dipole polarizability and neutron skins in pb, sn and 48ca ......dipole polarizability and neutron...

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

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

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?


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)


Mass – Radius Relation of Neutron Stars

P. B. Demorest et al., Nature 467, 1081 (2010)

How can one experimentally distinguish between various predictions?


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


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


Symmetry Energy: Expansion in Density and

Neutron Excess


Taylor expansion of (N-Z) dependent part

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


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


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]


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


S-DALINAC at TU Darmstadt


Structure of the PDR in 208Pb Measured at the

S-DALINAC


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


Proton Scattering at 0° on 208Pb at RCNP/Osaka


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- =


Measurement of Spin Observables

Scheme of the FPP / Grand Raiden Setup


Decomposition into Spinflip / Non-Spinflip

Cross Sections


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


Multipole Decomposition of Angular

Distributions

I. Poltoratska et al., Phys. Rev. C 85 (2012) 041304(R)


Comparison of Both Methods at Low Ex

Total

DS = 1

DS = 0


Comparison of Both Methods at High Ex

Total

DS = 1

DS = 0


B(E1) Strength: Low-Energy Region


Photoabsorption Cross Section: GDR


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)


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)


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)


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


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


Electric Dipole Strength Distribution in 120Sn

Note: Low energy strength contributes about 9% to αD

T. Hashimoto et al., Phys. Rev. C 92 (2015)


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))


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


X. Roca-Maza et al., Phys. Rev. C 92, 064304 (2015)

Motivation


Neutron Skin in 48Ca?

Analysis analogous to the one in 208Pb(p,p‘)


B(E1) Strength in 48Ca


Comparison of 40Ca/ 48Ca in the GDR Region

Cross sections are comparable but there is an energy shift of (1.0 ± 0.3) MeV


Photoabsorption Cross Section in 40Ca up to

160 MeV

Note: above Ex = 60 MeV cross section is negligibly small


Photoabsorption Cross Section in 48Ca and

Running Sum of αD


αD(exp) = (2.06 ± 0.11) fm3

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


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


EDF: J. Piekarewicz et al., Phys. Rev. C 85, 041302 (2012)

EDF RM: X. Roca-Maza et al., Phys. Rev. C 92, 064304 (2015)

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


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


Predictions for observables related to the

neutron distribution in 48Ca


G. Hagen et al., Nature Physics 12 (2016)

Double Differential Cross Section of 40Ca


Running Sum of αD from χEFT predictions for 40Ca


Running Sum of αD from χEFT predictions for 48Ca


dipole polarizability and neutron skins in pb, sn and 48ca ......dipole polarizability and neutron...

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