CREX WS 2013 Tamii - Jefferson Lab · 2013-03-19 · CREX WS, March 17-19, 2013 Determination of...

CREX WS, March 17-19, 2013

1

Dipole Polarizability of Nuclei(208Pb)

Atsushi Tamii

Research Center for Nuclear Physics (RCNP)Osaka University

I.Poltoratska, P. von Neumann‐Coseland the RCNP‐E282 Collaboration

CREX WorkshopMarch 17‐19, 2013 at Jefferson Lab.


Determination of the Symmetry Energy Term in EOS.

Lattimer et al., Phys. Rep. 442, 109(2007)

Accreting neutron star/white dwarf,X‐Ray burst, Superburst

Neutron Star Mass and Radius

Neutron Star Structure

Core‐Collapse Supernova

Neutron Star Cooling

Nucleosynthesis

K. Sumiyoshi, Astrophys. J. 629, 922 (2005)

http://www.astro.umd.edu/~miller/nstar.html

Langanke and Martinez‐Pinedo


Sn Sp

Particle （neutron） separation energy

0

PDR?IVGDRg.s.

oscillation of neutron skin against core?

oscillation between neutrons and protons

E1 1-

coreneutron skin

Low-Lying Dipole Strength

Electric Dipole (E1) Response


Sn Sp

(,xn)

GR and Continuum (Main Strength)Discrete (Small Strength)


(p,p’)

0

PDR IVGDRg.s.

208Pb(,)M1 strength measured by R.M. Laszewski et al, PRL61(1988)1710


(,’)NRF


P.‐G. Reinhard and W. Nazarewicz, PRC 81, 051303(R) (2010).

Self‐consistent mean field calc. based on the energy density functional theory using Skrym SV‐min interaction.‐ SV‐min parameters were determined to reproduce binding energies, r.m.s. radii, pairing gap, ls‐splitting, surface thickness, etc.

Correlation between the Neutron Skin Thicknessand Dipole Polarizability


(Electric) Dipole Polarizability



E1‐field restoring force symmetry energy

balanced



with neutron skinsmaller restoring force

w/o neutron skinlarger restoring force


larger restoring force



w/o neutron skin

thicker neutron skin

smaller restoring force

larger displacement

larger dipole polarizability




w/o neutron skinlarger restoring force

Sensitive to the difference between the proton and neutron density distribution.



= inversely energy weighted sum‐rule of B(E1)

: excitation energy

)1(

98

2 22

EdBdc absD


Sn Sp


0

PDR?IVGDRg.s.

oscillation of neutron skin against core?

oscillation between neutrons and protons

E1 1-

coreneutron skinLow-Lying

Dipole Strength



Coulomb Excitation at 0 deg.

Excited StateTarget Nucleus

Real Photon Measurements, NRF and (,xn)

Probing EM response of the target nucleus

Decay -rays or neutrons are measured.

Select low momentum transfer (q~0) kinematical condition,i.e. at zero degrees

Excited StateTarget Nucleus

Missing Mass Spectroscopy with Virtual Photon

Insensitive to the decay channel.Total strengths are measured.

Only the scattered protons are measured.

EM Interaction iswell known

(model independent)

A

A* A (or xn)

detector

(or A-x)

A

p pdetector

A*virtual photon q,


•An electromagnetic probe (Coulomb excitation)

•High‐resolution (20‐30keV), high (~90%)/uniform efficiency

•Covers a broad Ex of 5‐25MeV

•Insensitive to the decay property

•Requires small amount of target (several mili‐gram)and a few days of beam time

•Applicable to stable nuclei

Proton Inelastic Scattering at Forward Angles


Experimental Method

High-Resolution (p,p’) measurement at zero degrees and forward angles

AT et al., NIM A605, 326 (2009)


TOKYO

OSAKA

KYOTO

RIKENRCNP, Osaka Univ.

July 28 2008 seminar @ LNL

J-PARC


High-resolution Spectrometer

Grand Raiden

High-resolution WS beam-line(dispersion matching)

Research Center for Nuclear Physics, Osaka Univ.


