dipole polarizability and neutron skins in pb, sn and 48ca ......dipole polarizability and neutron...
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Dipole Polarizability and Neutron Skins in 208Pb, 120Sn and 48Ca from High-Resolution
Proton Scattering
Equation of State of neutron matter and neutron skin Proton scattering at 0° and electric dipole response Dipole polarizability of 208Pb
Dipole polarizability of 120Sn
Dipole polarizability of 48Ca
2016 | Achim Richter
Supported by the DFG within SFB 634 and SFB 1245
MSU 2016
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Neutron stars are remnants of
the supernova explosion of
massive stars
Extremely high densities and
exotic forms of nuclear matter
Properties are described by an
Equation of State (EoS) of
neutron matter
Neutron Stars
2016 | Achim Richter | 2
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Nuclear Equation of State (EoS)
Energy as a function of
density (or pressure)
Well defined at ρ/ρ0 = 1 by
properties of stable nuclei
Large differences of model
predictions at high
densities: stiff or soft EoS?
2016 | Achim Richter | 3
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Neutron Matter EoS
Result from chiral effective field theory
T. Krüger, I. Tews, K. Hebeler, A. Schwenk, Phys. Rev. C 88, 025802 (2013)
𝜌 (fm−3)
E/A (MeV)
2016 | Achim Richter | 4
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Mass – Radius Relation of Neutron Stars
P. B. Demorest et al., Nature 467, 1081 (2010)
How can one experimentally distinguish between various predictions?
2016 | Achim Richter | 5
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Binding Energy of (Infinite) Neutron Matter
volume surface Coulomb symmetry pairing
For (infinite) neutron matter the pairing contribution is small
enough to be neglected (at least for low densities) and the
Coulomb term vanishes
only volume and symmetry term contribute
The volume term can be estimated from the saturation properties
The symmetry energy represents the largest uncertainty for the
EoS of neutron matter
2016 | Achim Richter | 6
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Symmetry Energy and Neutron Skin of Nuclei
Nuclear force leads to constant
density in the interior (saturation)
In heavy stable nuclei N > Z
because the symmetry energy is
balanced by the Coulomb
repulsion between protons
Extra neutrons are concentrated
on the surface
formation of a neutron skin
Neutron skin thickness Rn -Rp depends on the parameters of
the symmetry energy
2016 | Achim Richter | 7
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Symmetry Energy: Expansion in Density and
Neutron Excess
2016 | Achim Richter | 8
Taylor expansion of (N-Z) dependent part
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Taylor expansion of (N-Z) dependent part
Symmetry energy approximately determined by J (or Sv) and L
L describes density dependence (stiff or soft EoS)
Experimental approach used here: Electric Dipole Polarizability
Symmetry Energy: Expansion in Density and
Neutron Excess
2016 | Achim Richter | 9
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Static nuclear dipole polarizability
αD is measure of neutron skin
Theoretical predictions
P.G. Reinhard, W. Nazarewicz,
PRC 81, 051303 (2010)
J. Piekarewicz, PRC 83, 034319 (2011)
Symmetry Energy and Neutron Skin
αD =ℏ𝑐
2𝜋2𝑒2⋅ 𝜎−2 =
ℏ𝑐
2𝜋2𝑒2 ⋅ 𝜎𝑎𝑏𝑠 𝐸𝑥
𝐸𝑥2 =
8𝜋
9 ⋅ 𝐵 𝐸1 𝐸𝑥𝐸𝑥
𝑓𝑚3
𝑒2
Next: experimental
determination of αD
2016 | Achim Richter | 10
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Electric Dipole (E1) Response in Nuclei
p/n
neutron
skin ?
IV GDR
Oscillations of neutrons against protons:
Giant Dipole Resonance (GDR)
Oscillations of neutrons in the skin against core with N≈Z
Pygmy Dipole Resonance (PDR)
Excitation energy [MeV]
2016 | Achim Richter | 11
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Pygmy Dipole Resonance
Soft E1 mode due to oscillation of neutron
skin vs. approximately isospin-saturated core
J. Piekarewicz, Phys. Rev. C 73 (2006) 044325. S. Typel, B. A. Brown, Phys. Rev. C 64 (2001) 027302
PDR related to neutron skin Neutron skin related to
neutron-matter EoS
2016 | Achim Richter | 12
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S-DALINAC at TU Darmstadt
2016 | Achim Richter | 13
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Structure of the PDR in 208Pb Measured at the
S-DALINAC
2016 | Achim Richter | 14
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Structure of Low-Energy E1 Modes
How can we elucidate the structure of the low-energy E1 modes ?
