Coherent and incoherent π 0 photoproduction from nuclei

Transcription

1 Coherent and incoherent π 0 photoproduction from nuclei Dan Watts, Claire Tarbert University of Edinburgh Crystal Ball@MAMI Collaboration EINN07, Milos Island, Greece, 2007

2 Talk Outline Neutral pion photoproduction Basic Amplitude Nuclear case - Coherent, Incoherent Matter form factor, transition matter form factor Crystal Ball/TAPS at MAMI New data on Coherent and incoherent reactions Summary and outlook

3 π 0 photoproduction amplitude Basic production amplitude ~ equal for protons and neutrons Dominated by (122) production Isospin structure of amplitude A(γp π 0 p) = 2/ A V + 1/(A IV A IS ) A(γn π 0 n) = 2/ A V + 1/(A IV + A IS ) has I=/2 -- A V only

4 π 0 production in the nucleus Access matter form factor and matter transition form factor with EM probe Clean test of π 0 -nucleus interaction & effect of medium on properties Test more specific aspects of the basic production amplitude

5 Why measure the Matter form factor? Our knowledge of the shape of stable nuclei is presently incomplete e.g. 208 Pb RMS charge radius known to < fm RMS neutron radius only known to ~0.2 fm!! Horowitz et al. PRC (2001) Piekarewicz et al. NPA 778 (2006) Coherent pion photoproduction - Close to ideal technique which is mature enough to address this fundamental problem (Finally!)

6 Why measure the matter form factor? 1) Fundamental quantity of Nuclear physics Relativistic mean field Skyrme HF

7 208 Why Pb Neutron measure skin the and matter Neutron form stars factor? Thick neutron skin Low transition density in neutron star New data from X-Ray telescopes mass, radii, temp of neutron stars! Solid Liquid Proton fraction as a function of density in neutron star URCA Cooling n p + e - + ν e - + p n + ν

8 Accurate matter distributions Photon probe Interaction well understood π 0 meson produced with ~equal probability on protons AND neutrons. Select reactions which leave nucleus in ground state Reconstruct π 0 from π 0 2γ decay Angular distribution of π 0 PWIA contains the matter form factor dσ/dω(pwia) = (s/m N2 ) A 2 (q π */2k γ ) F 2(E γ,θ π ) 2 F m (q) 2 sin 2 θ π π 0 distortion - theoretical models use complex optical potential (& incorporate effects of self-energy in nuclear medium)

9 How do we get the Coherent part? One technique is to use energy difference analysis (k γ, Eγ) (0, E) (k N, E N ) E π diff = E π (E γ ) E π (γ 1,γ 2 ) (k π, E π ) (k γ2 γ 2 γ 1 γ2, E γ2 ) (k γ1, E γ1 ) Best previous measurements segmented arrays Reliable coherent extraction limited due to sharply θ π dependent systematic effects in Eπ determination

10 γ Eγ ~ 2 MeV 10 8 γ sec -1 γ TAPS 528 BaF 2 crystals Crystal Ball 672 NaI crystals

11 Coherent and incoherent contributions E γ =175±5 MeV E π diff 208 Pb E γ =210±10 MeV 208 Pb E π diff Coherent maxima π 0 theta (deg) Non-coherent contributions π 0 theta (deg)

12 Fitting the pion energy difference Spectra E γ = ( )MeV, θ π = (42-4) E γ = ( )MeV, = ( ) θ π Counts 250 Counts E π [MeV] E π [MeV] Coherent Gaussian with σ(e π ) extracted from coherent maximum) Smeared step function at A(γ,π 0 N)A-1 threshold For light nuclei with well separated 1 st excited state(s) Include second gaussian centered at appropriate energy

13 208 Pb: Total coherent cross sections σ [µb] 10 4 CB@MAMI TAPS99@MAMI.5 PWIA DWIA DWIA+ self energy. 2.5 Theoretical prediction [MeV] E γ Dreschel, Tiator, Kamalov & Yang - NPA 660 (1999) π 0 production amplitude from Unitary Isobar Model π 0 interaction treated with momentum space optical potential supplemented with self-energy