Spectrometers in the 0-deg. experiment setup

Intensity : 3 ~ 8 nA

As a beam spot monitor in the vertical direction

Transport : Dispersive mode

Polarized Proton Beam at 295 MeV

Focal Plane Polarimeter




B(E1) strength distribution in 208Pb below the GDR region

I. Poltoratska, PhD thesis

B(E1) of discrete states


Multipole Decomposition

Neglect of data for >4: (p,p´) response too complex

Included E1/M1/E2 or E1/M1/E3 (little difference)


S=1 (M1)

S=0 (E1)

Concentration of spin‐M1 strength


Comparison between the two methods

Total

S = 1

S = 0




E1 Response of 208Pb and D

8.2 MeV 20 MeV 130 MeV

17.6 1.2D

in total 20.1±0.6 fm3/e2

AT et al., PRL107, 062502(2011)


Relativistic Quasiparticle Time Blocking Approximation

Quasiparticle Phonon Model

up to 130 MeV20.1±0.6 fm3/e2


Electric Dipole Polarizability


The dipole polarizability of 208Pb has been precisely determined.

D=20.1±0.6 fm3/e2

Theoretical models will be best constrained if neutron skin thickness (Rnp), in addition to D, is precisely determined,.

We try to extract Rnp symmetry energy parameters from D by using theoretical models.

accuracy of Rnp is not good enough yet


Calc. P.‐G. Reinhard and W. Nazarewicz, PRC81, 051303(R) (2010).

0.156+0.025‐0.021 fm

20.1±0.6 fm3/e2

PREX 0.33+0.16‐0.18 fm 0.49

proton elastic scattering0.211+0.054‐0.063 fm

0.15

0.15 0.27

Antiproton Atoms 0.18±0.02 fm0.16 0.20

J. Zenihiro et al., PRC82, 044611 (2010)

Friedman and Gal, Phys. Rep. 452, 89 (2007)

S. Abrahamyan et al., PRL108, 112502 (2012)

AT et al., PRL107, 062502(2011)


Correlation Between Dipole Polarizabilityand Neutron Skin Thickness

J. Piekarewicz et al., PRC85, 041302(2012)

769.0MODEL ABC


J. Piekarewicz, W. Nazarewicz, et al., PRC85, 041302(2012)

769.0MODEL ABC



J. Piekarewicz, W. Nazarewicz, et al., PRC85, 041302(2012)

769.0MODEL ABC



Neutron Skin Thickness Measurement by Electromagnetic Interaction


Neutron Skin Thickness of 208Pb

0.168±0.022 fm (this work)


Based on the work by X. Roca‐Maza et al., PRL106, 252501 (2011)

DP: Dipole Polarizability

L±15 MeV

Determination of Symmetry Energy

0.168±0.022 fm


PreliminaryGaussian weight func.

L±18 MeV



DP: Dipole PolarizabilityHIC: Heavy Ion CollisionPDR: Pygmy Dipole ResonanceIAS: Isobaric Analogue StateFRDM: Finite Range DropletModel (nuclear mass analysis)

n‐star: Neutron Star ObservationEFT: Chiral Effective Field Theory

Determination of Symmetry EnergyM.B. Tsang et al., PRC86, 015803 (2012).

I. Tews et al., PRL110, 032504 (2013)


PreliminaryL45±18 MeVJ=30.9±1.5 MeV

M.B. Tsang et al., PRC86, 015803 (2012).

and this work

DP: Dipole PolarizabilityHIC: Heavy Ion CollisionPDR: Pygmy Dipole ResonanceIAS: Isobaric Analogue StateFRDM: Finite Range DropletModel (nuclear mass analysis)

n‐star: Neutron Star ObservationEFT: Chiral Effective Field Theory


DP:

I. Tews et al., PRL110, 032504 (2013)


J. Birkhan et al.

18 keV

Existing data (E249)


J. Birkhan et al.


Multipole‐decomposition analysisin progress

Sorry, we don’t have the results yet.


The dipole polarizability of 208Pb has been precisely determined. D=20.1±0.6 fm3/e2

Model‐independent precise determination of the neutron skin thickness (Rnp), PREX‐II and CREX, are very important. Theoretical models will be best constrained if both D and Rnp are precisely determined.

