1. Presentation by T. Gogami 2015/6/15 (Mon)

2. Equation state of neutron matter

3. Density dependence of the symmetry energy Heavy ion collision Nuclear binding energy Isobaric analog state Neutron skin thickness M.B.Tsang, …, T.Murakami et al., PRC 86, 015803 (2012)

4. Difference of RMS radii between neutrons and protons

5. Neutron skin thickness of 208 Pb  Constraint for L L.W. Chen et al., PRC 72, 064309 (2005)

6. Measurements up to now [22] B. Klos et al., PRC 76 (2007) 014311 [23] B.A. Brown et al., PRC 76 (2007) 034305 [24] L.W. Chen et al., PRC 72 (2005) 064309 [25] A. Krasznahorkay et al., PRL 66 (1991) 1287 [15] A. Carbone et al., PRC 81 (2010) 041301 [17] A. Tamii et al., PRL 107 (2011) 062502 [20] J. Zenihiro et al., PRC 82 (2010) 044611 [21] E. Friedman, NPA 396 (2012) 46

7. Experiments with electromagnetic probes Different systematic errors from strongly interacting probes  No successful measurements of the neutron distribution

8. Elastic scattering of polarized electrons from 208 Pb  Parity-violating asymmetry: Weak Form factor  Neutron density S. Abrahamyan et al., PRL 108, 112502 (2012) X. Roca-Maza et al., PRL 106, 252501 (2011)

9. Coherent Photoproduction of π 0 meson from 208 Pb

10. MAMI at Johannes Gutenberg-Universität Mainz Okazaki Gutenberg Exp. hall

11. Schematic drawing of Experimental setup Beam: 180 – 240 MeV tagged photon Tagged photon resolution ~ 2 MeV full width 2×10 5 γ s -1 MeV -1 Enriched 208 Pb (0.52 mm, 99.5%) Crystal Ball: 672 NaI (94% of 4π) C.M. Tarbert et al., PRL 100, 132301 (2008)

12. Schematic drawing of Experimental setup Beam: 180 – 240 MeV tagged photon Tagged photon resolution ~ 2 MeV full width 2×10 5 γ s -1 MeV -1 Enriched 208 Pb (0.52 mm, 99.5%) Crystal Ball: 672 NaI (94% of 4π) C.M. Tarbert et al., PRL 100, 132301 (2008)

13. Analysis Energies and angles of 2γ  π 0 momentum  q = (P γ - P π )  Cross section as a function of q

14. Analysis (Yield of Coherent Reaction) π 0 energy assuming coherent reaction

15. Efficiency etc. π 0 detection efficiency: ~40% Photon tagging efficiency: ~40% π 0 not originating from target: ~1%

16. Fitting to the experimental results Known: a p =0.447 fm, c p =6.680 fm c n = 6.28 to 7.07 fm a n = 0.35 to 0.65 fm σ q = 0.02 – 0.03 fm -1 depending on E γ

17. Results

18. Neutron skin of 208 Pb  Halo character

19. Summary