Measurement of the neutron skin of heavy nuclei. G. M. Urciuoli INFN Sezione di Roma

Transcription

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

2 Why do we measure the neutron skin of heavy nuclei? Slope unconstrained by data Adding R N eliminate the dispersion in plot. from 08 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 (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 08 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 08 Pb is very important for studying the radius, composition, and cooling system of neutron stars.

3 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) Involve strong probes Magnetic scattering Most spins couple to zero. PREX (weak interaction) Theory MFT fit mostly by data other than neutron densities

4 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. Differential cross sections and analyzing powers for elastic scattering from 58 Ni and 04,06,08 Pb at Ep = 95MeV, 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 04,06,08 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 08 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 8 (010)

5 Pion-Nucleus Elastic Scattering The cross section of - elastic scattering on the nucleon is relatively large in the (133) 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 9.-and 49.5-MeV average energy

6 Coherent π 0 photoproduction 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

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

8 GDR KVI α of 196 MeV provided by the super-conducting cyclotron AGOR bombarded the enriched (99.0 %), self-supporting 08 Pb target with a thickness of 0 mg/cm. 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 08 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, 4 (004)

9 SDR 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, 10 Sn, 1 Sn, and 14 Sn targets with thicknesses of mg/cm. 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 8, 316 (1999)

10 PDR SIS-18 synchrotron at GSI Beam of 38 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 13 Sn passed through a 38 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 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 130,13 Sn A. Klimkiewicz et al. PHYSICAL REVIEW C 76, (R) (007)

11 Antiprotonic 08 Pb and 09 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 (pf) describing the proton and neutron densities, the neutron rms radii are deduced

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13 Lead ( 08 Pb) Radius Experiment : 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 08 Pb Hall A Collaboration Experiment

14 neutron weak charge >> proton weak charge is small, best observed by parity violation ) ( ) ( ) ˆ( 5 r A r V r V ) ( ) ( / / / 3 r r r Z r d r V ) ( ) ( ) 4sin (1 ) ( r N r Z G r A N P W F ) ( Q F d d d d P Mott ) ( ) ( 4 1 ) ( 0 3 r qr j r d Q F P P ) ( ) ( 4 1 ) ( 0 3 r qr j r d Q F N N ) ( ) ( 4sin 1 Q F Q F Q G d d d d d d d d A P N W F L R L R Electron - Nucleus Potential electromagnetic axial Neutron form factor Parity Violating Asymmetry A(r) 1 4sin 1 W Proton form factor 0

15 PREX Physics Impact Measured Asymmetry Correct for Coulomb Distortions Atomic Parity Violation Weak Density at one Q Small Corrections for G n E G s E MEC Neutron Density at one Q Mean Field & Other Models Assume Surface Thickness Good to 5% (MFT) Heavy Ions Neutron Stars R n

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

17 Consolidated techniques from the previous Hall A parity violating electron scatttering experiments (HAPPEX) Polarized Source P I T A Effect (Polarization Induced Transport Asymmetry) Intensity Feedback Beam Asymmetries

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

19 Error Source PREX Result Systematic Errors Absolute (ppm) Polarization (1) Beam Asymmetries () Detector Linearity BCM Linearity Rescattering Transverse Polarization Q (1) Target Thickness C Asymmetry () Relative ( % ) A ppm 0.060( stat) Statistics limited ( 9% ) Systematic error goal achieved! (%) ( syst) Inelastic States 0 0 TOTAL (1) Normalization Correction applied R N = fm () Nonzero correction (the rest assumed zero) Neutron Skin = R N - R P = fm R N A 3.40 A

20 PREX-II Approved by PAC (Aug 011) A Rating 35 days run in 013 / 014

21 CREX PARITY-VIOLATING MEASUREMENT of the WEAK CHARGE DISTRIBUTION of 48 Ca to 0.0 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.

22 Spare

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

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25 Measurement of the neutron skin in the past

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

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

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 N Z E( n, x) E( n, x 1/ ) S ( n) (1 x ) n n.m. density x ratio proton/neutrons Slope unconstrained by data 08 Adding R N from Pb will eliminate the dispersion in plot.

29 PREX & R calibrates EOS of N Neutron Rich Matter Crust Thickness Neutron Stars ( C.J. Horowitz, J. Piekarweicz ) - Thicker neutron skin in Pb means energy rises rapidly with density Quickly favors uniform phase. - Thick skin in Pb low transition density in star. Explain Glitches in Pulsar Frequency? Combine PREX R Neutron Star Radii with Obs. Phase Transition to Exotic Core? Strange star? Quark Star? N - The 08 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 - 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. fm all EOS models do not have direct URCA in 1.4 M stars. - If R n -R p >0.5 fm all models do have URCA in 1.4 M stars.

30 Atomic Parity Violation Low Q test of Standard Model Needs R to make further progress. H PNC APV G F N / 5 3 N ( r) Z (1 4sin ) ( r ) d r N 0 W P Isotope Chain Experiments e.g. Berkeley Yb e e

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

32 Neutron Skin and Heavy Ion Collisions (Alex Brown) E/N Skx-s15 N Skx-s0 N E/N Skx-s5 N E/N

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

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

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

36 PREX Asymmetry (P e x A) ppm Slug ~ 1 day

37 Electron Beam 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 B ). Flips spin without moving the 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 5 0 Septum magnet (augments the High Resolution Spectrometers) (Increased Figure of Merit) HRS-L HRS-R collimator collimator target

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

41 Beam-Normal Asymmetry in elastic electron scattering A T i.e. spin transverse to scattering plane S e ( k ek' e) Possible systematic if small transverse spin component New results PREX x k y S A T > 0 means z Pb: AT ppm 1 C: AT ppm Small A T for 08 Pb is a big (but pleasant) surprise. A T for 1 C qualitatively consistent with 4 He and available calculations (1) Afanasev ; () Gorchtein & Horowitz

42 08 Pb Radius from the Weak Charge Form Factor

43 Measured Asymmetry A ( stat) 0.014( syst) ppm Correct for Coulomb Distorsion W 0 1 e r a R F W ( q) 1 Q W d 3 r sin( qr) qr ( r) w Fourier Transform of the Weak Charge Density at q= ± fm -1 Small Corrections for G n E G s E MEC R n F W ( q) (exp) Helm Model 0.001(mod) R W (exp) 0.07(mod) fm Qw q N n R w q q p n Z N R ch r p Z N r n Z N q N n r s Assume Surface Thickness Good to 5% (MFT) R n Rw rs fm R N R n (exp) 0.06(mod) 0.005( str) fm (To be compared with R N = fm)

44 Asymmetry leads to R N A ( stat) 0.014( syst) ppm PREX data R N A 3.40 A

45 Future: PREX-II

46 r N - r P (fm) r N = r P PREX Result, cont. DATA A ( stat ) 0.014( syst ) ppm R N = fm DATA R N = fm Neutron Skin = R N - R P = fm Establishing a neutron skin at ~9 % CL theory: P. Ring Atomic Number, A

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

48 scattering chamber shielding Geant 4 Radiation Calculations J. Mammei, L. Zana PREX-II shielding strategies Number of Neutrons per incident Electron beamline 0-1 MeV Strategy Tungsten ( W ) plug Shield the W MeV MeV Energy (MeV) --- PREX-I --- PREX-II, no shield --- PREX-II, shielded Energy (MeV) x 10 reduction in 0. to 10 MeV neutrons Energy (MeV) 6

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 013 or 014) 3% statistical error