

theory: P. Ring

Atomic Number, A

r N-

r P

(fm

)

DATA

DATA

rN = rP

RN = 5.78 + 0.16 - 0.18 fm

Neutron Skin = RN - RP = 0.33 + 0.16 - 0.18

fm

G.M. Urciuoli

ppmsyststatA )(014.0)(060.0656.0

Establishing a neutron skin at ~92 % CL

RN = 5.78 + 0.16 - 0.18 fm

Collimators

Septum Magnet

target

HRS-L

Q1

HRS-R

Q1

PREX Region After Target

Former O-Ring location which failed & caused time loss during PREX-I

PREX-II to use all-metal seals

Tungsten Collimator & Shielding

Improvements for PREX-II

Geant 4 Radiation Calculations

PREX-II shielding strategies

J. Mammei, L. Zana

Number of Neutrons per incident Electron

Strategy

• Tungsten ( W ) plug

• Shield the W

• x 10 reduction in

0.2 to 10 MeV neutrons

00 37.0

0 - 1 MeV

Energy (MeV)

Energy (MeV)

Energy (MeV)

--- PREX-I--- PREX-II, no shield--- PREX-II, shielded

1 - 10

MeV

10 - 1200

MeV

beamline

shielding

scattering chamber

26

Summary

• Fundamental Nuclear Physics with many applications

• Because of significant time-losses due to O-Ring problem and radiation damage PREX achieved a 9% stat. error in Asymmetry (original goal was 3 %).

• PREX measurement of Rn is nevertheless the cleanest performed so far

• Several experimental goals (Wien filters, 1% polarimetry at 1 GeV, etc.) were all achieved.

• Systematic error goal was consequently achieved too.

• PREX-II approved (runs in 2013 or 2014) 3% statistical error

G.M. Urciuoli