1 Electric Dipole Response, Neutron Skin, and Symmetry Energy (II) Atsushi Tamii Research Center for Nuclear Physics (RCNP) Osaka University, Japan CNS Summer School 2013 August 28 – September 3, 2013

Outline of the lecture 1.Symmetry energy mass formula nuclear density distribution nuclear equation of state (EOS) 2.Determination the neutron skin thickness and the symmetry energy by using weak interaction strong interaction electro-magnetic interaction

Steiner et al., Phys. Rep (2005) 核子当たりのエネル ギー Nucleon Density (fm -3 ) E/A (MeV) E/N (MeV) Neutron Density (fm -3 ) Nuclear Equation of State (EOS) Neutron Matter (  =1) Prediction of the neutron matter EOS is much model dependent. Neutron Matter (  =1) Symmetry Energy (and Coulomb) Nuclear Matter (  =0)

Supernova Cycle Langanke and Martinez-Pinedo Type II Supernova

Determination of the Symmetry Energy Term in EOS. Lattimer et al., Phys. Rep. 442, 109(2007) Accreting neutron star/white dwarf, X-Ray burst, Superburst Neutron Star Mass and Radius Neutron Star Structure Core-Collapse Supernova Neutron Star Cooling Nucleosynthesis K. Sumiyoshi, Astrophys. J. 629, 922 (2005) Langanke and Martinez-Pinedo

Fundamental Questions: How large and how stiff is a neutron star? What is the inner structure? How much content of protons and electrons? Do meson-condensed states or hyperons exist? Neutron Star For answering to the questions, precise knowledge is required for the EOS of nuclear and neutron rich matter.

Nuclear Equation of State (EOS) Determination of L is becoming important. Symmetry energy L: Slope Parameter EOS for Energy per nucleon Saturation Density ~0.16 fm -3 (Baryonic Pressure)

Neutron density Proton density Neutron rms radius Proton rms radius Neutron Skin and the Density Dependence of the Symmetry Energy Neutron skin thickness Density dependence of the symmetry energy Density distribution of protons and neutrons in a nucleus X. Roca-Maza et al., PRL106, (2011)

Experimental Methods Symmetry Energy Nuclear mass formula Neutron skin thickness Heavy Ion Collision Isobaric analogue state energy Neutron-star observation … Neutron Skin Thickness Parity-violating electron elastic scattering Proton elastic scattering Electric dipole polarizability Giant dipole resonance Pygmy dipole resonance Spin dipole resonance Anti-protonic atom X-ray … Anti-analogue GDR of 208 Pb: talk by J. Yasuda PDR in Sn isotopes: talk by P. Schrock Posters by Nakatsuka, D.T. Khoa, … 208 Pb

10 [1] B. Frois et al, PRL38, 152(1977) charge radius: 5.50 fm point proton radius: 5.45 fm ( by using formula in [41]) charge radius: 5.50 fm point proton radius: 5.45 fm ( by using formula in [41]) Charge Density (Electron Scattering)

Outline of the lecture 1.Symmetry energy mass formula nuclear density distribution nuclear equation of state (EOS) 2.Determination the neutron skin thickness and the symmetry energy by using weak interaction strong interaction electro-magnetic interaction at J-Lab at RCNP

12 page-2 Parity Violating (PV) Cross Section Asymmetry in Electron Scattering [8] in PWBA R L e e ϑ ϑ R (L): Right (Left) helicity longitudinal polarization G F : Fermi coupling constant α: fine structure constant Q: four-momentum transfer (ω,q) F W : weak form factor F ch : charge form factor interference between EM and weak interactions helicity Coulomb distortion effect is included in the real analysis [9], also other effects [10]. Fourier transform of the weak charge density + 2 A PV from interference 208 Pb

13 Weak Charge Weak charge distribution is primarily determined by the neutron distribution J-F. Rajotte, arxiv: v1 ϑ w : Weinberg Angle or Weak Mixing Angle sin 2 ϑ w = (12) c.f. PDG 2012 ~ with radiative correction in the standard model BUT weak interaction is VERY weak... APV ~ 656 ppb =

Hall A at Jefferson Lab Hall A B C

PREX at J-Lab: Z 0 of weak interaction : sees the neutrons p n Electric charge 1 0 Weak charge Parity Violating Asymmetry Model independent determination of the neutron skin thickness Neutron Skin Thickness Measurement by Electroweak Interaction S. Abrahamyan et al., PRL108, (2012) C.J. Horowitz

Neutron Skin Thickness Measurement by Electroweak Interaction PREX PREX Result: S. Abrahamyan et al., PRL108, (2012) Theor. Calc.: X. Roca-Maza et al., PRL106, (2011) The model independent determination of  R np by PREX is quite important but the present accuracy is limited.

