Precision Measurement of the dipole polarizability αD
of 208Pb, with high intensity, monoenergetic MeV γradiation 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
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
Theoretical motivation for the
measurement of αD(208Pb)
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 & pEoS
» Functionals (e.g. ‘Skyrme based’) instead of ab initio calculations
with individual wave functions of all nucleons consisting of 2- or 3body 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!
UNEDF and neutron-rich matter in the Heavens and on Ea
132Sn
Equation of
state
In-medium
interactions
Many-body
theory
Neutron star
crust
Microphysics
(transport,…)
Laboratory
observables
Astronomical
observables
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) 208Pb
» 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
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
will
prevail
the predictions
• G.F. Bertschuncertainty
et al., Phys. Rev.
C 71,
054311 for
(2005).
» Recent works:• 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)
Correlation between two observables
• The product correlation between two observable A,B is:
=1: full alignment/correlation
=0: not aligned/statistically
independent
• 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!
Nuclear observables evaluated for rskin (208Pb)
bulk equilibrium
symmetry energy
symmetry energy
at surface density
slope of binding energy
of neutron matter
low-energy dipole
strength
dipole polarizability
neutron skin
Result: aD the best observable!
A.Veyssiere et al., Nucl. Phys. A 159, 561 (1970)
E. Lipparini and S. Stringari, Phys. Rep. 175, 103 (1989)
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!
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)
Experimental Considerations
208Pb(γ,σtot),
the GDR
1/E weighting of αD
~10% error for each point
σ [b]
NRF: Decrease in
Intensity is prop. σ(E)
Low-lying E1 transitions
Threshold
Energy [MeV]
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 photoexcitation 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
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
technology!
accelerator
vs
Charged
accelerator
» 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
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
End of Talk
Thanks for your attention
Based on:
P.G. Reinhard and WN, Phys. Rev. C (R) 2010; arXiv:1002.4140)
M. Kortelainen et al., 2010
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.
Consider a model described by coupling constants
Any 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
Objective
function
fit-observables
(may include pseudo-data)
Consider a model described by coupling constants
The optimum
parameter set
Hessian
The reasonable domain is defined as that multitude of parameters
around minimum that fall inside the covariance ellipsoid :
Uncertainty in variable A:
Correlation between variables A and B:
http://unedf.org
208Pb
48Ca
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.
Good isovector
indicators
Poor isovector
indicators
Nuclear Density Functional Theory and Extensions
Input
NN+NNN
interactions
Density Matrix
Expansion
Density dependent
interactions
Optimization
Fit-observables
• experiment
• pseudo data
•
•
•
•
•
Symmetry restoration
Multi-reference DFT (GCM)
Time dependent DFT (TDHFB)
two fermi liquids
self-bound
superfluid (ph and pp channels)
self-consistent mean-fields
broken-symmetry generalized product states
Energy Density
Functional
DFT variational principle
HF, HFB (self-consistency)
Symmetry breaking
Observables
• Direct comparison with
experiment
• Pseudo-data for reactions
and astrophysics
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
P. Klüpfel et al, Phys. Rev. C79, 034310 (2009)
RMF-d-t RMF functional
Includes 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.
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
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
HOW?
New generation of high
intensity laser systems
3rd generation light
sources
Laser systems as providers of monoenergetic γ beams
•
High intensity laser systems will be sources of monoenergetic 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 ‘warmLinac’ 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%
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
Magurele Site
NIPNE Director: V. Zamfir
Blue-print High-Power Site
Laser Induced Compton Backscattering,COBALD at Daresbury
Superconducting Elinac
energy recovery
of e-beam
• ELBE/150TW system @ FZ-Rossendorf is
similar
•Blueprint for ELI mono-energetic photon
beamline in 2nd phase (2015 onwards)
Laser/e-beam collision geometry
ϕ , the energy E is a defined
function of the scattering angle θ
ϕ = 1800 (head on)
ϕ = 900 (transverse)
For given
Thompson Scattering
•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
from Schoenlein RW et al., Science 274, 236 (1996)
E [keV]
Simulation of backscattered photons of LICB system,
40 keV photons are shifted by ~10 keV, but due to nonlinear effects, higher harmonics should occur
In relativistic regime non-linear QED effects lead to a red-shift
in the Compton scattered photons and the onset higher harmonics
Transformation of optical radiation into the keV and MeV regime
by multiple Compton backscattering on relativistic electrons
Origin of Gamma-ray bursts suggested by Wozniak et al., Astrophys J 691, 495,
Features of MEGa-Ray, blueprint for ELI
Barty et al., ELI-NP meeting, Apr 2010
SCAPA-like FEL system
Laser Plasma Wakefield
accelerator
Concept-Study
Conceptional Design: Nakajima, Nature Physics 4, 92 - 93
(2008)
208Pb(γ,σtot)
Critical regions can be scanned with
ELI-like systems with high δE resolution
σ [b]
1/E weighting
Low-lying E1 transitions
Energy [MeV]
Resolution should be
highest for low energies,
7-14 MeV and highest
amplitudes
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 photoexcitation 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
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
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
Various correlations reported…
Typel and Brown, Phys. Rev.
C 64, 027302 (2001)
Furnstahl, Nucl. Phys.
A 706, 85 (2002)
Klimkiewicz et al.,
Phys. Rev. C 76, 051603(R) (2007)
Yoshida and Sagawa,
Phys. Rev. C 69,
024318 (2004)
Skin(208Pb) [fm]
αD→
• Skin and Polarizability are strongly correlated calign=0.978 for 208
• 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 ‘S
• Some parameters e.g. κ show no correlation to ‘Skin’ at all