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Dipole P0larizability
and
Energy Density Functionals
Takashi Hashimoto
Institute for Basic Science (IBS)
Rare Isotope Science Project (RISP)
For RCNP-E282, E316 Collaborations
NuSYM15
June 29 – July 3 at Krakow, Poland
Table of Contents
1.
2.
3.
4.
5.
Physics motivation and Strategy
Experimental method
Results
Discussion
Summary
Physics Motivation and Strategy
Symmetry energy of Nuclear EoS is important
for nuclear physics as well as nuclear astrophysics
Structure of neutron star
Core collapse supernova
Y. Suwa, et.al. Apj764(2013)99
http://www.astro.umd.edu/~miller/nstar.html
Accreting neutron star
X-ray bursts
Neutron star mass vs
radius
http://science1.nasa.gov/science-news/science-at-nasa/1997/ast19sep97_3/
Physics Motivation and Strategy
EoS for Energy per nucleon
E
E
(  ,  )  (  ,0)  S (  ) 2  ....
A
A
 (r )   n (r )   p (r )
 n (r )   p (r )
 (r ) 
 n (r )   p (r )
Symmetry energy
K sym
L
2
S ( )  J 
(   0 ) 
(    0 )  ....
2
3 0
18 0
L: Slope parameter
L  P  Rnstar
P: baryonic pressure
Salutation density
0=~0.16 fm-3
4
Determination of J and L is important for
nuclear astrophysics related to neutron star
Physics Motivation and Strategy
Neutron matter
~L
Symmetry energy
(+
~ Coulomb)
J
Ksym
Saturation density
A. W. Steiner et al., Phys. Rep. 411(2005)325
B. A. Brown, Phys. Rev. Lett, 85(2000)5296
Prediction of the neutron matter EOS is much model dependent
Physics Motivation and Strategy
Slope parameter (L) and Neutron Skin
Large L ⇔ Small Esym in low  ⇔ Thick neutron skin
Small L ⇔ Large Esym in low  ⇔ Thin neutron skin
Lie-Wen Chen etal., PRL94(032701)
X. Roca-Maza et al., PRL106, 252501 (2011)
Physics Motivation and Strategy
Neutron Skin Thickness and Dipole Polarizability (aD)
P. –G. Reinhard, W. Nazarewicz, PRC81, 051303 (2010)
Covariance analysis of energy density
functional calculations with Skyrm
SV-min effective interaction
Strong correlation between the dipole
polarizability and
the neutron skin of 208Pb
X. Roca-Maza, et al., PRC88, 024316 (2013)
Correlations observed in
various interaction sets.
a
DM
D
»
p e2 A < r 2 > é
54
J
5L ù
eA ú
êë1+
3J û
insights from the droplet model
Physics Motivation and Strategy
Electric Dipole Polarizability (aD)
Inversely energy weighted sum-rule of B(E1)
B(E1)
8
aD 
9
dB( E1)
 Ex
?
Discrete E1
states
PDR
Sn
GDR
Excitation Energy
Key of experimental issue:
precise measurement of E1 strength in wide energy region
including PDR and GDR. (Especially, low excitation energy region is
Physics Motivation and Strategy
How to measure electric dipole response of nuclei, precisely?
NRF, (g, g’)
(g, xn)
B(E1)
(p, p’)
The (g, xn) reaction has been used
to measure the GDR region.
→ There is difficulty to measure at
around Sn due to
the threshold problem.
Discrete E1
states
PDR
Sn
GDR
The (g, g’) reaction has been used
to measure the PDR region.
→ Extraction of the E1 strength is
quite model-dependent.
Excitation Energy
Polarized proton inelastic scattering can measure the total strength in wide
excitation energy region
Physics Motivation and Strategy
Merits and demerits of relativistic proton inelastic scattering at
forward angles as probe of electric dipole response of nuclei
An electromagnetic probe (Coulomb excitation)
High-resolution (20 -30 keV), high and uniform detection efficiency in Ex
Covers a broad excitation energy of 5 – 22 MeV
Sensitive to the total strength
Insensitive to the decay channel
Requires a small amount of target material (several mili-gram)
and a few days of beam time
Applicable to stable nuclei.
