Pb, 120 Sn and 48 Ca from High-Resolution Proton Scattering MSU 2016

Transcription

1 Dipole Polarizability and Neutron Skins in 208 Pb, 120 Sn and 48 Ca from High-Resolution Proton Scattering MSU 2016 Equation of State of neutron matter and neutron skin Proton scattering at 0 and electric dipole response Dipole polarizability of 208 Pb Dipole polarizability of 120 Sn Dipole polarizability of 48 Ca Supported by the DFG within SFB 634 and SFB Achim Richter

2 Neutron Stars Neutron stars are remnants of the supernova explosion of massive stars Extremely high densities and exotic forms of nuclear matter Properties are described by an Equation of State (EoS) of neutron matter 2016 Achim Richter 2

3 Nuclear Equation of State (EoS) Energy as a function of density (or pressure) Well defined at ρ/ρ 0 = 1 by properties of stable nuclei Large differences of model predictions at high densities: stiff or soft EoS? 2016 Achim Richter 3

4 E/A (MeV) Neutron Matter EoS T. Krüger, I. Tews, K. Hebeler, A. Schwenk, Phys. Rev. C 88, (2013) 2016 Achim Richter 4 ρ (fm 3 ) Result from chiral effective field theory

5 Mass Radius Relation of Neutron Stars P. B. Demorest et al., Nature 467, 1081 (2010) How can one experimentally distinguish between various predictions? 2016 Achim Richter 5

6 Binding Energy of (Infinite) Neutron Matter volume surface Coulomb symmetry pairing For (infinite) neutron matter the pairing contribution is small enough to be neglected (at least for low densities) and the Coulomb term vanishes only volume and symmetry term contribute The volume term can be estimated from the saturation properties The symmetry energy represents the largest uncertainty for the EoS of neutron matter 2016 Achim Richter 6

7 Symmetry Energy and Neutron Skin of Nuclei Nuclear force leads to constant density in the interior (saturation) In heavy stable nuclei N > Z because the symmetry energy is balanced by the Coulomb repulsion between protons Extra neutrons are concentrated on the surface formation of a neutron skin Neutron skin thickness R n -R p depends on the parameters of the symmetry energy 2016 Achim Richter 7

8 Symmetry Energy: Expansion in Density and Neutron Excess Taylor expansion of (N-Z) dependent part 2016 Achim Richter 8

9 Symmetry Energy: Expansion in Density and Neutron Excess Taylor expansion of (N-Z) dependent part Symmetry energy approximately determined by J (or S v ) and L L describes density dependence (stiff or soft EoS) Experimental approach used here: Electric Dipole Polarizability 2016 Achim Richter 9

10 Symmetry Energy and Neutron Skin Static nuclear dipole polarizability α D = ħc 2π 2 e 2 σ 2 = ħc 2π 2 e 2 σ abs E x E x 2 = 8π 9 B E1 E x E x fm 3 e 2 α D is measure of neutron skin Theoretical predictions P.G. Reinhard, W. Nazarewicz, PRC 81, (2010) J. Piekarewicz, PRC 83, (2011) Next: experimental determination of α D 2016 Achim Richter 10

11 Electric Dipole (E1) Response in Nuclei neutron skin? p/n IV GDR 2016 Achim Richter 11 Excitation energy [MeV] Oscillations of neutrons against protons: Giant Dipole Resonance (GDR) Oscillations of neutrons in the skin against core with N Z Pygmy Dipole Resonance (PDR)

12 Pygmy Dipole Resonance Soft E1 mode due to oscillation of neutron skin vs. approximately isospin-saturated core PDR related to neutron skin Neutron skin related to neutron-matter EoS J. Piekarewicz, Phys. Rev. C 73 (2006) S. Typel, B. A. Brown, Phys. Rev. C 64 (2001) Achim Richter 12

