Probing the Nuclear Symmetry Energy and Neutron Skin from Collective Excitations. N. Paar

Transcription

1 Calcium Radius Experiment (CREX) Workshop at Jefferson Lab, March 17-19, 2013 Probing the Nuclear Symmetry Energy and Neutron Skin from Collective Excitations N. Paar Physics Department Faculty of Science University of Zagreb Croatia

2 CONTENTS What are relationships between the properties of collective modes of excitation, symmetry energy and neutron skin thickness? Which dynamic observables constrain the neutron distribution and neutron skin thickness in finite nuclei? Applications of dipole excitations and antianalog giant dipole resonance, based on recent experimental data and relativistic nuclear energy density functional, in constraining the neutron-skin thickness in nuclei, nuclear matter symmetry energy at saturation density and slope of the symmetry energy Assessing statistical correlations by means of covariance analysis involving response properties of nuclei, nuclear matter properties, and ground state properties. Theoretical uncertainties in modeling various observables. P.-G. Reinhard, W. Nazarewicz, X. Roca-Maza, G. Colò, J. Piekarewicz, D. Vretenar

3 THEORY FRAMEWORK RELATIVISTIC NUCLEAR ENERGY DENSITY FUNCTIONAL System of Dirac nucleons coupled by the exchange mesons and the photon field - unified microscopic description of the structure of finite nuclei - in the limit of small amplitude vibrations, fully self-consistent relativistic quasiparticle RPA (RQRPA) allows analysis of giant resonances, low-energy multipole response in weakly-bound nuclei, dynamics of exotic modes of excitation, weak interaction rates, neutrino-nucleus reactions, etc. D. Vretenar, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Phys. Rep. 409, 101(2005). N.P., D. Vretenar, E. Khan, G. Colò, Rep. Prog. Phys. 70, 1 (2007).

4 CONSTRAINTS ON THE SYMMETRY ENERGY AND NEUTRON SKINS In order to explore the evolution of the excitation spectra as a function of the density dependence of the symmetry energy, a set of interactions is used, that span a broad range of values for the symmetry energy at saturation density (J) and the slope parameter (L). R[e 2 fm 2 /MeV] Sn DD-ME J=30, L=30.0 MeV J=32, L=46.5 MeV J=34, L=62.1 MeV J=36, L=85.5 MeV J=38, L=110.8 MeV E E[MeV] Nuclear matter energy per part.: E(, ) =E(, 0) + S 2 ( ) =(N Z)/A Symmetry energy term: S 2 ( ) =J L +... =( 0 )/(3 0 ) L =3 0 ds 2 ( ) dr 0

5 Constraining the symmetry energy from dipole polarizability Theoretical constraints on the symmetry energy at saturation density (J) and slope of the symmetry energy (L) from dipole polarizability (α D ) using relativistic nuclear energy density functionals D = 8 9 e2 m 1 Exp. data from polarized proton inelastic scattering, α D =18.9(13)fm 3 /e 2 A. Tamii et al., PRL. 107, (2011) 24 DD-ME 208 Pb Pb α D [fm 3 ] 20 α D [fm 3 ] J [MeV] J=(32.6±1.4) MeV L [MeV] L=(50.9±12.6) MeV

6 PYGMY DIPOLE STRENGTH IN 68 Ni The pygmy dipole strength for 68 Ni and comparison to experimental data è γ decay from Coulomb excitation of 68 Ni at 600 MeV/nucleon (INFN,GSI, ) DD-ME2 S EW (E1) [e 2 fm 2 MeV] % EWSR (TRK) B(E1) [e 2 fm 2 ] RNEDF % 1.57 Exp ± 3.7 (5±1.5) % MeV: coherent neutron transitions: 2p3/2è 3s1/2 2p3/2, 2p1/2,1f5/2: 2p1/2è 2d3/2 1f5/2è 2d3/2 12 excess neutrons 1f5/2è 2d5/2 above N=Z core EXCESS NEUTRONS OSCILLATION MODE O. Wieland et al., PRL 102, (2009)