Outline of the lecture 1.Symmetry energy mass formula nuclear density distribution nuclear equation of state (EOS) 2.Determination the neutron skin thickness and the symmetry energy by using weak interaction strong interaction electro-magnetic interaction at J-Lab at RCNP

Determination of Neutron Density Distribution by Strong Interaction Polarized proton elastic scattering at 295 MeV (RCNP, Osaka University) Analysis with relativistic impulse approximation (RIA), medium modification fixed with 58 Ni data J.Zenihiro et al., PRC 82, (2010) d  /d  Ay  n (r) RIA + Medium Effect  r n /r n < 0.5% R n -R p =0.211 fm

Medium modification of RLF NN interaction Medium effect H. Sakaguchi et al., PRC57,  Phenomenological parameters; a j, b j  Universal form of density-dependent terms  At  =0, same as free NN interaction Need to calibrate with real data

X. Roca-Maza et al., PRL106, (2011)

Outline of the lecture 1.Symmetry energy mass formula nuclear density distribution nuclear equation of state (EOS) 2.Determination the neutron skin thickness and the symmetry energy by using weak interaction strong interaction electro-magnetic interaction at J-Lab at RCNP

P.-G. Reinhard and W. Nazarewicz, PRC 81, (R) (2010). Covariance analysis of energy density functional calculations with Skrym SV-min effective interaction. Neutron Skin Thickness Measurement by Electromagnetic Interaction Strong correlation between the (electric) dipole polarizability and the neutron skin of 208 Pb

(Electric) Dipole Polarizability Inversely energy weighted sum-rule of B(E1) P: electric dipole moment  : electric dipole polarizability

(Electric) Dipole Polarizability E1-field restoring force symmetry energy balanced

(Electric) Dipole Polarizability with neutron skin smaller restoring force w/o neutron skin larger restoring force

(Electric) Dipole Polarizability with neutron skin smaller restoring force w/o neutron skin thicker neutron skin smaller restoring force larger displacement larger dipole polarizability

(Electric) Dipole Polarizability with neutron skin smaller restoring force w/o neutron skin larger restoring force

(Electric) Dipole Polarizability Inversely energy weighted sum-rule of B(E1) P: electric dipole moment  : electric dipole polarizability

SnSn SpSp Particle （ neutron ） separation energy 0 (PDR) GDR g.s. oscillation of neutron skin against core? oscillation between neutrons and protons E1 1 - core neutron skin Low-Lying Dipole Strength Electric Dipole (E1) Response

Coulomb Excitation at 0 deg. Excited State Target Nucleus Real Photon Measurements, NRF and ( ,xn) Probing EM response of the target nucleus Decay  -rays or neutrons are measured. Select low momentum transfer (q~0) kinematical condition, i.e. at zero degrees Excited State Target Nucleus Missing Mass Spectroscopy with Virtual Photon Insensitive to the decay channel. Total strengths are measured. Only the scattered protons are measured. EM Interaction is well known (model independent) q,q,

High-resolution Spectrometer Grand Raiden High-resolution WS beam-line (dispersion matching) Research Center for Nuclear Physics, Osaka Univ.

Spectrometers in the 0-deg. experiment setup Intensity : 1-8 nA As a beam spot monitor in the vertical direction Dispersion Matching Polarized Proton Beam at 295 MeV Focal Plane Polarimeter AT et al., NIMA605, 326 (2009) 208 Pb target: 5.2 mg/cm 2

Setup for E282&E316

Excellent agreement between (p,p’) and ( ,  ’) below ~S n I. Poltoratska, PhD thesis B(E1): low-lying discrete states

Neglect of data for  >4: (p,p´) response too complex Included E1/M1/E2 or E1/M1/E3 (little difference) B(E1): continuum and GDR region Method 1: Multipole Decomposition

spinflip / non-spinflip separation Polarization observables at 0° E1 and M1 decomposition T. Suzuki, PTP 103 (2000) 859 E1 M1 model-independent B(E1): continuum and GDR region Method 2: Decomposition by Spin Observables

E1 Response of 208 Pb and  D AT et al., PRL107, (2011) combined data The B(E1) distribution and dipole polarizability of 208 Pb has been precisely determined.

Correlation Between Dipole Polarizability and Neutron Skin Thickness J. Piekarewicz et al., PRC85, (2012)

Correlation Between Dipole Polarizability and Neutron Skin Thickness Theoretical models can be much constrained if precise data on the neutron skin thickness is also available (but not).