14 208 Pb: π 0 angular distributions Eγ= MeV Eγ= MeV CB@MAMI TAPS99@MAMI DWIA + SE Eγ = ( )MeV dσ/dω [µb/sr] 10 Eγ= MeV Eγ=00-20 MeV θ π [ ]

15 40 Ca: Total coherent cross sections σ [µb] MAMI PWIA DWIA DWIA + mod [MeV] E γ

16 40 Ca: π 0 angular distributions Eγ= MeV CB@MAMI TAPS99@MAMI Eγ= MeV DWIA + SE. Eγ= MeV Eγ= MeV

17 12 C: Total coherent cross sections σ [µb] 500 MAMI PWIA DWIA DWIA + mod [MeV] E γ

18 Coherent π 0 - next steps Plot data as function of momentum transfer (q) Extract matter form factor from PWIA expression dσ/dω(pwia) = (s/m N2 2 γ π ) A (q/2k ) F γ 2(E,θ ) F m (q) sin θ π Obtain corrected F m (q) 2 - use ratio DWIA/PWIA from theory

19 208 Pb: Preliminary assessment of Neutron skin Eγ = ( )MeV No neutron skin 0.1 fm skin 0.2 fm skin 0. fm skin dσ/dω [µb/sr] 10 Assumes diffuseness same for proton and neutron distribution [ ] θ π

20 Incoherent pi photoproduction Incoherent gives access to transition matter form factor with an electromagnetic probe. Also allows test of more specific -nucleus interactions compared to coherent e.g. -N interactions important Also expect new mechanisms such as coherent followed by π scatter

21 Incoherent nuclear pion photoproduction Difficult to extract strength using E π diff Marginally resolvable for lowest E γ bins Detect nuclear decay photon in the same detector as the π 0 decay photons Opens up access to incoherent reaction to discrete nuclear states and up to higher π energies

22 Counts E γ = ( )MeV Ca Nuclear decay photons deg9 Entries Mean.507 χ 2 / ndf / 75 Height 91.9 ± 28.9 Centroid ± 0.05 Sigma ± p 8.59 ± p ± Counts E γ = ( )MeV Pb deg9 Entries 8681 Mean.295 RMS Underflow 0 Overflow 0 Integral 8.27e+04 Skewness 1.48 Height ± Centroid 2 ± 1.0 Sigma ± p 8.75 ± 0.09 p ± Counts E γ E γ [MeV] = ( )MeV 10 8 deg E γ [MeV] Entries E γ = ( )MeV 12 C Mean RMS Underflow O Height 2981 Centroid Sigma p 9.64 p Counts 4 deg9 Entries 2649 Mean 4.56 RMS 2.72 Underflow 0 Overflow 0 χ 2 / ndf / 65 Height 2 ± 48.2 Centroid 6.8 ± 0.01 Sigma ± p 9.42 ± p ± E γ [MeV] E γ [MeV]

23 Nuclear decay photons 12 C Counts [arb. units] E γ = ( )MeV θ π = (80-84) [ ] θ π E γ = ( )MeV [MeV] E γ E γ^ [MeV] Background predominantly from split-off clusters from pi0 detection

24 Incoherent nuclear pion photoproduction 12 C(γ,π o ) 12 C(2 +, 4.4 MeV) dσ/dω [µb/sr] Eγ=290±10 Eγ=25±10 MeV Takaki -hole model NPA 44 p570 (1985) Nuclear wavefunctions have configuration coefficients extracted from e- scattering Preliminary! E γ [MeV] [ ] dσ/dω corrected for both π 0 and nuclear decay γ detection efficiency First determination of incoherent photoproduction θ π

25 Summary Coherent process extracted with a new level of accuracy Data set of sufficient quality to extract information on matter form factor Nuclear decay photon analysis allows determination of incoherent production -> study in it s own right and use to improve coherent extraction