7 Constraining the symmetry energy Various constraints from dipole excitations on the slope of the symmetry energy (L) and symmetry energy at saturation density (J) DD-ME PDR - 68 Ni PDR Sn PDR Pb Energy weighted pygmy dipole strength in 68 Ni, 132 Sn, 208 Pb L [MeV] α D Pb Klimkiewicz et al PDR - 130,132 Sn Dipole polarizability in 208 Pb PDR/GDR B(E1) strength in 132 Sn, 130 Sn (Klimkiewicz et al. 2007) J [MeV] Based on exp. data on PDR & α D 68 Ni : O. Wieland et al, PRL. 102, (2009) 132,130 Sn: A. Klimkiewicz et al., PRC 76, (R) (2007) 208 Pb: I. Poltoratska et al., PRC 85, (R) (2012) 208 Pb (α D ): A. Tamii et al., PRL 107, (2011)

8 Constraining the symmetry energy Constraining the symmetry energy at saturation density and slope of the symmetry energy from various approaches: 120 HIC 100 QMC & neutron star FRDM L [MeV] IAS 208 Pb(p,p) PDR (Carbone 2010) PDR - 68 Ni, 132 Sn α D Pb J [MeV] Also see M. B. Tsang et al., PRC 86, (2012)

9 Covariance analysis Model dependence Pierson product-moment correlation Relativistic functionals: Relativistic point coupling model () Relativistic model with density dependent meson-nucleon couplings () The model parameters (9) of both interactions are constrained by the same set of (17) nuclei and their properties: binding energies, charge radii, diffraction radii, surface thickness (N.P.) (for relativistic EDFs FSUGold also see talk by J. Piekarewicz) Non-relativistic functionals (Skyrme): l (X. Roca-Maza, G. Colò) l COVARIANCE ANALYSIS IN CONNECTION TO EDFs c AB = A B A 2 B 2 Talks W. Nazarewicz J. Piekarewicz - (Skyrme type parameterization embraces nuclear bulk properties for selected semimagic nuclei) - (P.-G. Reinhard, W. Nazarewicz)

10 COVARIANCE ANALYSIS IN CONNECTION TO EDFs Covariance analysis allows calculation of theoretical uncertainty of any physical quantity of interest E.g., proton and neutron distribution radii (r p,r n ), neutron skin thickness (r np ) r p (fm) r n (fm) r np (fm) ± ± ± FSUGold ± ± ± ± ± ± (P.G.Reinhard) (J. Piekarewicz) (N.P.) r np (fm) (EXP.) PREX 0.33 ± 0.17 (p,p) ± (α,α ) 0.12 ± 0.07 Antiproton abs ± 0.03 S. Abrahamyan et al., PRL. 108, (2012). A. Tamii et al., PRL 107, (2011). A. Krasznahorkay et al., NPA 731, 224 (2004). A. Trzinska et al., PRL 87, (1991).

11 Which quantity correlates with the neutron skin thickness? Pierson product-moment correlation coefficient for various dynamic quantities of dipole excitations versus neutron skin thickness (r np ): J L K m*/m E(GMR) E(PDR) E(GDR) EWS(PDR) B(E1)(PDR) α D (PDR) EWS (all) B(E1) (all) α D (all) r np ( 208 Pb) c AB Strength-related quantities (B(E1),energy weighted strength (EWS), α D ) are better correlated with r np than excitation energies. Both the PDR and overall strength properties are correlated with the neutron skin thickness.

12 CORRELATIONS WITH THE SYMMETRY ENERGY AT SATURATION DENSITY (J) approx. J - α D J - r np c AB c AB J - PDR J - GDR c AB c AB

13 CORRELATIONS WITH DIPOLE POLARIZABILITY α D - J α D - r np c c AB AB α D - K α D - GDR c c AB AB

14 CORRELATIONS WITH THE PYGMY DIPOLE STRENGTH PDR - GDR PDR - J c AB c AB PDR - r np PDR - K c c AB AB

15 CORRELATIONS WITH THE WEAK CHARGE FORM FACTORS q=0.778 fm -1 corresponding to the CREX experiment J J L L K K R n ( 208 Pb) R n ( 208 Pb) R np ( 208 Pb) R np ( 208 Pb) R np ( 132 Sn) R np ( 48 Ca) F W ( 48 Ca) R np ( 132 Sn) R np ( 48 Ca) F W ( 48 Ca) F W ( 208 Pb) c AB F W ( 208 Pb) c AB Weak charge form factors ( 48 Ca) reasonably correlate with the neutron radii ( 208 Pb), and neutron skin thicknesses ( 48 Ca, 132 Sn, 208 Pb).

