Coherent and incoherent π 0 photoproduction from nuclei Dan Watts, Claire Tarbert University of Edinburgh Crystal Ball@MAMI Collaboration EINN07, Milos Island, Greece, 2007
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
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
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
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 < 0.001 fm RMS neutron radius only known to ~0.2 fm!! Horowitz et al. PRC6 025501 (2001) Piekarewicz et al. NPA 778 (2006) Coherent pion photoproduction - Close to ideal technique which is mature enough to address this fundamental problem (Finally!)
Why measure the matter form factor? 1) Fundamental quantity of Nuclear physics Relativistic mean field Skyrme HF
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
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)
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
γ Eγ ~ 2 MeV 10 8 γ sec -1 γ TAPS 528 BaF 2 crystals Crystal Ball 672 NaI crystals
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)
Fitting the pion energy difference Spectra E γ = (200-220)MeV, θ π = (42-4) E γ = (200-220)MeV, = (101-102) θ π Counts 250 Counts 70 60 200 150 100 50 50 40 0 20 10 0 0-10 -25-20 -15-10 -5 0 5 10 15 20 E π [MeV] -20-0 -20-10 0 10 20 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
208 Pb: Total coherent cross sections σ [µb] 10 4 CB@MAMI TAPS99@MAMI.5 PWIA DWIA DWIA+ self energy. 2.5 Theoretical prediction 2 1.5 1 0.5 160 180 200 220 240 260 280 00 [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
208 Pb: π 0 angular distributions Eγ=160-170 MeV Eγ=170-180 MeV CB@MAMI TAPS99@MAMI DWIA + SE Eγ = (200-220)MeV dσ/dω [µb/sr] 10 Eγ=200-220 MeV Eγ=00-20 MeV 2 10 10 0 20 40 60 80 100 120 140 θ π [ ]
40 Ca: Total coherent cross sections σ [µb] 1.6 1.4 10 CB@ MAMI TAPS99@MAMI 1.2 1 0.8 PWIA DWIA DWIA + mod. 0.6 0.4 0.2 0 140 160 180 200 220 240 260 [MeV] E γ
40 Ca: π 0 angular distributions Eγ=160-170 MeV CB@MAMI TAPS99@MAMI Eγ=170-180 MeV DWIA + SE. Eγ=200-220 MeV Eγ=220-240 MeV
12 C: Total coherent cross sections σ [µb] 500 CB@MAMI TAPS99@ MAMI 400 00 PWIA DWIA DWIA + mod. 200 100 140 160 180 200 220 240 [MeV] E γ
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 2 2 2 ) 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
208 Pb: Preliminary assessment of Neutron skin Eγ = (200-220)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 2 10 0 5 40 45 50 [ ] θ π
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
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
Counts E γ = (200-220)MeV 10 2.5 2 1.5 1 0.5 40 Ca Nuclear decay photons deg9 Entries 86420 Mean.507 χ 2 / ndf 112.4 / 75 Height 91.9 ± 28.9 Centroid 4.011 ± 0.05 Sigma 0.564 ± 0.0524 p 8.59 ± 0.027 p4-0.4097 ± 0.0056 Counts E γ = (200-220)MeV 10 2.5 2 1.5 1 0.5 208 Pb deg9 Entries 8681 Mean.295 RMS 1.975 Underflow 0 Overflow 0 Integral 8.27e+04 Skewness 1.48 Height 0.664 ± 16894.2891 Centroid 2 ± 1.0 Sigma 0.4009 ± 0.8057 p 8.75 ± 0.09 p4-0.448 ± 0.026 Counts E γ 7 6 5 4 0 0 2 4 6 8 10 12 E γ [MeV] = (200-220)MeV 10 8 deg9 0 0 2 4 6 8 10 12 E γ [MeV] Entries 245547 E γ = (200-220)MeV 12 C Mean.709 10 RMS 1.991 Underflow 0 6 16 O Height 2981 Centroid 4.72 5 Sigma 0.6754 p 9.64 p4-0.915 Counts 4 deg9 Entries 2649 Mean 4.56 RMS 2.72 Underflow 0 Overflow 0 χ 2 / ndf 254.1 / 65 Height 2 ± 48.2 Centroid 6.8 ± 0.01 Sigma 1.191 ± 0.021 p 9.42 ± 0.051 p4-0.498 ± 0.0195 2 1 0 0 2 4 6 8 10 12 E γ [MeV] 2 1 0 0 2 4 6 8 10 12 E γ [MeV]
Nuclear decay photons 12 C Counts [arb. units] E γ 500 400 00 = (220-240)MeV θ π = (80-84) [ ] θ π E γ 180 160 140 120 = (220-240)MeV 200 100 0 0 2 4 6 8 10 12 [MeV] E γ 100 80 60 40 20 0 0 2 4 6 8 10 12 14 16 18 20 E γ^ [MeV] Background predominantly from split-off clusters from pi0 detection
Incoherent nuclear pion photoproduction 12 C(γ,π o ) 12 C(2 +, 4.4 MeV) dσ/dω [µb/sr] 25 16 14 20 12 Eγ=290±10 Eγ=25±10 MeV Takaki -hole model NPA 44 p570 (1985) 10 15 8 Nuclear wavefunctions have configuration coefficients extracted from e- scattering 6 10 4 52 Preliminary! 0 0 20 20 40 60 60 80 80 100 100120120 140 140 160 160 180 E γ [MeV] [ ] dσ/dω corrected for both π 0 and nuclear decay γ detection efficiency First determination of incoherent photoproduction θ π
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