1. Neutron skins from coherent pion photoproduction
Dan Watts,
University of Edinburgh 1

2. Talk Outline Why measure the neutron skin ?
Basics of coherent p0 photoproduction process
Apparatus - The Crystal Ball at MAMI
Analysis & results for 208Pb
Future plans

3. 208Pb neutron skin from nuclear models
Main features obtained from 2PF
parameterisation
Analytic relationship
a, c and √<r2>
ap=0.46 fm
Diffuseness (a)
Neutron Skin (Drnp) fm c

4. Neutron skin of 208Pb and neutron EOS
Warda, Centelles, Vinas Roca-Masa, arxiv (2012)

5. Neutron skins and neutron stars
208Pb Neutron skin and Neutron stars
Thick neutron skin
→ Low transition density in neutron star
New data from
X-Ray telescopes
→ mass, radii, temp
of neutron stars !
Liquid
Solid
Proton fraction as a
function of density in neutron star
Rutel et al, PRL (2005)
Horowitz, PRL (2001)
Horowitz, PRC (2001)
Carriere, Astrophysical Journal 593 (2003)
Tsuruta, Astrophysical Journal Lett. 571 (2002)
Direct URCA Cooling
n → p + e- + n
e- + p → n + n
Constrains gravitational wave emission from neutron stars –
Frequency and damping modes!! PRC (2009)

6. Previous skin measurements for 208Pb
Recent reviews
Tsang PRC (2012)
Fattoyev arxiv: (2013) }
Droplet [PRL ]
Analyses using
theory, expt
observation
Nstar+QMC [PRL ]
Latimer ARNPS ]
Tsang [PRC ]
PREX [PRL ]
Pygmy dipole [PRC ]
Electric dipole [PRL ]
Heavy ion diffusion [PRC ]
Antiprotonic atoms [PRC ]
Proton scattering [PRC ]
Pion beam [NPA ]
Drnp
Most experimental information from strongly interacting probes
Information on shape of neutron distribution also desirable

7. Coherent pion photoproduction
Photon probe 
Interaction well understood
p0 meson – produced with
~equal probability on
protons AND neutrons.
Reconstruct p0
from p0→2g decay
Angular distribution of p0 → PWIA contains the matter form factor
p0 final state interactions - use latest complex optical potentials tuned to p-A scattering data. Corrections modest at low pion momenta
ds/dW(PWIA) = (s/mN2) A2 (qp*/2kg) F2(Eg*,qp*)2 |Fm(q)|2 sin2qp*
I lead an experiment which will measure the matter distribution of the nucleus using pion photoproduction. The process is shown schematically here. A photon is incident on the target nucleus and interacts to produce a pi0 meson which occurs with ~ equal probabliity on both neutrons and protons. If the nucleus remains in its ground state the probabliiy or amplitude for producing the pi0 from each nucleon adds coherently and you get a diffraction pattern in the angle of the emitted pi0s which contains accurate information on the distribution of matter in the nucleus.
From consideration of the theoretical model predictions and computer simulations of the detector apparatus we will get an accuracy in the rms matter radius close to what we presently know the charge radius. This will be sufficient to pin down any differences in the proton and neutron distributions.

8.  photoproduction - amplitude
Basic production amplitude ~ equal for protons and neutrons in D region
PWA (MAID,SAID) - close agreement Eg>180 MeV for p,n cross sections
 M1 well established multipole
Electromagnetic probe of the matter distribution!
Isospin structure of amplitude
A(p→0p) = √2/3 AV3 +√1/3(AVI –AIS)
A(n→0n) = √2/3 AV3 +√1/3(AVI +AIS)
 has I=3/2  AV3 only
EM couplings identical for p,n
As dominated by delta (I=3/2) only isosppin changing poart of amplitude contributes.
Therefore no differnce in reaction on proton and neutron – only arise from isoscalar isovector componoents. 8

9. The MAMI facility  100% duty factor electron microtron
MAMI-C 1.5 GeV upgrade
(MAMI-B 0.85 GeV)
One of the MAMI-C magnets  e 9

10. Upgraded Tagger
Goniometer
e- beam

11. Crystal Ball arrives at Frankfurt11

12. Crystal Ball at MAMI g DEg ~ 2 MeV 108 g sec-1 g TAPS
528 BaF2 crystals
Crystal Ball
672 NaI crystals

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

14. Extraction of coherent yield : Eg=210±10 MeV
q =0.415
(1st maxima)
q =0.655
(1st minima)
Yield (au)
Epdiff
q =1.25
(2nd minima)
q =0.845
(2nd maxima)