Proton scattering at 0° Coulomb excitation of 1- states
high resolution: ∆E = 25 – 30 keV (FWHM)
angular distribution (E1/M1 separation)
polarization observables (spinflip / non-spinflip separation)
Electron scattering (preferentially at 180°) high resolution
transverse form factors needed
very sensitive to structure of the different modes
2016 | Achim Richter | 15
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Proton Scattering at 0° on 208Pb at RCNP/Osaka
2016 | Achim Richter | 16
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Polarization observables at 0° spinflip / non-spinflip separation
(model-independent)
E1/M1 Decomposition by Spin Observables
T. Suzuki, Prog. Theor. Phys. 103, 859 (2000)
sideway normal longitudinal
+ +
NNSSDD 0At
0ΔS
1ΔS
for
for
0
1
4
)2(3TransferSpinTotal
LLSS
DD
DSS DNN DLL -1 for DS = 1 1+
3 for DS = 0 1- =
2016 | Achim Richter | 17
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Measurement of Spin Observables
Scheme of the FPP / Grand Raiden Setup
2016 | Achim Richter | 18
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Decomposition into Spinflip / Non-Spinflip
Cross Sections
2016 | Achim Richter | 19
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Multipole Decomposition of Cross Section
DWBAdata
)()(
D
Dd
da
d
d
L
L
Restrict angular distribution to = 4°
(response at larger angles too complex)
DL = 0 isovector spin M1
DL = 1 E1 (Coulomb + nuclear)
DL > 1 only E2 (or E3) considered
2016 | Achim Richter | 20
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Multipole Decomposition of Angular
Distributions
I. Poltoratska et al., Phys. Rev. C 85 (2012) 041304(R)
2016 | Achim Richter | 21
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Comparison of Both Methods at Low Ex
Total
DS = 1
DS = 0
2016 | Achim Richter | 22
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Comparison of Both Methods at High Ex
Total
DS = 1
DS = 0
2016 | Achim Richter | 23
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B(E1) Strength: Low-Energy Region
2016 | Achim Richter | 24
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Photoabsorption Cross Section: GDR
2016 | Achim Richter | 25
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Polarizability and Neutron Skin
Precision value αD(208Pb) = 20.09(59) fm3/e2 (from all existing data up
to 130 MeV)
Within the model of Reinhard and Nazarewicz*
rskin = 0.156 ± fm0.021
0.025
Present model-independent measurement by PREX: rskin = 0.34 ± fm0.170.15
Improvement necessary for true constraint of any microscopic interaction
*P.G. Reinhard and W. Nazarewicz
PRC 81 (2010) 051303 (similar
results exist from J. Piekarewicz)
2016 | Achim Richter | 26
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Neutron Skin in 208Pb
1G. W. Hoffmann et al., PRC 21, 1488 (1980) 2A.Krasznahorkay et al., NPA 567, 521 (1994) 3A. Trzcińska et al., PRL 87, 082501 (2001) 4M. Csatlós et al., NPA 719, C304 (2003) 5E. Friedman et al, Phys. Rep. 452, 89 (2007)
6B. Kłos et al., PRC 76, 014311 (2007) 7A. Klimkiewicz et al., PRC 76, 051603 (2007) 8J. Zenihiro et al., PRC 82, 044611 (2010) 9A.Carbone et al., PRC 81, 041301 (2010)
2016 | Achim Richter | 27
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Constraints on Energy Density Functionals
Relation between αD and
rskin is model-dependent
Important constraint by 208Pb result
J. Piekarewicz et al., Phys. Rev. C 85 (2012) 041302(R)
2016 | Achim Richter | 28
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Neutron Skin Thickness and Symmetry Energy
X. Roca-Maza et al., Phys. Rev. C 88, 024316 (2013)
88, 024316
(2013).
