Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity,...

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Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ-radiation for the evaluation of neutron skin and the enhancement of UNEDF theory K M Spohr, KWD Ledingham SUPA collaboration; University of the West of Scotland (UWS), Paisley & University of Strathclyde, Glasgow, Collaborators: Oak Ridge Nat. Lab, USA; IFIN-HH, Romania

Transcript of Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity,...

Page 1: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Precision Measurement of the dipole polarizability αD

of 208Pb, with high intensity, monoenergetic MeV γ-radiation for the evaluation of neutron skin and the

enhancement of UNEDF theory

K M Spohr, KWD Ledingham

SUPA collaboration; University of the West of Scotland (UWS), Paisley & University of Strathclyde, Glasgow, Collaborators: Oak Ridge Nat. Lab, USA; IFIN-HH, Romania

Page 2: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Overview

• Theoretical Motivation for the measurement of αD

(208Pb)(Inspired by W. Nazarewicz, Director HRIBF Oak Ridge & visiting Carnegie Professor UWS)

– Universal Nuclear Energy Density Functional (UNEDF), a leap forward

» UNEDF and Neutron-rich Matter in the Heavens and Earth• Neutron equation of state, neutron-rich matter and the n-skin (rskin) of

208Pb» Neutron matter, theoretical advise

• New theoretical approach, correlation between two observables• Dipole polarizability as the best observable for rskin

• The need for high presision

• Experimental considerations – Photonuclear reaction rate of 208Pb(γ,σtot)– ELI-NP ‘γ source’

» Intensity, Accuracy, Challenges & Timeline

• Summary

Page 3: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Theoretical motivation for the measurement of αD(208Pb)

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UNEDF, a leap forward in theory

• Universal Nuclear Energy Density Functional (UNEDF)– ‘Functionals’ aim to describe all measured and predict

unknown nuclear properties from finite nuclei to neutron stars n-EoS & p-EoS

» Functionals (e.g. ‘Skyrme based’) instead of ab initio calculations with individual wave functions of all nucleons consisting of 2- or 3-body Hamiltonians

• Based on ‘Density Functional Theory’ derived for atomic systems (W. Kohn)

• Ab initio to A~60, (2011); progress: A+1 per year

– Unprecedented theoretical effort in history of Nuclear Physics » 15 leading US institutions, chaired by W. Nazarewicz (Oak Ridge)» Use of worlds leading open computing facilities (Jaguar Oak

Ridge)• Highlighted by DoE and 43 million processor hrs approved

– New Theory: Crucial UNEDF functionals for n-EoS can best be probed with selected (208Pb) high precision photonuclear (NRF) measurements achievable with the ELI ‘γ source’ in the near future!

» ELI will inform core nuclear physics issues, basic research by photons!

» Directive for experimentalist and ideally suited for 3rd and 4th generation systems

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Neutron star crust

Neutron star crust

Astronomical observables

Astronomical observables

Laboratory observablesLaboratory

observables

132Sn132Sn

UNEDF and neutron-rich matter in the Heavens and on EarthUNEDF and neutron-rich matter in the Heavens and on Earth

Many-body theory

Many-body theory

In-medium interactionsIn-medium interactions

Equation of state

Equation of state

Microphysics(transport,…)Microphysics(transport,…)

Page 6: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Evaluating UNEDF,neutron matter in the labs

• Neutron Equation of State is very elusive to study in labs– Best cases ‘skin’ of: 208Pb and 48Ca (Doubly magic nuclei)

» little interfering of shell and pairing effects for 208Pb– No direct evidence of neutron skin yet (PREX soon?)

» PREX: 208Pb(e,e’) experiment at JLAB (12 year programme)

» Neutron-rich nuclei: rskin= rn – rp= 0.19 fm (208Pb)» rp (208Pb) is well known: 5.45 fm

208Pb

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Neutron matter, theoretical advise

• Recent theory: dipole polarizability αD (208Pb) the best observable to deduce rskin

(208Pb) with high precision.– Nucleons communicate with us through a lot of observables

» Some are important, others not » Some subsets of observables may be statistically correlated

(linked) » Some are very easy to measure, others extremely complicated

– Challenge for theory to guide experimentalists to select observables with the optimal information content

» Needs a lot of theoretical calculations, statistical modelling» Results can be astonishing und unexpected» A theoretical statistical uncertainty will prevail for the

predictions» Recent works:

• G.F. Bertsch et al., Phys. Rev. C 71, 054311 (2005).• M. Kortelainen et al., Phys. Rev. C 77, 064307 (2008).• J. Toivanen et al., Phys. Rev. C 78, 034306 (2008).• P. Klüpfel et al., Phys. Rev. C 79, 034310 (2009).• P.-G. Reinhard and W. Nazarewicz, Phys. Rev. C 81, 051303(R) (2010).• M . Kortelainen et al., Phys. Rev. C 82, 024313 (2010)

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Correlation between two observables

• The product correlation between two observable A,B is:

• Reinhard’s and Nazarewicz’s newest covariance analysis is the least biased and most exhausting way to find out the correlations between all conceivable observables in one model and derive theoretical uncertainties within the model!– Different models do not allow to deduce correlation between

observables!

=1: full alignment/correlation=0: not aligned/statistically independent

Page 9: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Nuclear observables evaluated for rskin (208Pb)

bulk equilibriumsymmetry energy

symmetry energyat surface density

slope of binding energyof neutron matter

dipole polarizability

neutron skin

low-energy dipole strength

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Result: aD the best observable!

A 10% uncertainty makes it impossible to use the currently best value for aD as an independent check on neutron skin. New experiment in need!

A.Veyssiere et al., Nucl. Phys. A 159, 561 (1970)

E. Lipparini and S. Stringari, Phys. Rep. 175, 103 (1989)

Page 11: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Uncertainty for n-EoS, the need for high precision

The UNEDF (n-EoS) theory improves dramatically for an uncertainty of δrskin /rskin< 0.4%, allowing to devise and(!) conclude on suggested functionals (SV-min-Rn)

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Experimental Considerations

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Low-lying E1 transitions

1/E weighting of αD

Energy [MeV]

σ

[b]

208Pb(γ,σtot), the GDR

NRF: Decrease in Intensity is prop. σ(E)

~10% error for each point

Threshold

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Measurements of rn in 208Pb with ELI

• Monochromatic, high intensity γ-beams with E1 multipolarity will allow highest precision measurements of αD (208Pb)– Reduction of photo transmission is proportional to photo-

excitation cross section– Polarisation of γ beam allows disentanglement of E1,M1 and E2 – Nuclear Resonance Fluorescence NRF experiments with

semiconductor detectors can be applied» Could use small targets e.g. for 48Ca (2nd best system)» Auxiliary neutron detectors could be used eventually

– σGDR (208Pb) ~200-300 mbar → Σ~0.01cm-1

» with >1013 photons/s high yields will be achieved, even for thin targets– Challenges:

» Beam stability (yield, energy, bandwidth), influence of high flux in target» Characterisation, use and development of radiation hardened detectors» Simulation

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ELI-NP γ source • Peak brilliance of 1022-23 ph mm-2 msrad-2 s-1 (0.1%BW)-1 at a

bandwidth of 1 ×10-3 will allow a high precision NRF measurement of αD(208Pb) and hence deduction of rskin (208Pb) with ELI-NP (2014)– The 100 mA ELI-ERL system will allow to even enhance the precision

by orders of magnitude (2017)» The experimental campaign can go along with the development of source

features

• Precision of NRF experiment can be realised in the regime demanded by theory of Reinhard and Nazarewicz! – Feeding into UNEDF theory

• rskin(208Pb) with ELI-NP more precise than any forthcoming PREX results(?) (δrskin /rskin~1.2% at best estimation for PREX)– Mass/Chargeless accelerator vs Charged accelerator

technology!» Possible PREX results could be independently verified, with higher

precision

• Unique possibility to proof the correlation of observables as predicted by Reinhard and Nazarewicz and inform UNEDF theory

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Summary • UNEDF which aims to get a full description of nuclear interaction for

ALL nuclei informing a gamut of related research fields can be informed by ELI-NP in a unique manner– Dipole polarizability (αD) is strongest correlated to rskin of 208Pb (rskin = c ×

αD) (Nazarewicz & Reinhard)– NRF measurement of αD to establish rskin (208Pb) – Testing of prediction from ‘SV-min-R’ : 0.191(24) fm

» “The most exciting NRF measurement to make”, W. Nazarewicz» δrSkin is as important as the value rSkin for the validation of the

functional ‘SV-min-R’ and hence for the deduction of n-EoS!• High precision NRF program for αD is feasible with the forthcoming

ELI’s ‘γ source’ as accuracy demands by theory can be matched with the superb beam qualities of ELI-NP and esp. ELI-100mA ERL