Summary

Our methods can be applied to other stable nuclei for studying systematically dipole‐polarizability, PDR’s, and their dependence on mass, neutron excess, and deformation.

CREX WS, March 17-19, 2013Summary•Other nuclei: DP, PDR, spin‐M1 (data analysis in progress)96Mo (DCS and PT): Dirk Martin 48Ca (DCS): Jonny Birkhan90Zr (DCS): C. Iwamoto

(PDR‐region, published in PRL108, 262501 (2012))120Sn (DCS and PT): A.M. Krumbholtz, T. Hashimoto154Sm (DCS and PT): A. Krugmann88Sr, 92Mo (DCS): C. Iwamoto70Zn (DCS):


44

Collaborators RCNP, Osaka UniversityA. Tamii, H. Matsubara, H. Fujita, K. Hatanaka,

H. Sakaguchi Y. Tameshige, M. Yosoi and J. Zenihiro

Dep. of Phys., Osaka UniversityY. Fujita

Dep. of Phys., Kyoto UniversityT. Kawabata

CNS, Univ. of TokyoK. Nakanishi,

Y. Shimizu and Y. Sasamoto

CYRIC, Tohoku UniversityM. Itoh and Y. Sakemi

Dep. of Phys., Kyushu UniversityM. Dozono

Dep. of Phys., Niigata UniversityY. Shimbara

IKP, TU-DarmstadtP. von Neumann-Cosel, A-M. Heilmann,

Y. Kalmykov, I. Poltoratska, V.Yu. Ponomarev,A. Richter and J. Wambach

KVI, Univ. of GroningenT. Adachi and L.A. Popescu

IFIC-CSIC, Univ. of ValenciaB. Rubio and A.B. Perez-Cerdan

Sch. of Science Univ. of WitwatersrandJ. Carter and H. Fujita

iThemba LABSF.D. Smit

Texas A&M CommerceC.A. Bertulani

GSIE. Litivinova

RCNP‐E282


0‐5.3 deg

90Zr(p,p’) PDR region

0‐1.8 deg3.8‐5.3 deg

C. Iwamoto, et al., PRL108, 262501 (2012).

E=~20 keV


A. Krugmann et al., analysis in progress


Lattimer et al., arXiv1203.4286v1(2012)

Constant term of the Symmetry Energy

Slop

e Pa

rameter of the Sym

metry Energy


Determination of the dipole polarizability of 208Pb strongly constrain model parameters

Calc. for 208Pb dipole polarizabilityby J. Piekarewicz


Relativistic Quasiparticle Time Blocking Approximation

Quasiparticle Phonon Model

up to 130 MeV20.1±0.6 fm3/e2


Electric Dipole Polarizability


Thank You


C. Iwamoto, et al.,

Sn=12.0 MeVSn=11.1 MeV Sn=12.7 MeV


A. Carbone PRC81, 041301(R) (2010)

Correlation between the TRK sum rule of PDR and L


Nuclear Equation of State (EOS)

rr

rrr

pn

pn

rrr pn

Ksym is discussed from studies of e.g. isoscalar giant monopole resonances (ISGMRs).Determination of L is becoming important.

...0,, 2 SAE

AE

...183

202

00

0

symKLJS

Symmetry energy

L: Slope Parameter

EOS for Energy per nucleon

:0

Saturation Density~0.16 fm‐3

4starn RPL

(Baryonic Pressure)


Steiner et al., Phys. Rep. 411 325(2005)

核子

当たりの

エネル

ギー

Nucleon Density (fm‐3)E/A (M

eV)

E/N (M

eV)

Neutron Density (fm‐3)

Nuclear Equation of State (EOS)

Neutron Matter(=1)

Prediction of the neutron matter EOS is much model dependent.