13 S-DALINAC at TU Darmstadt 2016 Achim Richter 13

14 Structure of the PDR in 208 Pb Measured at the S-DALINAC 2016 Achim Richter 14

15 Structure of Low-Energy E1 Modes How can we elucidate the structure of the low-energy E1 modes? Proton scattering at 0 Coulomb excitation of 1 - states high resolution: E = kev (FWHM) angular distribution (E1/M1 separation) polarization observables (spinflip / non-spinflip separation) Electron scattering (preferentially at 180 ) high resolution transverse form factors needed very sensitive to structure of the different modes 2016 Achim Richter 15

16 Proton Scattering at 0 on 208 Pb at RCNP/Osaka 2016 Achim Richter 16

17 E1/M1 Decomposition by Spin Observables Polarization observables at 0 spinflip / non-spinflip separation (model-independent) -1 for DS = 1 1 D + SS + D NN + D LL = 3 for DS = sideway normal longitudinal At 0 D SS D NN Total Spin Transfer 3 ( 2 D SS D LL 4 ) 1 0 for for ΔS ΔS 1 0 T. Suzuki, Prog. Theor. Phys. 103, 859 (2000) 2016 Achim Richter 17

18 Measurement of Spin Observables Scheme of the FPP / Grand Raiden Setup 2016 Achim Richter 18

19 Decomposition into Spinflip / Non-Spinflip Cross Sections 2016 Achim Richter 19

20 Multipole Decomposition of Cross Section d ( d ) data D L a D L d ( d ) DWBA Restrict angular distribution to = 4 (response at larger angles too complex) DL = 0 isovector spin M1 DL = 1 E1 (Coulomb + nuclear) DL > 1 only E2 (or E3) considered 2016 Achim Richter 20

21 Multipole Decomposition of Angular Distributions I. Poltoratska et al., Phys. Rev. C 85 (2012) (R) 2016 Achim Richter 21

22 Comparison of Both Methods at Low E x Total DS = 1 DS = Achim Richter 22

23 Comparison of Both Methods at High E x Total DS = 1 DS = Achim Richter 23

24 B(E1) Strength: Low-Energy Region 2016 Achim Richter 24

25 Photoabsorption Cross Section: GDR 2016 Achim Richter 25

26 Polarizability and Neutron Skin Precision value αd(208pb) = 20.09(59) fm3/e2 (from all existing data up to 130 MeV) Within the model of Reinhard and Nazarewicz* rskin = ± fm *P.G. Reinhard and W. Nazarewicz PRC 81 (2010) (similar results exist from J. Piekarewicz) Present model-independent measurement by PREX: rskin = 0.34 ± fm Improvement necessary for true constraint of any microscopic interaction 2016 Achim Richter 26

27 Neutron Skin in 208 Pb 1 G. W. Hoffmann et al., PRC 21, 1488 (1980) 2 A.Krasznahorkay et al., NPA 567, 521 (1994) 3 A. Trzcińska et al., PRL 87, (2001) 4 M. Csatlós et al., NPA 719, C304 (2003) 5 E. Friedman et al, Phys. Rep. 452, 89 (2007) 6 B. Kłos et al., PRC 76, (2007) 7 A. Klimkiewicz et al., PRC 76, (2007) 8 J. Zenihiro et al., PRC 82, (2010) 9 A.Carbone et al., PRC 81, (2010) 2016 Achim Richter 27

28 Constraints on Energy Density Functionals Relation between α D and r skin is model-dependent Important constraint by 208 Pb result 2016 Achim Richter 28 J. Piekarewicz et al., Phys. Rev. C 85 (2012) (R)

29 Neutron Skin Thickness and Symmetry Energy X. Roca-Maza et al., Phys. Rev. C 88, (2013) 88, (2013). Strong correlation between α D J and the neutron skin, i.e. L 2016 Achim Richter 29