→ Coulomb excitation/dissociation
in inverse kinematics for unstable nuclei
Physics Motivation and Strategy
The results of 208Pb(p ,p’)
A. Tamii et al., PRL107(2011) 062502
X. Roca-Maza et al., PRC88(2013) 024316
S = 1 → Spin M1
S = 0 → E1
aD= 20.1 ± 0.6 fm3
Drnp= 0.165 ± (0.009)expt ±
(0.013)theor ± (0.021)est fm
for the estimated J = 31 ± 2est
Physics Motivation and Strategy
All EDFs agree on the strong correlation aD, rskin, L,
but the prediction for a given aD differ considerably.
→ - 208Pb result already exclude many Skyrme interactions
- Modern Skyrme-Hartree-Fock and relativistic models can be brought into agreement
without distorting the fit of the interaction parameters
Experimental information on aD in other nuclei is high interest to further constrain
the isovector part of the EDF interaction.
We focused Sn isotopes
Z = 50
1.24
(A-Z)/Z
1.48
(g, xn)
(g, g’)
Coulomb
dissociation
At first, we have been measured
the electric dipole response of 120Sn
1.64
Experimental Method
High-resolution polarized (p, p’) measurement
at zero degrees and forward angles
Experimental method
Experimental method
High-resolution WS beam-line
(dispersion matching)
RING cyclotron
AVF cyclotron
High-resolution spectrometer
Grand RAIDEN
Polarized proton beam
Energy: 295 MeV
Energy resolution: ~25 keV
Intensity: 2 nA
Averaged polarization: ~ 0.7
(both of longitudinal and sideway)
Experimental method
Grand Raiden spectrometer @ RCNP
Focal plane detectors
p
VDC
VDC
PLA
PLA
C block
MWPC
MWPC
p
Focal plane
Polarimeter
Polarized
Proton beam
Ep = 295 MeV
Total Spin Transfer (S)
3  (2 DSS  DLL )
S
4
DSS and DLL : Spin transfer observable
Polarized
Proton beam
Ep = 295 MeV
120Sn
target
Thickness: 6.5 mg/cm2
Purity 98.4 %
Results
Dipole polarizability of 120Sn
Results
Differential Cross Section (mb/sr/MeV)
Excitation energy spectrum
120Sn(p,
p’)
Ep = 295 MeV
q = 0° – 2.5°
Excitation Energy (MeV)
Results
E1 and spin-M1 decomposition
Polarization observable at 0 degs
Spin flip/non-spin flip separation
120Sn(p,
p’)
120Sn(p, p’), E1
120Sn(p, p’), Spin M1
120Sn(p, p’), E2 (DWBA)
Total Spin Transfer
3  (2 Dss  DLL )
S
4
=
1 for DS = 1 (Spin M1)
0 for DS = 0 (E1)
Results
E1 and spin-M1 decomposition
Comparison with Multi-pole Decomposition Analysis
Good agreement
within respective error bars
MDA was performed by A. M. Krumbholtz
PLB 744(2015)7
Results
The B(E1) strength distribution
Comparison with (g, xn) results
(p, p’), present
(g, n)
H. Utsunomiya et al.,PRC84(2011)055805
(g, xn)
S.C. Flutz et al.,PR186(1969)1255
(g, xn)
A. Lepretre et al.,NPA219(1974)39
All data agree with
each other
Results
Electric Dipole Polarizability
Ex
0.0
aD
22.0
10.0
1.12
7.00
135 MeV
28.9
0.51
120Sn(g,
0.31
xn’)
natSn(g,
xn’)
fm3
Total: 8.93 ±0.36 fm3
Results
Electric Dipole Polarizability
Dipole Polarizability is saturating
at around 30 MeV
Results
Quasi-Deuteron Excitation Contribution?
