measurement of the neutron skin of heavy nuclei
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Measurement of the neutron skin of heavy nuclei . G. M. Urciuoli INFN Sezione di Roma. Why do we measure the neutron skin of heavy nuclei?. - PowerPoint PPT PresentationTRANSCRIPT
Measurement of the neutron skin 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)
• Theory MFT 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 Thedashed and dash-dotted lines are from the original MH model with DH and realistic nucleon densities.
Best-fit results for neutron density distributionsin 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 Scattering
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
Coherent π0 photoproduction
photon beam derived from the production of Bremsstrahlungphotons during thepassage 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 were detected 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 GSIBeam of 238U ions of 550 MeV/nucleon
Secondary radioactive ions were produced by fission in a Be targetFission products with a mass-to-chargeratio around that of 132Sn passed through a 238Pb targetDipole-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
)()()(ˆ5 rArVrV
||)()(///3 rrrZrdrV )()()sin41(
22)( 2 rNrZ
GrA NPW
F
22 |)(| QFdd
dd
PMott
)()(41)( 0
32 rqrjrdQF PP )()(
41)( 0
32 rqrjrdQF NN
)()(
sin4122 2
22
2
QFQFQG
dd
dd
dd
dd
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 Q 2
Correct for CoulombDistortions
Small Corrections forG
nE G
sE MEC
Assume Surface Thickness Good to 25% (MFT)
Atomic Parity Violation
Mean Field & Other Models
Neutron
Stars
R n
PREX Physics Impact
Heavy Ions
Experimental Method
Flux Integration Technique:HAPPEX: 2 MHzPREX: 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 1.1BCM Linearity 0.0010 0.2Rescattering 0.0001 0Transverse Polarization 0.0012 0.2 Q2 (1) 0.0028 0.4 Target Thickness 0.0005 0.112C Asymmetry (2) 0.0025 0.4Inelastic States 0 0TOTAL 0.0130 2.0
Systematic Errors
(1) Normalization Correction applied
(2) Nonzero correction (the rest assumed zero)
)(0140.0)(060.0656.0
syststatppmA
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 theoreticalpredictions 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
CEBAFHall 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. density
ratio proton/neutrons
• Slope unconstrained by data• Adding R from Pb will eliminate the
dispersion in plot.
N208
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
PNC35/2 )()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 dayG.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
Septum Magnet
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
x S
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 forG n
Es
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
qrrdQ
qF wW
W
q
= 0.475 ± 0.003 fm-1
222222s
nnpch
n
pw
n
wn r
NqNZr
NZrR
NqZq
RNq
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