16 ANTI-ANALOG GDR AND NEUTRON-SKIN THICKNESS 1, T 1 AGDR 0 0, 1, 2, T 1 IVSGDR + 0, T 0 + 1, T GT IAS T z=t 1 0 Daughter nucleus L=1 L=1, S=1 S=1 Strong (p,n) GDR E1 T z= T 0 1,T Target nucleus 0 + 0,T 0 E DR -E IAS (MeV) AGDR - (E) AGDR (S - -S + ) GTR - (E) GTR (S - -S + ) IVSGDR Sn isotopes AGDR Mass number (A) r np c AB

17 ANTI-ANALOG GDR AND NEUTRON-SKIN THICKNESS TEST CASE: 124 Sn E(AGDR)-E(IAS) (MeV) E(AGDR)-E(IAS) [MeV] * 124 Sn R pn =0.205(50) METHOD ΔR pn (fm) (p,p) 0.8 GeV 0.25 ± 0.05 (α,α ) IVGDR 120 MeV 0.21 ± 0.11 Antiproton absorption 0.19 ± 0.09 ( 3 He,t) IVSGDR 0.27 ± 0.07 Pygmy dipole resonance 0.19 ± 0.05 (p,p) 295 MeV ± 0.05 AGDR - present result 0.21 ± R pn (fm) neutron skin thickness A. Krasznahorkay, N. P., D. Vretenar, M.N. Harakeh, Phys. Lett. B 720, 428 (2013).

18 FINAL REMARKS Dipole excitations, charge exchange excitations, parity violating electron scattering (PREX II, CREX) provide valuable constraints on the neutron skin thickness and nuclear matter symmetry energy. Statistical covariance analysis based on various effective interactions (,,,) indicates important correlations between various quantities and observables and provides the insight into the features of model dependence. Possible extensions and improvements of the isovector part of the EDFs? E.g. point coupling interactions with four isovector terms (isovector-vector + isovector-scalar, 4 parameters), revised exp. data sets? Constraining theoretical models using PREX, CREX, (p,p), (p,n) data?

19 Application of the PDR : constraints on the symmetry energy The pygmy dipole mode provides possible way to constrain the nuclear matter properties and neutron skin thickness in finite nuclei. Why? 1) PDR is dominated by neutron transitions, its transition densities at the surface are dominated by neutrons. 2) PDR strength is strongly sensitive on the neutron excess (more than GDR) 3) Covariance analysis with,, effective interactions indicates correlation between the PDR transition strength and symmetry energy at saturation density: PDR - J J. Piekarewicz, PRC 83, (2011) c AB

20 ISOVECTOR AND ISOSCALAR DIPOLE EXCITATIONS What can we learn from comparison between the isovector and isoscalar dipole transition strength in neutron rich nuclei? DD-ME2 Ô T =1 1µ = N N + Z Z p=1 r p Y 1µ Z N + Z N n=1 r n Y 1µ Ô T =0 1µ = A i=1 r r2 0 r Y 1µ Both in the isoscalar and isovector channel, pronounced low-energy dipole transition strengths are peaked at exactly the same energy. Their structure is dominated by identical neutron transitions with similar relative contributions in the transition strength (apart from the decoherence in the isovector channel).

21 THEORY FRAMEWORK 1. Relativistic point coupling model L = L free + L 4f + L hot + L der + L em, L free = (i µ m), L 4f = 1 2 S( )( ) 1 2 V( µ )( µ ) 1 2 TS( ~ ) ( ~ 1 ) 2 TV( ~ µ ) ( ~ µ ), L hot = 1 3 S( ) S( ) V[( µ )( µ )] 2, L der = 1 2 S (@ )(@ ) 1 2 V (@ µ )(@ µ ) 1 2 TS (@ ~ ) (@ ~ ) 1 2 TV (@ ~ µ ) (@ µ ~ ), L em = ea µ [(1 3 )/2] µ 1 4 F µ F µ. T. Buervenich et al., PRC 65, (2002)

22 THEORY FRAMEWORK 2. Relativistic model with density-dependent meson-nucleon couplings L = m) (@ 1 )2 2 m µ µ m2!! 2 1 R 4 ~ µ R ~ µ m2 ~ F µ F µ g g!! g ~ ~ e A (1 3 ) 2 The density dependence of the vertex functions g i ( ) =g i ( sat )f i (x) for i =,! f i (x) =a i 1+b i (x + d i ) 2 1+c i (x + d i ) 2 g ( ) =g ( sat )exp[ a (x 1)]