Absorption of a photon by a virtual deuteron in nuclei
120Sn
120Sn
aD(120Sn) = 8.93 ± 0.36 fm3
quasi-d: 0.34 ± 0.08 fm3
cf. 208Pb case
aD(208Pb) = 20.1 ± 0.6 fm3
quasi-d: 0.51 ± 0.15 fm3
quasi-d contribution
The contribution is small but is include in the numbers. It is unclear
whether it should be removed it for comparison with theoretical predictions.
Discussion
Test of EDF by using aD of 120Sn and 208Pb
Neutron skin thickness of 120Sn
Discussion
Skyrme interaction
SkM*
SG-II
BSk4
SV-min
SkT6
SkP
SkI3
SLy6
UNEDF2
SV-bus
RD-min
Theoretical calculations:
P-.G. Reinhard
J. Piekarewicz (FSU series)
Relativistic mean field model
DD-PC-min
FSU
DD-ME-min
(Parameters were optimized)
FSU2
Open symbols:
result varying symmetry energy param.
(J = 30 -34 MeV)
SV-min
RD-min
0.08 +0.3 –0.4 fm
Antiproton annihilation
0.16 ± 0.03 fm
(proton inelastic scattering)
0.18 ± 0.07 (spin dipole)
0.148 ± 0.034 fm
Discussion
Neutron Skin Thickness
Summary
Electric Dipole response of 208Pb and 120Sn have been precisely measured by
proton inelastic scattering at very forward angles including 0 degrees.
The continuous excitation energy spectrum was obtained
from PDR to GDR region.
The E1 and spin-M1 cross section is decomposed by using the total spin
transfer (PT) and Multi-Pole Decomposition analysis.
The PT and MDA results are consistent with each other.
The extracted E1 cross sections are good agree with the results of (g, xn)
measurements.
Electric Dipole Polarizability (aD) is clearly defined as the inversely energy
weighted sum-rile of B(E1) strength with less ambiguity in the integration
range and good convergence up to 30 MeV.
aD(208Pb) = 20.1 ± 0.6 fm3
aD(120Sn) = 8.93 ± 0.36 fm3
Summary
Theoretical models are indispensable for extracting the neutron skin
thickness and the symmetry energy parameters.
The correlation between aD of 208Pb and 120Sn provides an important test of
EDFs.
- Skyrme interactions can describe the data
- Relativistic mean field models are not good.
Obtained neutron skin thickness of 120Sn
Drskin(120Sn) = 0.148 ± (0.034) expt+thor fm
Considering the importance of polarizability data, systematic study is called
for.
Measurement on 112,114,124Sn and on 92,94,96Zr was done at last month
Data analysis on 90Zr, 96M0, 48Ca, 154Sm
Collaborators
Thank you
Backup Slides
PDR in 120Sn
A. M. Krumbholtz et. al., PLB 744(2015)7
PDR in 120Sn
A. M. Krumbholtz et. al., PLB 744(2015)7
(g, g): B. Ozel-Tahenov et al., PRC90(2014)024304
PDR in 120Sn
A. M. Krumbholtz et. al., PLB 744(2015)7
The observed strength by (g, g’) is significantly
smaller than the present (p, p’) data
GRAF (Grand RAiden Forward beam line)
To measure g-ray at around the target position of GR,
low background condition is necessary.
Primary beam particles are led to wall beam dump!
GRAF
Beam dump
CAGRAF (CAGRA+GRAF)
Combined between GR (GRAF mode) +
g-ray detector array
LaBr3
CAGRA
GRAF
Beam dump
BRILLIANT project
Beam system for Reaction of Isotopes of Long-life with
Light-Ions Applying Normal kinemaTics
This plan extend to unstable nuclei the
know-how of precise nuclear
spectroscopy by using light ion scattering
that is developing at RCNP.
Recoil mass separator
Gas Cather , gas jet
ISOL etc..
Production target
Implantation Long life unstable nuclei, which are
of isotope
produced by fragmentation, fusion,
fission, and transfer reaction, are
implanted in a material to use as a
reaction target.
Light ion beam
100Sn
138Sn
year
sec
min
day
min
sec
msec
Quasi-deuteron contribution
Quasi-d removed
Quasi-d removed