1. Photopion photoproduction neutron radii and neutron stars Dan Watts, Claire Tarbert University of Edinburgh Crystal Ball and A2 collaboration at MAMI CB meeting, Mainz, September 2008

2. Neutron skins, EOS and Neutron stars (covering recent PREX neutron skins workshop) Present status of coherent and incoherent measurement Possible future measurements Talk Outline

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. Neutron skins over the nuclear chart

5. Nuclear equation of state

6. Equation of state for n rich matter

7. Nuclear equation of state

8. Correlation of neutron skin and EOS

10. Nuclear EOS from Chiral EFT

11. 208 Pb Neutron skin and Neutron stars Matter form factor and neutron stars Formed supernovae of massive star (>8M o ) Typical ly ~12km radius, ~1.5Mo Correlation to nuclei not Obvious – 18 OOM in size and 5 OOM in density ! But have shared dependence on the equation of state

12. EOS and neutron stars

14. Neutron star astronomy

16. Neutron star astronomy – future plans Measure mass and radii from hydrogen atmosphere Parallax measurement to get distances to 1%

17. Neutron star astronomy – future plans Direct URCA Rule out last non-”exotic” Cooling mechanism? Requires high proton fraction so that P F (p) + P F (e) > P F (n)

18. 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   

19. 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

20. 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

21. 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 with Bessel fn. E  =200-220 MeV

22. 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

23. 208 Pb form factors from model predictions

24. Implications of a small skin ~MAMI preliminary + rule out Direct URCA as viable cooling mechanism ??

25. Skin thicknesses in isotopic chain Isotopic chain e.g. Stable Ca isotopes (40,42,44,46,48) ? Stable Sn isotopes ? (112 -124) Common problem – need isotopically pure Target loan/preparation

26. 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 in the same detector as the   decay photons 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

27. 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

28. Spin dependent / independent in medium 12 C(  0 ) 12 C(4.4MeV) E  =310  10 MeV 12 C(  0 ) 12 C(4.4MeV) E  =420  20 MeV

29. 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

30. 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) Transition matter form factors 12 C(  0 ) 12 C(4.4MeV) E  =220  10 MeV 00

31. New high quality nuclear  0 photoproduction data will give timely constraints on nuclear structure and neutron stars – topic of high current interest Complementary measurement to PREX experiment at JLAB with different systematic uncertainties Nuclear decay photon detection to tag incoherent processes -> accurate matter form factors for lighter nuclei Potential for important new measurements in the future Summary 342 BaF2 crystals

34. Symmetrised Fermi distributions

35. 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)

36. Skx-s15 Neutron skin effects in diff nuclei show correlation

37. Coherent production on Oxygen

38. Skx-s15

39. Coherent production on Calcium

40. 208 Pb: Total coherent cross sections ▬ PWIA ▬ DWIA ▬ DWIA+  self energy. CB@MAMI TAPS99@MAMI Theoretical prediction Dreschel, Tiator, Kamalov & Yang - NPA 660 (1999)   production amplitude from Unitary Isobar Model   interaction treated with momentum space optical potential supplemented with  self-energy

41. Skx-s20

42. J.Brudvik, J. Goetz, B.M.K.Nefkens, S.N.Prakhov, A.Starostin, I. Saurez, University of California, Los Angeles, CA, USA J.Ahrens, H.J.Arends, D.Drechsel, D.Krambrich, M.Rost, S.Scherer, A.Thomas, L.Tiator, D. von Harrach and Th.Walcher Institut fur Kernphysik, University of Mainz, Germany R. Beck, M. Lang, A. Nikolaev, S. Schumann, M. Unverzagt, Helmholtz-Institut fur strahlen und Kernphysik, Universitat Bonn, S.Altieri, A.Braghieri, P.Pedroni, A.Panzeri and T.Pinelli INFN Sezione di Pavia and DFNT University of Pavia, Italy J.R.M.Annand, R.Codling, E.Downie, J. Kellie, K.Livingston, J.McGeorge, I.J.D.MacGregor, R. Owens D.Protopopescu and G.Rosner Department of Physics and Astronomy, University of Glasgow, Glasgow, UK C.Bennhold and W.Briscoe George Washington University, Washington, USA S.Cherepnya, L.Fil'kov, and V.Kashevarow Lebedev Physical Institute, Moscow, Russia V.Bekrenev, S.Kruglov, A.Koulbardis, and N.Kozlenko Petersburg Nuclear Physics Institute, Gatchina, Russia B.Boillat, B.Krusche and F.Zehr, Institut fur Physik University of Basel, Basel, Ch P. Drexler, F. Hjelm, M. Kotulla, K. Makonoyi, R.Novotny, M. Thiel and D. Trnka II. Phys. Institut, University of Giessen, Germany D.Branford, K.Foehl, D. Glazier, T. Jude, C.Tarbert and D.P.Watts, School of Physics, Univ. of Edinburgh, Edinburgh, UK V.Lisin, R.Kondratiev and A.Polonski Institute for Nuclear Research, Moscow, Russia J.W. Price California State University, Dominguez hills, CA, USA D.Hornidge Mount Allison University, Sackville, Canada P. Grabmayr and T. Hehl Physikalisches Institut Universitat Tubingen, Tubingen, Germany D.M. Manley Kent State University, Kent, USA M. Korolija and I. Supek Rudjer Boskovic Institute, Zagreb, Croatia D. Sober, Catholic University, Washington DC M. Vanderhaeghen, College of William and Mary, Williamsburg, USA CB@MAMI