30 Neutron skin thickness Constraints on Symmetry Energy Parameter M.B. Tsang et al., Phys. Rev. C 86 (2012) I. Tews et al., Phys. Rev. Lett. 110 (2013) A. Tamii, PvNC, I. Poltoratska, Eur. Phys. J. A 50, 28 (2014) QMC DP: Dipole Polarizability HIC: Heavy Ion Collision PDR: Pygmy Dipole Resonance IAS: Isobaric Analogue State FRDM: Finite Range Droplet Model n-star: Neutron Star Observation χeft: Chiral Effective Field Theory QMC: Quantum Monte Carlo Theory Density independent part of the EoS 2016 Achim Richter 30

31 Electric Dipole Strength Distribution in 120 Sn T. Hashimoto et al., Phys. Rev. C 92 (2015) Note: Low energy strength contributes about 9% to α D 2016 Achim Richter 31

32 Correlation of Experimental α D Values of 208 Pb and 120 Sn Experimental values of α D constrain the EDFs Relativistic EDFs seem to have a problem Darmstadt-Osaka Collaboration (T. Hashimoto et al., Phys. Rev. C 92 (2015)) 2016 Achim Richter 32

33 Correlation of Experimental α D Values of 208 Pb, 120 Sn and 68 Ni X. Roca-Maza et al., Phys. Rev. C 92, (2015) Only a handful of EDFs are able to describe the correlations Those EDFs predict for 48 Ca: α D = ( ) fm 3 and r skin = ( ) fm 2016 Achim Richter 33

34 Motivation 2016 Achim Richter 34

35 Neutron Skin in 48 Ca? Analysis analogous to the one in 208 Pb(p,p ) 2016 Achim Richter 35

36 B(E1) Strength in 48 Ca 2016 Achim Richter 36

37 Comparison of 40Ca/ 48Ca in the GDR Region Cross sections are comparable but there is an energy shift of (1.0 ± 0.3) MeV 2016 Achim Richter 37

38 Photoabsorption Cross Section in 40 Ca up to 160 MeV Note: above E x = 60 MeV cross section is negligibly small 2016 Achim Richter 38

39 Photoabsorption Cross Section in 48Ca and Running Sum of αd αd(exp) = (2.06 ± 0.11) fm Achim Richter 39

40 Photoabsorption Cross Section and Running Sum of αd compared to χeft predictions αd(exp) = (2.06 ± 0.11) fm Achim Richter 40 αd(χeft) = ( ) fm3

41 Present Status of Experiment and Theory for the Dipole Polarizability of 48 Ca Still needed: Correlation analysis (e.g. α D J vs. r skin ) to constrain the neutron skin 40 Ca: α D = (1.87 ± 0.03) fm 3 48 Ca: α D = (2.06 ± 0.11) fm 3 α D ( 40 Ca) - α D ( 48 Ca) provides an additional constraint for the neutron skin 2016 Achim Richter 41 EDF: J. Piekarewicz et al., Phys. Rev. C 85, (2012) EDF RM: X. Roca-Maza et al., Phys. Rev. C 92, (2015)

42 Experimentalists and Theorists in the 48 Ca Project Experiment: Darmstadt-Osaka Theory: Darmstadt-Tennessee-TRIUMF S. Bacca S. Bassauer J. Birkhan G. Hagen H. Matsubara M. Miorelli P. von Neumann-Cosel T. Papenbrock N. Pietralla A. Richter A. Schwenk A. Tamii 2016 Achim Richter 42

43 Comparison of 40Ca/ 48Ca in the GDR Region Cross sections are comparable but there is an energy shift of (1.0 ± 0.3) MeV 40Ca (GDR): αd = (1.50 ± 0.02) fm3 48Ca (GDR): αd = (1.75 ± 0.11) fm Achim Richter 43

44 Predictions for observables related to the neutron distribution in 48 Ca G. Hagen et al., Nature Physics 12 (2016) 2016 Achim Richter 44

45 Double Differential Cross Section of 40 Ca 2016 Achim Richter 45

46 Running Sum of α D from χeft predictions for 40 Ca 2016 Achim Richter 46

47 Running Sum of α D from χeft predictions for 48 Ca 2016 Achim Richter 47