Strong correlation between αDJ and the neutron skin, i.e. L
2016 | Achim Richter | 29
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DP: Dipole Polarizability
HIC: Heavy Ion Collision
PDR: Pygmy Dipole Resonance
IAS: Isobaric Analogue State
FRDM: Finite Range Droplet Model
n-star: Neutron Star Observation
χEFT: Chiral Effective Field Theory
QMC: Quantum Monte Carlo Theory
M.B. Tsang et al., Phys. Rev. C 86 (2012) 015803
I. Tews et al., Phys. Rev. Lett. 110 (2013) 032504
A. Tamii, PvNC, I. Poltoratska, Eur. Phys. J. A 50,
28 (2014)
QMC
Constraints on Symmetry Energy Parameter
Density independent part of the EoS
Neutr
on s
kin
thic
kness
2016 | Achim Richter | 30
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Electric Dipole Strength Distribution in 120Sn
Note: Low energy strength contributes about 9% to αD
T. Hashimoto et al., Phys. Rev. C 92 (2015)
2016 | Achim Richter | 31
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Correlation of Experimental αD Values of 208Pb and 120Sn
Experimental values of αD constrain the EDFs
Relativistic EDFs seem to have a problem
Darmstadt-Osaka Collaboration (T. Hashimoto et al., Phys. Rev. C 92 (2015))
2016 | Achim Richter | 32
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Correlation of Experimental αD Values of 208Pb,
120Sn and 68Ni
Only a handful of EDFs are able to describe the correlations
Those EDFs predict for 48Ca: αD = (2.06-2.52) fm3 and rskin = (0.15-0.18) fm
2016 | Achim Richter | 33
X. Roca-Maza et al., Phys. Rev. C 92, 064304 (2015)
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Motivation
2016 | Achim Richter | 34
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Neutron Skin in 48Ca?
Analysis analogous to the one in 208Pb(p,p‘)
2016 | Achim Richter | 35
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B(E1) Strength in 48Ca
2016 | Achim Richter | 36
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Comparison of 40Ca/ 48Ca in the GDR Region
Cross sections are comparable but there is an energy shift of (1.0 ± 0.3) MeV
2016 | Achim Richter | 37
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Photoabsorption Cross Section in 40Ca up to
160 MeV
Note: above Ex = 60 MeV cross section is negligibly small
2016 | Achim Richter | 38
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Photoabsorption Cross Section in 48Ca and
Running Sum of αD
2016 | Achim Richter | 39
αD(exp) = (2.06 ± 0.11) fm3
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Photoabsorption Cross Section and Running
Sum of αD compared to χEFT predictions
αD(exp) = (2.06 ± 0.11) fm3 αD(χEFT) = (1.8 - 2.6) fm
3
2016 | Achim Richter | 40
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Present Status of Experiment and Theory for
the Dipole Polarizability of 48Ca
Still needed: Correlation analysis
(e.g. αDJ vs. rskin) to constrain the
neutron skin
40Ca: αD = (1.87 ± 0.03) fm3
48Ca: αD = (2.06 ± 0.11) fm3
αD(40Ca) - αD(
48Ca) provides an
additional constraint for the
neutron skin
2016 | Achim Richter | 41
EDF: J. Piekarewicz et al., Phys. Rev. C 85, 041302 (2012)
EDF RM: X. Roca-Maza et al., Phys. Rev. C 92, 064304 (2015)
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Experimentalists and Theorists in the 48Ca
Project
Experiment: Darmstadt-Osaka
Theory: Darmstadt-Tennessee-TRIUMF
S. Bacca
S. Bassauer
J. Birkhan
G. Hagen
H. Matsubara
M. Miorelli
P. von Neumann-Cosel
T. Papenbrock
N. Pietralla
A. Richter
A. Schwenk
A. Tamii
2016 | Achim Richter | 42
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Comparison of 40Ca/ 48Ca in the GDR Region
Cross sections are comparable but there is an energy shift of (1.0 ± 0.3) MeV 40Ca (GDR): αD = (1.50 ± 0.02) fm
3
48Ca (GDR): αD = (1.75 ± 0.11) fm3
2016 | Achim Richter | 43
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Predictions for observables related to the
neutron distribution in 48Ca
2016 | Achim Richter | 44
G. Hagen et al., Nature Physics 12 (2016)
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Double Differential Cross Section of 40Ca
2016 | Achim Richter | 45
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Running Sum of αD from χEFT predictions for 40Ca
2016 | Achim Richter | 46
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Running Sum of αD from χEFT predictions for 48Ca
2016 | Achim Richter | 47
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