» ELI γ source offers a unique way to deduce rskin , n-EoS and UNEDF functionals

» Experimental program can progress with advance of ELI γ source features

• Intensity, maximum gamma energy, resolution

• ELI-NP as fine-tuneable Game Changer for Nuclear Physics, the dawn of a new era for understanding nuclear matter and the whole Universe

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End of TalkThanks for your attention

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Based on:P.G. Reinhard and WN, Phys. Rev. C (R) 2010; arXiv:1002.4140)

M. Kortelainen et al., 2010

Consider a model described by coupling constantsAny predicted expectation value of an observable is a function of these parameters. Since the number of parameters is much smaller than the number of observables, there must exist correlations between computed quantities. Moreover, since the model space has been optimized to a limited set of observables, there may also exist correlations between model parameters.

How to confine the model space to a physically reasonable domain?Statistical methods of linear-regression and error analysis

To what extent is a new observable independent of existing ones and what new information does it bring in? Without any preconceived knowledge, all different observables are independent of each other and can usefully inform theory. On the other extreme, new data would be redundant if our theoretical model were perfect. Reality lies in between.

fit-observables(may include pseudo-data)

fit-observables(may include pseudo-data)

ObjectivefunctionObjectivefunction

Page 19: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Consider a model described by coupling constants

The optimumparameter set

Uncertainty in variable A:

Correlation between variables A and B:

The reasonable domain is defined as that multitude of parameters around minimum that fall inside the covariance ellipsoid :

Hessian

Page 20: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

http://unedf.orgtowards n-stars

208Pb

48Ca

Page 21: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

To estimate the impact of precise experimental determination of neutron skin, we generated a new functional SV-min-Rn by adding the value of neutron radius in 208Pb, rn=5.61 fm, with an adopted error 0.02 fm, to the set of fit observables. With this new functional, calculated uncertainties on isovector indicators shrink by about a factor of two.

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Good isovectorindicators

Good isovectorindicators

Poor isovectorindicators

Poor isovectorindicators

Page 23: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.
Page 24: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

NN+NNNinteractions

Density MatrixExpansion

Input

Energy DensityFunctional

Observables

• Direct comparison with experiment

• Pseudo-data for reactions and astrophysics

Density dependentinteractions

Fit-observables• experiment• pseudo data

Optimization

DFT variational principleHF, HFB (self-consistency)

Symmetry breaking

DFT variational principleHF, HFB (self-consistency)

Symmetry breaking

Symmetry restorationMulti-reference DFT (GCM)

Time dependent DFT (TDHFB)

Symmetry restorationMulti-reference DFT (GCM)

Time dependent DFT (TDHFB)

Nuclear Density Functional Theory and Extensions

• two fermi liquids• self-bound• superfluid (ph and pp channels)• self-consistent mean-fields• broken-symmetry generalized product states

Page 25: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

P. Klüpfel et al, Phys. Rev. C79, 034310 (2009)

The model used: DFT (EDF + fitting protocol)

The fit-observables embrace nuclear bulk properties (binding energies, surface thicknesses, charge radii, spin-orbit splittings, and pairing gaps) for selected semi-magic nuclei which are proven to allow a reasonable DFT description.

SV-min Skyrme functional

RMF-d-t RMF functionalIncludes isoscalar scalar, vector, isovector vector, tensor couplings of vector fields, isovector scalar field with mass 980 MeV, and the Coulomb field; the density dependence is modeled only by non-linear couplings of the scalar field. Since the resulting NMP of this model (K=197MeV, asym=38MeV,m*/m=0.59) strongly deviate from the accepted values, we use this model only to discuss the robustness of our certain predictions and to illustrate the model dependence of the statistical analysis.

Page 26: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

rn (208Pb), current experimental status and what needs to be done

• Existing data can only predict αD within 10% at best, so the theoretical work by Reinhard and Nazarewicz demands a precision re-assessment of the dipole polarizability of 208Pb with a fine tuned experiment using a high precision tool, such as a mono-energetic gamma ray source emerging from high power laser systems – PREX experiment is supposed to deliver rn by end of 2010 with

1% accuracy– Skin of 208Pb lead has been measured in different experiments

» Hadron scattering: ratio of π+/π-=0.0(1), elastic proton scattering at 0.8GeV: 0.14(4), inelastic alpha scattering 0.19(9)