43. Potential future measurements Isotopic chain e.g. Stable Ca isotopes (40,42,44,46,48) rms neutron radii ?? Stable Sn isotopes (112,114,115,116,117,118,119,120,122,124) As expect to also see skin of similar size to 208Pb Common problem – target loan/preparation

44. 208 Pb : Momentum transfer distributions

45.   photoproduction - amplitude Basic production amplitude ~ equal for protons and neutrons Dominated by  production Isospin structure of amplitude A(  p→  0 p) = √2/3 A V3 +√1/3(A vI – A IS ) A(  n→  0 n) = √2/3 A V3 +√1/3(A VI + A IS )  has I=3/2 -- A V3 only

46. 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  Nuclear decay photon Momentum transfer direction sin 2 (2  ) distribution Passed through Detector acceptance Alpha (deg) Counts [arb. Units]

47. Nuclear (  0 ) photoproduction 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  ~ 2 MeV 10 8  sec -1 672 NaI crystals 528 BaF 2 crystals

48. 40 Ca 208 Pb Nuclear decay photons in the Crystal Ball !! 12 C 16 O

49. Neutron density for 208 Pb Shows the shell layers (Dashed line is the proton density)

50. 208 Pb: Preliminary evaluation of Neutron skin effects ▬ No neutron skin ▬ 0.1 fm skin ▬ 0.2 fm skin ▬ 0.3 fm skin

51.   photoproduction as a nuclear probe Precision test of our understanding of the  nucleon interaction Access matter form factor and matter transition form factors Test specific aspects of the pion production amplitude Gives information on the matter distribution with EM probe  0 production ~ identical probability from protons & neutrons  

52. Strong sin 2 (2  ) distribution for 4.4 MeV photons - Spin independent amplitude dominant (  ) ( Tryasuchev and Kolchin Phys. At. Nuc. 70 827 (2007))  observable has potential to separate spin dependent and independent parts of amplitude !! Alignment of recoiling 12 C nucleus sin 2 (2  ) distribution Passed through Detector acceptance Alpha (deg) Counts [arb. Units]   q  

53. Takaki  -hole model ( NPA 443 p570 (1985)) ▬ Full calculation --- Without  -N interaction ▬ Tryasuchev (Phs At. Nuc. 70 827 (2007)) CM Tarbert, DP Watts et. al., Phys. Rev. Lett (2008) Transition matter form factors E  =220-240 MeV E  =240-260 MeV Theta  0

54. Why is neutron radius hard to establish? “Insensitivity of the elastic proton–nucleus reaction to the neutron radius of 208 Pb” Piekarewicz and Pieper NPA 778 10 (2006) Maybe mention antiproton stuff?

