1. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Coherent  0 Photoproduction on Nuclei Claire Tarbert, University of Edinburgh Spokesperson: Dan Watts

2. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Overview 1.Very briefly… background, motivation 2.Analysis Outline 3.Cross Sections 4.Status and Future work

3. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Cross section contains information on matter distribution F 2 m (q) is Fourier Transform of Matter Density as a function of radius.  r.m.s matter radius Similarities with elastic electron scattering. Complicated by presence of pion – nucleus final state interactions (FSI)  extraction of form factor is model dependent. CoherentA(  0 )A Coherent  Nuclear  0 Photoproduction

4. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Nuclear Matter Radii Neutron Skin: Difference between rms proton and neutron radii. Matter radii (protons and neutrons) poorly known. Theory predicts a neutron skin for n-rich nuclei ( 208 Pb ~0.1 – 0.3 fm) Traditionally use strong probes to probe matter radius e.g. p, a scattering Encounter problems with model dependency – initial and final state interactions. Elastic Electron Scattering Nuclear Charge Radii Matter radii are important as: A test of Nuclear Theories A constraint for Atomic Parity Non-Conservation A constraint on the properties of Neutron Stars

5. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Crab Pulsar 208 Pb and the Equation of State 208 Pb Neutron Skin Possible Equations of State for Neutron Stars Energy per particle in infinite nuclear matter as a function of density and isospin asymmetry: E/A(n,I) Where n is the number density (sometimes written as r) and I = (N – Z)/A = (nn – np)/n From this all Infinite Nuclear Medium parameters follow. Example: Semi-empirical mass formula Gives a good description of symmetric nuclear matter at nuclear denisities. Extending the equation of state to higher densities and more asymmetric matter – e.g. neutron stars.

6. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Crab Pulsar Calibrates symmetry energy as a function of density at low densities. Large neutron skin  large crust on neutron star. Large neutron skin + small neutron star radius  phase transition in EOS  strange quark matter? PREX measurement @ JLAB cited 80 times according to SPIRES (Phys. Rev. C63, 025501 (2001)) 208 Pb and Neutron Stars 208 Pb Possible Equations of State for Neutron Stars Derivative of Eos Neutron Skin Thickness Derivative of Symmetry Energy

7. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh 1.Calibration of Crystal Ball using low energy  0 s. 2.Particle identification. 3.Select  0 s, don’t detect recoil. 4.Separation of Coherent/Incoherent events. - Analysis Framework  E  = E  (  1,  2 ) – E  (E  ) E  (  1,  2 ) = detected pion energy (cm) E  (E  ) = calculated pion energy (cm) Not trivial – typical energy of first nuclear excited state a few MeV! Nuclear decay  s. Experimental Details 208 Pb 40 Ca 16 O 12 C 2 weeks April 2005 E  = 883MeV M2 trigger

8. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Fitting to the pion missing energy obviously difficult. Don’t try to fit entire incoherent background. Exploit areas that are clearly dominated by coherent peak to get a good sample of coherent shape. Use this information on width, position to constrain fits in regions where coherent is not dominant. Analysis Framework: Fits to  E 

9. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Fitting to the pion missing energy obviously difficult. Don’t try to fit entire incoherent background. Exploit areas that are clearly dominated by coherent peak to get a good sample of coherent shape. Use this information on width, position to constrain fits in regions where coherent is not dominant. Analysis Framework: Fits to  E 

10. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Analysis Framework: Fits to  E  Crystal Ball TAPS 2001 data Widths of coherent peaks taken from fits to coherent dominated part of spectrum. Confirmed widths via comparison with simulation.

11. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Analysis Framework: Empty Target Crystal Ball TAPS 2001 data

12. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Analysis Framework: H 2 0 Target Crystal Ball TAPS 2001 data Hydrogen

13. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Analysis Framework: Nuclear Decay  s TAPS 2001 data 12 C 16 O

14. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Analysis Framework: Nuclear Decay  s Coherent minimum Coherent maximum 16 O Try to sample pion missing energy from incoherent by cutting on decay gammas. Will develop this technique with full simulation of decay gammas.

15. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Analysis Framework:  0 Detection Efficiency Crystal Ball TAPS 2001 data Throw  0 s isotropically – 100000/MeV See effect of Pb target – important to get radius (2.1cm) right in simulation See effect of missing TAPS at higher photon energies. + 208 Pb + 40 Ca + 12 C + 16 O

16. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Analysis: 4x4 effect in TDCs TAPS 2001 data Pb M3 trigger Pb M2 trigger Ca M2 trigger O M2 trigger C M2 trigger See familiar 4x4 structure in Ca-40, Pb-208 (M2) and Pb-208 (M3) data. Rate dependent: Ladder OR 3 times higher for Pb than C12, CB OR 4 times higher for Pb than C12.

17. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Final 208 Pb Cross Sections + CB data + Glasgow TAPS data -- Delta Resonance Energy Model (DREN - Kamalov) DREN includes effect of pion- nucleus final state scattering via a pion-nucleus optical potential. Also includes modification and propagation of  in the medium.

18. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Final 208 Pb Cross Sections

19. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Final 208 Pb Cross Sections + CB data + Glasgow TAPS data -- Delta Resonance Energy Model (DREN - Kamalov)

20. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh 208 Pb Total Cross Section + CB data + Glasgow TAPS data

21. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh 40 Ca Cross Sections + CB data + Glasgow TAPS data -- Delta Resonance Energy Model (DREN - Kamalov)

22. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh 16 O Cross Sections + CB data + Glasgow TAPS data -- Delta Resonance Energy Model (DREN - Kamalov)

23. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh 12 C Cross Sections

24. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh 12 C Cross Sections

25. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Kinematic Fitting Have dabbled with Derek Glazier’s kinematic fitting classes. Use only one constraint – mass of the  0. Definetely see different shape to missing energy. Possibly gain ~0.5MeV in widths of coherent peaks at low energys. Need new  resolutions for solid targets from simulation. + No kin fit + Kin fit E  = (190-200)MeV,   = 40-42( o ) 16 O

26. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh What can we say about the 208 Pb neutron skin? Neutron radius = proton radius (no skin) 0.15fm neutron skin 208 Pb

27. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh What can we say about the 208 Pb neutron skin? Compare with Krusche’s TAPS data – see a definite shift in minimum to larger momentum transfer i.e. larger neutron skin. + Krusche TAPS + Glasgow TAPS + CB

28. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh The Way Forward to the 208 Pb Matter Distribution 208 Pb cross sections in theta are now finalised. Need the equivalent as a function of momentum transfer. Use improved Kamalov calculations to correct for pion FSI. Extract form factor and transform to a matter distribution using the techniques pioneered for electron scattering expts.

29. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Cross Sections: PbDifferential cross sections look good and are essentially finalised. See good agreement in magnitude of cross section with previous data but with better statistics, angular resolution and a more physical shape. CaDifferential cross sections look good. O, CShould benefit from a kinematic fit – first attempts look promising. Matter Distributions: See hints of neutron skin on Pb. Next step: full extraction done in terms of the momentum transfer to the nucleus. Conclusions & Future Work

30. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Future Work: 6 month post doc at Edinburgh Extract matter radius of 208 Pb and publish. Also start investigating decay gammas seriously: Incoherent  0 photoproduction Nuclear astrophysics applications. Conclusions & Future Work

31. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh END

32. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Diffraction from a circular disc:  r m ~ 5.85fm Comparison to Theory + Data -- DREN Compare one energy bin to DREN calculation –  r m ~ 5.78fm (cf r c = 5.45fm)  r m – r c ~ 0.33fm DREN calculation by Kamalov

33. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Crab Pulsar 208 Pb and the Equation of State 208 Pb Neutron Skin Possible Equations of State for Neutron Stars

34. Crystal Ball Collaboration Meeting, Mainz, October 2007 Claire Tarbert, Univeristy of Edinburgh Analysis: Tagging Efficiencies TAPS 2001 data + 208 Pb + 40 Ca + 12 C + 16 O 4mm collimator