Correlation Between Dipole Polarizability and Neutron Skin Thickness

Neutron Skin Thickness Measurement by Electromagnetic Interaction PES: Proton Elastic Scattering, Zenihiro et al., PRC.

Based on the work by X. Roca-Maza et al., PRL106, (2011) DP: Dipole Polarizability L  ±15 MeV

X. Roca-Maza et al., arXiv:  D J is a strong isovector indicator. Insights from the droplet model Talk by X. Roca-Maza (next session)

X. Roca-Maza et al., arXiv: It would be better to use the correlation between  D J and L (or  np ) than use the correlation between  D and L (or  np) to extract constraints. We have used the correlation between  D J and L (gray band in the right figure) to extract a constraint band in the J-L plane.

DP: Dipole Polarizability HIC: Heavy Ion Collision PDR: Pygmy Dipole Resonance IAS: Isobaric Analogue State FRDM: Finite Range Droplet Model (nuclear mass analysis) n-star: Neutron Star Observation  EFT: Chiral Effective Field Theory Constraints on J and L M.B. Tsang et al., PRC86, (2012). I. Tews et al., PRL110, (2013)

DP: Dipole Polarizability HIC: Heavy Ion Collision PDR: Pygmy Dipole Resonance IAS: Isobaric Analogue State FRDM: Finite Range Droplet Model (nuclear mass analysis) n-star: Neutron Star Observation  EFT: Chiral Effective Field Theory M.B. Tsang et al., PRC86, (2012). I. Tews et al., PRL110, (2013) DP: + theoretical uncertainty Constraints on J and L

DP: Dipole Polarizability HIC: Heavy Ion Collision PDR: Pygmy Dipole Resonance IAS: Isobaric Analogue State FRDM: Finite Range Droplet Model (nuclear mass analysis) n-star: Neutron Star Observation  EFT: Chiral Effective Field Theory M.B. Tsang et al., PRC86, (2012). I. Tews et al., PRL110, (2013) QMC by S. Gandolfi et al., QMC Constraints on J and L DP: + theoretical uncertainty

“The concordance of experimental, theoretical and observational analyses suggests that neutron star radii, in the mass range 1 M -2 M, lie in the narrow window 11 km < R < 12 km.” Lattimer et al., arXiv v1(2012) QMC

Earth Sun 110 times larger than the earth 1 M

RIKEN Size of a Neutron Star (R~12km) (1.4 M ) Neutron star

Size of a Neutron Star (R~12km) (1.4 M ) Neutron star R ~ 12 km 208 Pb nucleus R ~ 6 fm

Summary of the part 2 I have discussed experimental attempts to determine the neutron skin thickness of 208Pb by measuring parity-violating electron scattering (weak int.) proton elastic scattering (strong int.) 3dipole polarizability (EM int.) present constraints on the symmetry energy parameters J and L.

The electric dipole response of 208 Pb has been precisely measured by using proton inelastic scattering as an electro magnetic probe. as  D =20.1±0.6 fm 3 /e 2 Summary A lot of data under analysis: 96 Mo (DCS and PT): D. Martin 48 Ca (DCS): J. Birkhan 90 Zr (DCS): C. Iwamoto (PDR-region, published in PRL108, (2012)) 120 Sn (DCS and PT): A.M. Krumbholtz, T. Hashimoto 154 Sm (DCS and PT): A. Krugmann 88 Sr, 92 Mo (DCS): C. Iwamoto 70 Zn (DCS):

55 Collaborators RCNP, Osaka University A. Tamii, H. Matsubara, H. Fujita, K. Hatanaka, H. Sakaguchi Y. Tameshige, M. Yosoi and J. Zenihiro Dep. of Phys., Osaka University Y. Fujita Dep. of Phys., Kyoto University T. Kawabata CNS, Univ. of Tokyo K. Nakanishi, Y. Shimizu and Y. Sasamoto CYRIC, Tohoku University M. Itoh and Y. Sakemi Dep. of Phys., Kyushu University M. Dozono Dep. of Phys., Niigata University Y. Shimbara IKP, TU-Darmstadt P. von Neumann-Cosel, A-M. Heilmann, Y. Kalmykov, I. Poltoratska, V.Yu. Ponomarev, A. Richter and J. Wambach KVI, Univ. of Groningen T. Adachi and L.A. Popescu IFIC-CSIC, Univ. of Valencia B. Rubio and A.B. Perez-Cerdan Sch. of Science Univ. of Witwatersrand J. Carter and H. Fujita iThemba LABS F.D. Smit Texas A&M Commerce C.A. Bertulani GSI E. Litivinova RCNP-E282

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