55. 208 Pb: Preliminary evaluation of Neutron skin effects ▬ No neutron skin ▬ 0.1 fm skin ▬ 0.2 fm skin ▬ 0.3 fm skin

56. Strong sin 2 (3  ) component Expected from 3 - to 0 + transition Alignment of recoiling 16 O nucleus  Nuclear decay photon Momentum transfer direction

57. Equation of state for n rich matter EOS is a function of density (  ) and isospin asymmetry (  ) Can be expanded in a Taylor Series about the nuclear Saturation density (  0 ) and  =0 (symmetric matter)  Asymmetry energy First derivative of symmtyry energy with respect to density

59. Coherent → Gaussian with  (E  ) extracted from coherent maximum) Smeared step function at A( ,   N)A-1 threshold For light nuclei with well separated 1 st excited state(s) Include second gaussian centered at appropriate energy Fitting the pion energy difference Spectra

60. How do we get the Coherent part? One technique is to use energy difference analysis (k , E  ) (0, E) (k N, E N ) (k , E  ) (k , E  ) (k , E  ) E  diff = E  (E  )   E  (  1,  2 ) Best previous measurements → segmented arrays Reliable coherent extraction limited due to sharply   dependent systematic effects in E  determination  

61. Combined p0 and decay g detection efficiency

63. 208 Pb:  0 angular distributions ▬ DWIA +  SE CB@MAMI TAPS99@MAMI E  =160-170 MeVE  =170-180 MeV E  =200-220 MeV..... + spectra up to E  =700 MeV

64. 208 Pb( ,  0 ) E  =185±5 MeV E  =195±5 MeV 208 Pb( ,  0 ) E  =205±5 MeV 208 Pb( ,  0 ) Theta pion (deg) No Skin 0.2 fm Skin

65. Also evident in Nuclear Decay photon spectra Picked up by CB!! E  =185±5 MeV E  =195±5 MeV 40 Ca( ,  0 ) 40 Ca shows large Incoherent contamination At larger  0 angles

66. Proton scattering Seminal analysis by Hoffman for all data (0.3 - 1 GeV).  r np ( 208 Pb) = -0.02 → 0.5 fm Pickup reactions. Recent analysis of p and n pickup gave  r np ~0.5fm for 208 Pb Antiprotonic atoms   r np ~ 0.15fm for 208 Pb. D p p N p Neutron Skins - present situation Coherent pion photoproduction

67. Nuclear decay photons 12 C Background predominantly from split-off clusters from pi0 detection

70. Pion – Nucleus interactions Diffraction pattern distorted due to effects of  -A interactions (FSI) Optical potential constructed from pi-N amplitude in p space Intermediate  also included (important at higher P   ) Accurately describes wealth of A(  / ) data If  (FSI) ~ 10%   ~ (0.07)×(±2 o )×0.1 = ±0.014 fm Each q occurrs for different P  at different incident E  – check predicted FSI effects 208 Pb

71. 40 Ca

72. 40 Ca: Total coherent cross sections CB@ MAMI TAPS99@MAMI ▬ PWIA ▬ DWIA ▬ DWIA +  mod.

73. 40 Ca:  0 angular distributions ▬ DWIA +  SE. E  =160-170 MeV E  =170-180 MeV E  =200-220 MeV E  =220-240 MeV CB@MAMI TAPS99@MAMI

74. 12 C: Total coherent cross sections CB@MAMI TAPS99@ MAMI ▬ PWIA ▬ DWIA ▬ DWIA +  mod.

77. Photon Tagger upgrade

78. Goniometer Upgraded Tagger e- beam

79. Crystal Ball arrives at Frankfurt

82. Good angular and energy resolution, close to 4  acceptance Setup at MAMI Tracker & Particle-ID    GeV)  ~41cm ~25cm          sin 

83. d  /d  A 2 (q/k  )P 3 2 |F m (q)| 2 sin 2   A gs (  0 )A gs coherent  0 photoproduction

84. 208 Pb:  0 angular distributions ▬ DWIA +  SE CB@MAMI TAPS99@MAMI E  =160-170 MeVE  =170-180 MeV E  =200-220 MeV E  =300-320 MeV

86. 100% duty factor electron microtron MAMI-C 1.5 GeV upgrade (Completed!!) (MAMI-B 0.85 GeV) The MAMI facility One of the MAMI-C magnets  e

87. MWPC & Particle-ID in situ

90.   photoproduction amplitude Basic production amplitude ~ equal for protons and neutrons Dominated by  production Isospin structure of amplitude A(  p→  0 p) = √2/3 A V3 +√1/3(A IV – A IS ) A(  n→  0 n) = √2/3 A V3 +√1/3(A IV + A IS )  has I=3/2 -- A V3 only

91.   production in the nucleus “Clean” test of  0 -nucleus interaction & effect of medium on  properties Access matter form factor and matter transition form factor with EM probe Test more specific aspects of the basic production amplitude