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 (  r np ), defined as the difference between the neutron (r n ) and proton (r p ) root-mean-square (rms) radii (  r np ≡ r n − r p ), 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 precise measurement of the skin thickness of 208 Pb is very important for studying the radius, composition, and cooling system of neutron stars. Slope unconstrained by data Adding R N from 208 Pb 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 Scattering 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. J. Zenihiro et al., Phys. Rev. C 82 (2010) RCNP, Osaka University 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 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 204,206,208 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 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 and MeV average energy

Coherent π 0 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 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 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 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 photo- nuclear strength distribution σ γ E)

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

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 130,132 Sn A. Klimkiewicz et al. PHYSICAL REVIEW C 76, (R) (2007) 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.

Antiprotonic 208 Pb and 209 Bi 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, (2007)

Lead ( Pb) Radius Experiment : PREX Pb 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 Electron - Nucleus Potential electromagneticaxial Neutron form factor Parity Violating Asymmetry Proton form factor

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

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 SourceAbsolute (ppm) Relative ( % ) Polarization (1) Beam Asymmetries (2) Detector Linearity BCM Linearity Rescattering Transverse Polarization Q 2 (1) Target Thickness C Asymmetry (2) Inelastic States00 TOTAL Systematic Errors (1) Normalization Correction applied (2) Nonzero correction (the rest assumed zero)  Statistics limited ( 9% )  Systematic error goal achieved ! (2%) PREX Result R N = fm Neutron Skin = R N - R P = fm

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

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.

Spare

Other Nuclei Shape Dependence ? RNRN RNRN Surface thickness arXiv: [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 - Source Hall 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. Reflects poor understanding of symmetry energy of nuclear matter = the energy cost of n.m. density ratio 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 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…  - 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 in Pb the lower the threshold mass for direct URCA cooling. -If R n -R p <0.2 fm all EOS models do not have direct URCA in 1.4 M ¯ stars. -If R n -R p >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 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 Neutron Skin and Heavy – Ion Collisions ( Alex Brown)

G.M. Urciuoli High Resolution Spectrometers Elastic Inelastic detector 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 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 (P e 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 B 2 ). Flips spin without moving the beam ! Double Wien Filter Crossed 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 NOT melted

Septum Magnet target HRS-L HRS-R collimator 5 0 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 < nonlinearity. 120 Hz pair windows asymmetry distribution. No Gaussian tails up to 5 standard deviations.

y z x + - A T > 0 means Beam-Normal Asymmetry in elastic electron scattering i.e. spin transverse to scattering plane Possible systematic if small transverse spin component New results PREX 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

208 Pb Radius from the Weak Charge Form Factor 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 R N Helm Model = ± fm -1 G (To be compared with R N = fm)

Asymmetry leads to R N PREX data G.M. Urciuoli

Future: PREX-II G.M. Urciuoli

PREX Result, cont. theory: P. Ring Atomic Number, A r N - r P (fm) DATA r N = r P R N = fm Neutron Skin = R N - R P = fm G.M. Urciuoli Establishing a neutron skin at ~92 % CL R N = 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 MeV Energy (MeV) --- PREX-I --- PREX-II, no shield --- PREX-II, shielded MeV 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