» Deviating results, systematic problems resulting in high systematic uncertainties, estimation S=0.17, Karatiglidis et al., PRC 65 (4), 044306, 2002

» Estimation of PREX working group ~5% accuracy at best for rn

Page 27: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

A word on PREX• PREX (Pb-Radius Experiment) is a big project aimed to

measure the neutron skin of 208Pb– Scheduled to run in autumn 2010 at the Jefferson Lab (Jlab)

USA– 1st proof of the existence of the neutron skin

» Neutron skin detection is very elusive!, project inaugurated 1999– Promises accuracy of ~1%

» New UNEDF functional depicted before as this demands <0.4%– Intends to measure the parity-violating electroweak

asymmetry in the elastic scattering of polarised 850MeV electrons on 208Pb (Z0 Boson)

» Based on a coincidence that the axial potential A(r) depends mainly on the neutron radius only, as the proton distribution gets weighted by the factor (1 - 4sin2θW) which is close to zero

• PREX does not render any further investigations obsolete!– Model dependence– Further independent proof– Higher accuracy possible with mono-energetic gamma sources

Page 28: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

HOW?

New generation of high intensity laser systems

3rd generation light sources

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• High intensity laser systems will be sources of mono-energetic γ beams (3rd generation light source)

– Aimed to provide high photon yields of 1013 photons/s (2015)– With hitherto unreachable high values for spectral brilliance:

1022-25 photons/ mm2 mrad2 s (0.1%BW) (2015-2020)• In principle TWO technological approaches

– Inverse Compton Backscattering of laser light on electron bunches

» Provided by ‘traditional’ ELINAC (warm-LINAC), energy recovering LINAC (new concept, ALICE accelerator Daresbury, U.K., 2010) ERL

• ELI foresees to follow the technological path of the MEGa-Ray ‘warm-Linac’ solution (Lawrence Livermore) in the first stage 2015

• From 2016 on the ERL solution is envisaged in a second phase

– Free Electron Laser systems» SCAPA (Scottish Centre for the Application of Plasma

Acceleration), 2014» Storage ring driven FEL ‘High Intensity Gamma-Ray Source’ (HIGS)

exists Duke University (USA), but 2nd generation light source with 5% BW

• 2 to 20 MeV photons at Iγ ~ 107 with 5% BW, best 2nd generation light source

Laser systems as providers of mono-energetic γ beams

Page 30: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

ELI & SCAPA, C’est quoi?

• ELI (Extreme Light Infrastructure)– Biggest European Laser Infrastructure initiated by G.

Mourou with 20 PW system to be build at the NIPNE in Magurele, Bucharest solely for laser based nuclear physics

» Aimed to achieve 20 PW with 1 Hz rep rate and I~1024-25 Wcm-2

» 1st phase to be completed 2014-15 with ~280M€ (allocated!)» ~80M€ allocated for the Gamma-ray infrastructure» April 2010 decision taken to follow the MEGa-Ray approach

(first 3rd generation light source, with unique intensity and spectral quality features, esp. reduced bandwidth)

– Collaboration of 13 (+x) European countries» Three additional sites in, Prague (High energy e-beam facility) and

Szeged (Attosecond science) + another, fourth high power system envisaged

• SCAPA (Scottish Centre for the Application of Plasma Acceleration)– £20M research infrastructure to be build @ Strathclyde

University– Tuneable γ source for energies of up to 20-50 MeV (2015)– FEL laser concept with laser produced high energy

electrons» Laser Plasma Wakefield accelerations: Schlenvoigt et al.,

Nature Phys 4, 130 (2008)

Page 31: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Blue-print High-Power Site

Magurele Site

NIPNE Director: V. Zamfir

Page 32: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Laser Induced Compton Backscattering,COBALD at Daresbury

Superconducting Elinac

• ELBE/150TW system @ FZ-Rossendorf is similar

• Blueprint for ELI mono-energetic photon beamline in 2nd phase (2015 onwards)

energy recovery of e-beam

Page 33: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

from Schoenlein RW et al., Science 274, 236 (1996)

Laser/e-beam collision geometry

• normalised vector potential of the laser field• electromagnetic energy gained across laser

wavelength compared to electron rest-mass• ~0 (classical Compton scattering), > 1 non-linear

Thompson Scattering

For given ϕ , the energy E is a defined

function of the scattering angle θ ϕ = 1800 (head on)

ϕ = 900 (transverse)

Page 34: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.
Page 35: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

