Neutron skins from
coherent pion
photoproduction
Dan Watts,
University of Edinburgh
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
neutron skin from nuclear models
Diffuseness (a)
208Pb
• Main features
obtained from 2PF
parameterisation
• Analytic relationship
a, c and √<r2>
• ap=0.46 fm
Neutron Skin (Drnp) fm
c
r(r) =
r0
æ r -c ö
÷
è a ø
1+exp ç
Neutron skin of 208Pb and neutron EOS
Warda, Centelles, Vinas Roca-Masa, arxiv 1202.4622 (2012)
208Pb
Neutron skin
and
Neutron
stars
Neutron
skins
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 95 122501 (2005)
Horowitz, PRL 86 5647 (2001)
Horowitz, PRC 062802 (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 80 025801 (2009)
Previous skin measurements for 208Pb
Recent reviews
Tsang PRC 015803 (2012)
Fattoyev arxiv:1306.6034 (2013)
Droplet [PRL 108 052501]
Nstar+QMC [PRL 108 081102]
Latimer ARNPS 62 485]
Tsang [PRC86 015803]
}
Analyses using
theory, expt
observation
PREX
[PRL 108 112502]
Pygmy dipole [PRC 76 051603]
Electric dipole [PRL 107 062502]
Heavy ion diffusion [PRC 72 064309]
Antiprotonic atoms [PRC 76 0143301]
Proton scattering [PRC 82 044601]
Pion beam [NPA 896 46]
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Drnp
• Most experimental information from strongly interacting probes
• Information on shape of neutron distribution also desirable
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
ds/dW(PWIA) = (s/mN2) A2 (qp*/2kg) F2(Eg*,qp*)2 |Fm(q)|2 sin2qp*
p0 final state interactions - use latest complex optical potentials tuned to p-A
scattering data. Corrections modest at low pion momenta
p0 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(gp→p0p) = √2/3 AV3 +√1/3(AVI –AIS)
A(gn→p0n) = √2/3 AV3 +√1/3(AVI +AIS)
D has I=3/2  AV3 only
EM couplings identical for p,n
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
g
e
Crystal Ball at MAMI
g
DEg ~ 2 MeV
108 g sec-1
g
TAPS
528 BaF2 crystals
Crystal Ball
672 NaI crystals
Coherent pion photoproduction - analysis
Eg=175±5 MeV
208Pb
Epdiff
Epdiff = Epcalc - Epdet
Eg=210±10 MeV
208Pb
Epdiff
Coherent
maxima
p0 theta (deg)
Non-coherent
contributions
p0 theta (deg)
Yield (au)
Extraction of coherent yield : Eg=210±10 MeV
q =0.415
(1st maxima)
q =0.655
(1st minima)
Epdiff
q =0.845
(2nd maxima)
q =1.25
(2nd minima)
Momentum transfer distributions
Eg=185  5 MeV
-- PWIA calculation
− Full calculation
Drechsel et. al. NPA 660 (1999)
Square root scale
Eg=195  5 MeV
Eg=210 10 MeV
Fitting procedure
Calculate grid
cn=6.28-7.07 fm
an=0.35-0.65 fm
Predictions smeared by q resolution
Eg=230  10 MeV
Interpolated fit to experimental data
(q = 0.3 - 0.9)
Free param. : norm, cn, an,
Fixed param. : cp=6.68 ap= 0.447
(PRC 76 014211 (2011))
Low Eg limit: D dominates
High Eg limit: p FSI not too large
(p-wave interactions set in)
The extracted skin properties
an = 0.55± 0.01(stat.)
ap
+0.02
-0.03
(sys.)
cn = 6.70 ± 0.03(stat.)fm
Drnp = 0.15± 0.03(stat.)
+0.01
(sys.)
-0.03
•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
Comparison with previous measurements
14
12
Coherent pion
10
Droplet
Nstar + QMC
Latimer
Tsang
8
}
Analyses using theory,
expt, observation.
PREX
Pygmy dipole
Electric dipole
Heavy ion diffusion
Antiprotonic atoms
6
4
Proton scattering
Pion scattering
2
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Drnp
• New result in general agreement with other methods
0.5
Comparison with theory
PRL 112 242502 (2014)
Future plans
•
Data under analysis for 116Sn, 120Sn, 124Sn & 56Ni
•
Plans for 48Ca, 40Ca in future
•
Discussions on Xenon isotopic chain
Eg=180  5 MeV
Ratio 116Sn/124Sn
(Arbitrary units)
Experimental data
•
qp
Very early stage analysis
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 !
Comparison of amplitudes for p0 production
Ratio p0 production cross section
( neutron / proton )
1.50E+00
1.30E+00
1.10E+00
MAID
9.00E-01
SAID-SN11
7.00E-01
5.00E-01
3.00E-01
140
150
160
170
180
190
200
210
220
230
240
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, 142001 2014
New PWA fit – D unaffected - large changes in N* couplings
Early results from tin isotope data
Eg=175  5 MeV
Ratio
116Sn/124Sn
(Arbitrary units)
Experimental data
Theoretical prediction
(without exp resolution)
qp
qp
•
Assuming SKM* neutron
distribution
•
Early stage analysis
2PF sum
2PF single
4
3.5
3
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
eries1
S
eries2
S
Estimate of systematics from p-A potential
Eg=185  5 MeV
-- PWIA calculation
− Full calculation
Drechsel et. al. NPA 660 (1999)
Eg=195  5 MeV
1st min/max shifted by ~0.01fm-1
10% accuracy -> 0.001fm-1
 ~0.01fm-1 systematic skin
Square root scale
(0.1fm skin~0.01fm-1 min/max position)
Eg=210 10 MeV
FSI shift in minima/maxima ~0.13 fm-1
Reproduces shift in data to <10%
Eg=230  10 MeV
c2 for fits
Eg=185  5 MeV
c2=0.33
-- PWIA calculation
− Full calculation
Drechsel et. al. NPA 660 (1999)
Square root scale
Eg=195  5 MeV
c2=0.38
Eg=210 10 MeV
c2=0.59
Note: expt error bars
Increased to give more
weight to minima in fit.
- hence values <1
Eg=230  10 MeV
c2=1.0
10% change in weighting of amplitudes
Form factors – 1st minima and 2nd maxima
Momentum transfer (fm-1)
Proton scattering data
Background fit parameters: data
Background fit parameters: Quasi free model
Extraction of coherent yield
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
Targets and test holder
5 MeV wide bin
Simple cut on M(p0)
Want to achieve similar stats as
208Pb
data ---> ~65k in 200 +-2.5 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)
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?
Form factors – 1st minima and 2nd maxima
Momentum transfer (fm-1)
Form factors approach to 1st minima
Momentum transfer (fm-1)
Pion elastic and inelastic scattering
Effect of diffuseness parameter on heights of maxima
Diffuseness
qp
qp
Diffuseness
qp
qp
Summary
• New high quality nuclear p0 photoproduction
data will give timely constraints on nuclear
structure and neutron stars
• Complementary measurement to PREX with
different systematic uncertainties
342 BaF2 crystals
• Nuclear decay photon detection to tag
incoherent processes -> accurate matter form
factors for lighter nuclei
672 NaI crystals