Measurement of the neutron skin of heavy nuclei

1. Measurement of the neutronskin of heavy nuclei G. M. Urciuoli INFN Sezione di Roma

2. Why do wemeasure the neutronskin of heavynuclei? 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 RNfrom 208Pb will eliminate the dispersion in plot.

3. How do wemeasure the neutronskin 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 Involve strong probes Most spins couple to zero. MFT fit mostly by data other than neutron densities

4. With high-energypolarizedprotons 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. Proton-Nucleus Elastic Scattering 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 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 Calibration of medium-effectparametersby 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. RCNP, Osaka University J. Zenihiro et al., Phys. Rev. C 82 (2010) 044611

5. 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. TRIUMF R. R. Johnson et al., PHYS REV LETT 43, 844 (1979) Π- of 29.2-and 49.5-MeV averageenergy

6. Coherentπ0photoproduction Mainz MicrotronMAMI photon beam derived from the production of Bremsstrahlung photons during the passage of the MAMI electron beam through a thin radiator. Crystal Ball Detector

7. 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.

8. GDR KVI α of 196 MeVprovided by the super-conducting cyclotron AGOR bombarded the enriched (99.0 %), self-supporting 208Pb target with a thickness of 20 mg/cm2. The energy and the scattering angle of the αparticles were measured with the Big-Bite Spectrometer. The emittdγrayswere 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 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) macroscopicmodelswereadopted. Coulombexcitation 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) A. Krasznahorkay et al., NuclearPhysics A 731, 224 (2004)

9. RCNP, Osaka 3He++ of 90.1 MeVaccelerated with the AVF cyclotronwerinjected 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“GrandRaiden”. The ejectile tritons were detected with two multiwire driftchambers (MWDC’s) SDR Krasznahorkay et al., PhysRevLett 82, 3216 (1999)

10. PDR SIS-18 synchrotronat GSI Beam of 238U ions of 550 MeV/nucleon Secondary radioactive ions were produced by fission in a Be target Aseries of fully self-consistent RHB model plus RQRPA calculationsof 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 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. A. Klimkiewicz et al. PHYSICAL REVIEW C 76, 051603(R) (2007)

11. Antiprotonic208Pb 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 atn=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)

13. Lead( Pb) Radius Experiment : PREX 208 Elastic Scattering Parity Violating Asymmetry E = 1 GeV, electrons on lead • Spokespersons • Krishna Kumar • Robert Michaels • Kent Pascke • Paul Souder • Guido Maria Urciuoli 208Pb Hall A Collaboration Experiment

14. Electron - Nucleus Potential electromagnetic axial is small, best observed by parity violation neutron weak charge >> proton weak charge Proton form factor Neutron form factor Parity Violating Asymmetry

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

16. Flux Integration Technique: HAPPEX: 2 MHz PREX: 850 MHz Experimental Method

17. Consolidatedtechniquesfrom the previous Hall A parityviolating electron scattteringexperiments (HAPPEX) Polarized Source P I T A Effect (Polarization Induced Transport Asymmetry) Intensity Feedback Beam Asymmetries

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

19. PREX Result Systematic Errors • Statistics limited ( 9% ) • Systematic error goal achieved ! (2%) (1) Normalization Correction applied (2) Nonzero correction (the rest assumed zero) RN = 5.78 + 0.16 - 0.18 fm Neutron Skin = RN - RP = 0.33 + 0.16 - 0.18 fm

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

21. PARITY-VIOLATING MEASUREMENT of the WEAK CHARGE DISTRIBUTION of 48Ca to 0.02 fm ACCURACY CREX 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.

