1. Neutral pion photoproduction and neutron radii Dan Watts, Claire Tarbert University of Edinburgh Crystal Ball and A2 collaboration at MAMI Eurotag Meeting September 2008 Presented by Bob Owens Glasgow University

2.  0 photoproduction from nuclei Coherent - Accurate Matter form factors Neutron skins of stable nuclei (neutron stars) Incoherent - Transition matter form factors New observable for production amplitude Talk Outline   E x, q

3. Why measure the matter form factor? e.g. 208 Pb RMS charge radius accuracy < 0.001 fm RMS neutron radius accuracy ~0.2 fm !! Our knowledge of the shape of stable nuclei is presently incomplete Horowitz et al. PRC63 025501 (2001) Piekarewicz et al. NPA 778 (2006) Relativistic mean field Skyrme HF Mass Number (A)

4. Proton fraction as a function of density in neutron star Thick neutron skin → Low transition density in neutron star New data from X-Ray telescopes → mass, radii, temp of neutron stars ! 208 Pb Neutron skin and Neutron stars Liquid Solid Direct URCA Cooling n → p + e - + e - + p → n + Matter form factor and neutron stars Rutel et al, PRL 95 122501 (2005) Horowitz, PRL 86 5647 (2001) Horowitz, PRC 062802 (2001) Carriere, Astrophysical Journal 593 (2003) Tsuruta, Asttrophysical Journal Lett. 571 (2002)

5. Angular distribution of  0 → PWIA contains the matter form factor  0 final state interactions - use latest complex optical potentials tuned to  -A scattering data. Corrections modest at low pion momenta Coherent pion photoproduction Photon probe Interaction well understood  0 meson – produced with ~equal probability on protons AND neutrons. Select reactions which leave nucleus in ground state Reconstruct   from   →  decay d  /d  PWIA) = (s/m N 2 ) A 2 (q  */2k  ) F 2 (E  ,    ) 2 |F m (q)| 2 sin 2   

6. TAPS Crystal Ball 528 BaF 2 crystals 672 NaI crystals   E  ~ 2 MeV 10 8  sec -1  Coherent pion photoproduction

7. 208 Pb Coherent maxima 208 Pb E  diff   theta (deg ) Non-coherent contributions E  =210±10 MeV   theta (deg ) Coherent pion photoproduction - analysis E  =175±5 MeV E  diff = E  measured  - E  calc 208 Pb data

8. 208 Pb : Momentum transfer distributions ▬ Unitary isobar model (  ) with complex optical potential Dreschel et. al. NPA 660 (1999) |q| = p  -p  0 (fm -1 ) E  =180-190 MeV E  =190-200 MeV E  =200-220 MeV E  =220-240 MeVE  =240-260 MeV

9. 208 Pb: Simple correction for distortion For first preliminary assessment 1) Carry out simple correction of q shift using the theory 2) Analyse corrected minima - fit to determine q min E  =200-220 MeV

10. 208 Pb neutron skin – preliminary assessment See effects of a neutron skin of ~0.1 fm (preliminary!!) More detailed analysis in progress ▬ implement various predicted FF ▬ “model independent” analysis No Skin 0.1 fm skin 0.2 fm skin Proton scattering NPA 778 (2006) 10 Antiprotonic atom PRC 76 034305 (2007) 0.3 fm skin

11. Incoherent nuclear  0 photoproduction Measurement of neutral pion production to a discrete excited nuclear state has proven elusive for many decades → Detect nuclear decay photon also in the Crystal Ball Important if want to extract matter form factors for light nuclei (Coherent/incoherent goes as A 2 /A = A)   E x, q In coincidence with 12 C(  0 ) E  =200-220 MeV

12. Takaki  -hole model ( NPA 443 p570 (1985) ) ▬ Full calculation --- Without  -N interaction Tryasuchev model (Phys At.Nuc. 70 827 (2007)) --- Full calculation CM Tarbert et. al., PRL 100 132301 (2008) Incoherent cross section 12 C(  0 ) 12 C(4.4MeV) E  =220  10 MeV 00

13. Strong sin 2 (2  ) distribution for 4.4 MeV photons 2 + to 0 + transition from aligned residual nucleus Degree of alignment - new experimental observable!! Alignment of recoiling 12 C nucleus sin 2 (2  ) distribution Passed through Detector acceptance Alpha (deg) Counts [arb. Units]   q  

14. New high quality nuclear  0 photoproduction data will give timely constraints on nuclear structure and neutron stars Nuclear decay photon detection to tag incoherent processes -> accurate matter form factors for lighter nuclei Summary 672 NaI crystals 342 BaF2 crystals

15. Strong sin 2 (2  ) distribution for 4.4 MeV photons - Spin independent amplitude dominant (  ) ( Tryasuchev and Kolchin Phys. At. Nuc. 70 827 (2007)) Spin dependent predicted to give cos 2 (2  ) – use  to separate the in medium amplitude? Alignment of recoiling 12 C nucleus Alpha (deg) Counts [arb. Units]   q   sin 2 (2  ) cos 2 (2  ) Incl..detector acceptance 12 C(  0 ) 12 C(4.4MeV) E  =300  10 MeV

16. E  dependence of spin dependent / independent in medium 12 C(  0 ) 12 C(4.4MeV) E  =175  5 MeV 12 C(  0 ) 12 C(4.4MeV) E  =310  10 MeV 12 C(  0 ) 12 C(4.4MeV) E  =420  20 MeV

17. Decay  angular distributions – other targets Ca 40 (  0 ) 40 Ca* E  =230  10 MeV O 16  0 ) 16 O* E  =230  10 MeV 16 O 40 Ca

18. Symmetrised Fermi distributions

19. Coherent production on Oxygen

20. Coherent production on Calcium