Neutron Matter(=1)

Symmetry Energy(and Coulomb)

Nuclear Matter (=0)


X. Roca‐Maza et al., PRL106, 252501 (2011)

208Pb

Correlation between the Neutron Skin Thickness of 208Pb and the Slope Parameter (L)


Neutron density

Proton density

Neutron rms radius

Proton rms radius

Density distribution of protons and neutrons in a nucleus

My “simple explanation” of the correlation between the neutron skin thickness and the slope parameter (L)


Smaller S2 at higher

Larger S2 at lower

larger skin




Larger S2 at higher

Smaller S2 at lower

smaller skin


Neutron skin thickness

Density dependence of the symmetry energy


Larger S2 at higher

Smaller S2 at lower

smaller skin

Energy minimization= equilibrium condition


PREX at J-Lab: Z0 of weak interaction : sees the neutrons

proton neutron

Electric charge 1 0

Weak charge 0.08 1

Neutron form factor

)()(41)( 0

32 rqrjrdQF NN

Parity Violating Asymmetry

)()(sin41

22 2

22

2

QFQFQGA

P

NW

F

0

T.W. Donnelly, J. Dubach, I. Sick

C.J. Horowitz

NPA503, 589, 1989

6/16

)(sin41

22 22

2

QFQG

dd

dd

dd

dd

AP

WF

LR

LR

Model Independent Determination of Neutron Skin Thickness

Neutron Skin Thickness Measurement by Electroweak Interaction

C. J. Horowitz, S. J. Pollock, P. A. Souder, R. Michaels

PRC 63, 025501, 2001

measurement at q=0.475 fm‐1

CREX WS, March 17-19, 2013Neutron Skin Thickness Measurement by Electroweak Interaction

PREX at J-labS. Abrahamyan et al., PRL108, 112502 (2012)

CREX WS, March 17-19, 2013Neutron Skin Thickness Measurement by Electroweak Interaction

PREX

PREX Result: S. Abrahamyan et al., PRL108, 112502 (2012)

Theor. Calc.: X. Roca‐Maza et al., PRL106, 252501 (2011)

•Alternative approach at RCNP by using electromagnectic interaction

•The model independent determination of Rnp by PREX and futureprojects is quite important.

CREX WS, March 17-19, 2013My “very simplified picture” of the correlation between neutron skin thickness and dipole polarizability

One dimensional nucleus without surface diffuseness

E1

larger skin thickness smaller restoring force

E1

larger dipole polarizability

With finite diffuseness the relation becomes smoother.


PREX : Z0 of weak interaction : sees the neutrons

proton neutron

Electric charge 1 0

Weak charge 0.08 1

Neutron form factor

)()(41)( 0

32 rqrjrdQF NN

Parity Violating Asymmetry

)()(sin41

22 2

22

2

QFQFQGA

P

NW

F

0

T.W. Donnelly, J. Dubach, I. Sick

C.J. Horowitz

Nucl. Phys. A 503, 589, 1989

C. J. Horowitz, S. J. Pollock, P. A. Souder, R. Michaels

Phys. Rev. C 63, 025501, 2001

6/16Talk by C. Horowitz

)(sin41

22 22

2

QFQG

dd

dd

dd

dd

AP

WF

LR

LR

Model Independent Determination of Neutron Skin Thickness


Neutron Skin = RN - RP = 0.33 + 0.16 - 0.18 fm

Establishing a neutron skin at ~95 % CL Asymmetry leads to RN

proposed

published

Also considering a new 48Ca proposal

Spokespersons

K. Kumar R. Michaels K. PaschkeP. A. Souder G. Urciuoli

9/16

S. Abrahamyan et al. Phys. Rev. Lett. 108, 112502 (2012)


•Missing Mass Measurement

•insensitive to the decay property of the excited states and to the decay threshold.

•no feeding from upper excited states

•measure of the total (not partial) width

•At 0 deg, E1 states are dominantly excited by Coulomb interaction.Coulomb interaction is well known and is model independent.

•High‐resolution (20‐30keV). High (~100%) and uniform detection efficiency.

• Single shot measurement in a broad excitation energy region of 5‐25MeV.

• Cross section is high. We need thin (a few mg/cm2) target.

• E1/M1 decomposition by two methods: polarization transfer and angular distribution of the C.S. (MDA)

Proton Inelastic Scattering at Forward Angles

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CREX WS 2013 Tamii - Jefferson Lab · 2013-03-19 · CREX WS, March 17-19, 2013 Determination of...

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