22. Spare

23. Other Nuclei RN Shape Dependence ? Surface thickness Parity Violating Electron Scattering Measurements of Neutron Densities Shufang Ban, C.J. Horowitz, R. Michaels RN Surface thickness arXiv:1010.3246  [nucl-th]

25. Measurement of the neutronskin in the past

26. Polarized e- Source Hall A Hall A at Jefferson Lab

27. Pol. Source Hall A CEBAF PREX in Hall A at JLab Spectometers Lead Foil Target

28. Nuclear Structure:Neutron density is a fundamental observable that remains elusive. Reflects poor understanding of symmetry energy of nuclear matter = the energy cost of ratio proton/neutrons n.m. density • Slope unconstrained by data • Adding R from Pb will eliminate the dispersion in plot. 208 N

29. PREX & Neutron Stars ( C.J. Horowitz, J. Piekarweicz ) R calibrates EOS of Neutron Rich Matter    N - Thicker neutron skin in Pb means energy rises rapidly with density  Quickly favors uniform phase. - Thick skin in Pb low transition density in star. Crust Thickness Explain Glitches in Pulsar Frequency ? • - 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… Combine PREX R with Obs. Neutron Star Radii N Phase Transition to “Exotic” Core ? Strange star ?Quark Star ? • - 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. Some Neutron Stars seem too Cold

30. Atomic Parity Violation • Low Q test of Standard Model • Needs R to make further progress. 2 Isotope Chain Experiments e.g. Berkeley Yb N APV

31. 2 Measurement at one Q is sufficient to measure R Pins down the symmetry energy (1 parameter) N ( R.J. Furnstahl )

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

33. High Resolution Spectrometers Spectrometer Concept: Resolve Elastic Elastic detector Inelastic Left-Right symmetry to control transverse polarization systematic Quad target Dipole Q Q

34. An electromagneticprobe, due to its simple reaction mechanism, can extract precise information about the density deep inside a nucleus

35. Parity Quality Beam ! Helicity – Correlated Position Differences < ~ 3 nm Wien Flips helped ! Points: Not sign corrected Average with signs = what exp’t feels Units: microns Slug # ( ~ 1 day)

36. PREX Asymmetry (Pe x A) ppm Slug ~ 1 day

37. Double Wien Filter 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 B2). • Flips spin without moving the beam ! Electron Beam SPIN Joe Grames, et. al.

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

39. 50 Septum magnet (augments the High Resolution Spectrometers) (Increased Figure of Merit) HRS-L HRS-R collimator Septum Magnet collimator target

40. Integrating Detection Deadtime free, 18 bit ADC with < 10-4 nonlinearity. DETECTORS 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 120 Hz pair windows asymmetry distribution. No Gaussian tails up to 5 standard deviations.

41. y AT > 0 means - x + z 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 AT for 208Pb is a big (but pleasant) surprise. • AT for 12C qualitatively consistent with 4He and available calculations (1) Afanasev ; (2) Gorchtein & Horowitz

42. 208Pb Radiusfrom the WeakChargeFormFactor

43. Measured Asymmetry Correct for Coulomb Distorsion Fourier Transform of the Weak Charge Density at = 0.475 ± 0.003 fm-1 Helm Model Small Corrections for n s G G MEC E E Assume Surface Thickness Good to 25% (MFT) R N (To be compared with RN = 5.78 + 0.16 - 0.18 fm)

44. Asymmetry leads to RN PREX data

45. Future: PREX-II

46. PREX Result, cont. rN = rP DATA RN = 5.78 + 0.16 - 0.18 fm  RN = 5.78 + 0.16 - 0.18 fm Neutron Skin = RN - RP = 0.33 + 0.16 - 0.18 fm DATA rN - r P (fm) Establishing a neutron skin at ~92 % CL theory: P. Ring Atomic Number, A

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

48. Geant 4 Radiation Calculations PREX-II shielding strategies J. Mammei, L. Zana scattering chamber shielding Number of Neutrons per incident Electron 0 - 1 MeV beamline Energy (MeV) --- PREX-I --- PREX-II, no shield --- PREX-II, shielded 1 - 10 MeV • Strategy • Tungsten ( W ) plug • Shield the W • x 10 reduction in • 0.2 to 10 MeV neutrons Energy (MeV) 10 - 1200 MeV Energy (MeV) 26

49. 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