15. Momentum transfer distributions
E=185  5 MeV
-- PWIA calculation
− Full calculation
Drechsel et. al. NPA 660 (1999)
E=195  5 MeV
Square root scale
Fitting procedure
Calculate grid cn= fm
an= fm
Predictions smeared by q resolution
Interpolated fit to experimental data
(q = )
Free param. : norm, cn, an,
Fixed param. : cp=6.68 ap= 0.447
(PRC (2011))
Low Eg limit: D dominates
High Eg limit: p FSI not too large
(p-wave interactions set in)
E=210 10 MeV
E=230  10 MeV

16. The extracted skin properties ap
Systematics:
i) Normalisation parameter within ±5% of unity for all bins
i) Eg dependences – an high Eg bin 3.5s away from average
ii) Vary yield fitting procedure
iii) 10% variation relative p,n amplitudes in the model (mainly affects diffuseness)
iv) Different fit ranges 

17. Comparison with previous measurements
Coherent pion }
Droplet
Nstar + QMC
Analyses using theory, expt, observation.
Latimer
Tsang
PREX
Pygmy dipole
Electric dipole
Heavy ion diffusion
Antiprotonic atoms
Proton scattering
Pion scattering
Drnp
New result in general agreement with other methods

18. Comparison with theory
Diffuseness of neutron equal to proton would be an-ap = 0.0
Relativistic mean field models tend to give larger skins (and Cn-Cp)
Experimental evidence that difueseness of neutron distribution is larger than for protons in stable heavy nuclei has been lacking
PRL (2014)

19. Future plans Data under analysis for 116Sn, 120Sn, 124Sn & 56Ni
Plans for 48Ca, 40Ca in future
Discussions on Xenon isotopic chain
E=180  5 MeV
Ratio 116Sn/124Sn
(Arbitrary units)
Experimental data
Very early stage analysis qp

20. Summary Neutron skin powerful observable for nuclear structure
and the equation of state
Coherent pion photoproduction  complimentary
measurement with electromagnetic probe
First results for 208Pb agree with previous data for neutron skin
& additionally constrain the neutron diffuseness
More data to come !

21. Comparison of amplitudes for p0 production
Ratio p0 production cross section
( neutron / proton )
Photon energy (MeV)
New data on p0 production from p,n will improve
amplitudes away from the D(1232)
e.g. Krusche Phys. Rev. Lett. 112,
New PWA fit – D unaffected - large changes in N* couplings

22. Early results from tin isotope data
E=175  5 MeV
Experimental data
Assuming SKM* neutron
distribution
Early stage analysis
Ratio 116Sn/124Sn (Arbitrary units) qp
Theoretical prediction
(without exp resolution) qp

23. 2PF sum
2PF single

24. Estimate of systematics from p-A potential
E=185  5 MeV
-- PWIA calculation
− Full calculation
Drechsel et. al. NPA 660 (1999)
1st min/max shifted by ~0.01fm-1
10% accuracy -> 0.001fm-1
 ~0.01fm-1 systematic skin
(0.1fm skin~0.01fm-1 min/max position)
E=195  5 MeV
Square root scale
E=210 10 MeV
FSI shift in minima/maxima ~0.13 fm-1
Reproduces shift in data to <10%
E=230  10 MeV

25. c2 for fits -- PWIA calculation − Full calculation c2=0.33 c2=0.38
E=185  5 MeV
-- PWIA calculation
− Full calculation
Drechsel et. al. NPA 660 (1999)
c2=0.33
E=195  5 MeV
c2=0.38
Note: expt error bars
Increased to give more
weight to minima in fit.
- hence values <1
Square root scale
E=210 10 MeV
c2=0.59
E=230  10 MeV
c2=1.0

26. 10% change in weighting of amplitudes

27. Form factors – 1st minima and 2nd maxima
Momentum transfer (fm-1)

28. Proton scattering data

29. Background fit parameters: data

30. Background fit parameters: Quasi free model

32. Extraction of coherent yield

33. Fit signal + background with 2 Gaussians
Constrain signal from fit to coherent peak (below)
First iteration leave background parameters free
Second iteration constrain from fits to first iteration parameters

34. Targets and test holder
5 MeV wide bin
Simple cut on M(p0)
Want to achieve similar stats as 208Pb data ---> ~65k in MeV bin
~3 hours data Sn gave ~2.5k – need ~3 days get 45k
Need ~6 days for ½ mm thick target (similar to the proposal)

35. Isotopically pure targets
New enriched Sn targets – obtained from Russian company (Concettina)
5.2 g 112Sn and tin 124Sn – targets ½-1mm thick dependent on diameter.
Other targets
UK money available to buy further targets
6Li target (Edinburgh)
14C target (Basel) – compare with 12C
48Ca target in Mainz?

36. Form factors – 1st minima and 2nd maxima
Momentum transfer (fm-1)

37. Form factors approach to 1st minima
Momentum transfer (fm-1)

38. Pion elastic and inelastic scattering

39. Effect of diffuseness parameter on heights of maxima 
Diffuseness  

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