In relativistic regime non-linear QED effects lead to a red-shift in the Compton scattered photons and the onset higher harmonicsÞ Transformation of optical radiation into the keV and MeV regimeby multiple Compton backscattering on relativistic electrons

Origin of Gamma-ray bursts suggested by Wozniak et al., Astrophys J 691, 495, 2009

Simulation of backscattered photons of LICB system,40 keV photons are shifted by ~10 keV, but due to non-linear effects, higher harmonics should occur

E [keV]

Page 36: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Features of MEGa-Ray, blueprint for ELI

Barty et al., ELI-NP meeting, Apr 2010

Page 37: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

SCAPA-like FEL system

Conceptional Design: Nakajima, Nature Physics 4, 92 - 93 (2008)

Concept-StudyLaser Plasma Wakefield accelerator

Page 38: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Low-lying E1 transitions

Am

plitu

de a

roun

d T

hres

hold

1/E weighting

Energy [MeV]

σ

[b]

208Pb(γ,σtot)

Critical regions can be scanned withELI-like systems with high δE resolution

Resolution should be highest for low energies, 7-14 MeV and highest amplitudes

Page 39: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Measurements of rn in 208Pb (48Ca) with ELI & SCAPA

• Monochromatic, high intensity γ-beams with E1 multipolarity will allow highest precision measurements of αD (208Pb)– Reduction of photo transmission is proportional to photo-

excitation cross section– Polarisation of γ beam allows disentanglement of E1,M1 and E2 – Nuclear Resonance Fluorescence NRF experiments with

semiconductor detectors can be applied» Could use small targets e.g. For 48Ca» Auxiliary neutron detectors could be used eventually

– σGDR (208Pb) ~200-300 mbar → Σ~0.01cm-1

» with 1013 photons/s high yields will be achieved, even for thin targets– Challenges:

» Influence of high flux onto target matter (heating, plasma effects?)» Characterisation, use and development of radiation hardened detectors» Simulation

Page 40: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Summary

• The aim of the talk was to show how important the neutron equation of state (EoS) is to address a manifold of fundamental open physics questions in a variety of fields such as nuclear and astrophysics, determined by the quest to optimise the UNEDF – 208Pb is the best testing case for dense neutron matter in the

laboratory, as it is a stable doubly magic isotope, readily available

» Measurements can inform the behaviour of neutron stars – New theory links αD (208Pb) with the existence and magnitude of

a neutron skin in 208Pb and predicts the thickness with highest accuracy

» Thus demands a re-assessment of αD (208Pb) with high precision» A proof of the predictions will allow to establish a good functional for

UNEDF– Emerging, laser driven γ sources such as MEGa-Ray and the

future ELI and SCAPA systems promise high photon yields with MeV energies thus enabling such high precision measurements

» offering a complementary route to test predictions and existing data with regard to the neutron EoS, by ~2015

» Potentially this 3rd generation laser driven light sources can provide the highest accuracy, which is of need to benchmark the theoretical predictions

Page 41: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Merci, on behalf of the SUPA nuclear group, including the laser buffins:

Klaus Spohr (UWS)

Mahmud Hassan (UWS, SUPA PhD )

Malte Roesner (UWS, SUPA-PhD, 09/2010)

Jody Melone (Strath)

Tom McCanny (Strath)

Ken Ledingham (Strath)

+2 new SUPA employments

In memoriam:

Wilfred Galster (Strath)

1948-2009

With special thanks to

Witek Nazarewicz,

Visiting Carnegie Professor, UWS

Page 42: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

Typel and Brown, Phys. Rev. C 64, 027302 (2001)

Various correlations reported…

Klimkiewicz et al., Phys. Rev. C 76, 051603(R) (2007)

Yoshida and Sagawa, Phys. Rev. C 69, 024318 (2004)

Furnstahl, Nucl. Phys. A 706, 85 (2002)

Page 43: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

αD→

Ski

n(2

08P

b) [

fm]

Page 44: Precision Measurement of the dipole polarizability α D of 208 Pb, with high intensity, monoenergetic MeV γ- radiation for the evaluation of neutron skin.

• Skin and Polarizability are strongly correlated calign=0.978 for 208Pb• Skins for 132Sn and 208Pb are strongly correlated

• Similar nature of neutron skins for doubly magic nuclei

• Other measurable entities are not as strongly correlated with ‘Skin’ functional • Some parameters e.g. κ show no correlation to ‘Skin’ at all