overview of the experimental constraints on symmetry energy betty tsang, nscl/msu
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Overview of the experimental constraints on symmetry energy
Betty Tsang, NSCL/MSU
Nuclear Equation of State
Relationship between energy, temperature pressure, density in nuclear matter
E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A
Nuclear Structure – What is the nature of the nuclear force that binds protons and neutrons into stable nuclei and rare isotopes?
Nuclear Astrophysics – What is the nature of neutron stars and dense nuclear matter?
Symmetry energy calculations with effective interactions constrained by Sn masses
This does not adequately constrain the symmetry energy at higher or lower densities
E/A (,) = E/A (,0) + d2S()
d = (n- p)/ (n+ p) = (N-Z)/A
a/s
2 A/EP
Brow
n, Phys. R
ev. Lett. 85, 5296 (2001)
Symmetry energy at
0
=1
-20
-10
0
10
20
30
0 0.1 0.2 0.3 0.4 0.5 0.6
EOS for Asymmetric Matter
Soft (=0, K=200 MeV)asy-soft, =1/3 (Colonna)asy-stiff, =1/3 (PAL)
E/A
(M
eV)
(fm-3)
=(n-
p)/(
n+
p)
How does E/A depend on and ?
Symmetry energy calculations with effective interactions constrained by Sn masses
This does not adequately constrain the symmetry energy at higher or lower densities
Brow
n, Phys. R
ev. Lett. 85, 5296 (2001)
Symmetry energy at
0
=1
Overview of the experimental constraints on symmetry energy around saturation density
...183
2
0
0
0
0
BsymB
osym
KLSE
symB
sym PE
LB
00
33
0
Experimental Observables:• Heavy Ion Collisionsn/p ratiosIsospin diffusions
• Mass model (FRDM)• Isobaric Analog States (IAS)• Giant dipole Resonance (GDR)
208Pb skin measurements• PREX• antiprotonic atom systematics• 208Pb(p,p)• 208Pb(p,p’) –dipole polarizability• Dipole Pygmy Resonance (DPR)
Summary and Outlook
Introduction
Overview of the experimental symmetry energy constraints around nuclear matter density
Strategies used to study the symmetry energy with Heavy Ion collisions below E/A=100 MeV
Vary the N/Z compositions of projectile and targets
• 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn
Measure N/Z compositions of emitted particles
• n & p yields• isotopes yields: isospin
diffusion Simulate collisions with
transport theory• Find the symmetry energy
density dependence that describes the data.
• Constrain the relevant input transport variables.
Neutron Number N
Pro
ton
Nu
mb
er Z
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZAasym
2)2(
Isospin degree of freedom
Hub
ble
S
TCrab Pulsar
B.A. Li et al., Phys. Rep. 464, 113 (2008)
Two HIC observables: n/p ratios and isospin diffusion
E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A
-100
-50
0
50
100
0 0.5 1 1.5 2
Li et al., PRL 78 (1997) 1644
Vasy
(MeV
)
/ o
NeutronProton
u =
stiff
soft
Y(n)/Y(p); t/3He, p+/p-
Projectile
Target
124Sn
112Sn
Isospin Diffusion; low r, Ebeam
Tsang et al., PRL 92 (2004) 062701
Experimental Layout
Courtesy Mike Famiano
Wall A
Wall BLASSA – charged particlesMiniball – impact parameter
Neutron walls – neutronsForward Array – time startProton Veto scintillators
E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A
-100
-50
0
50
100
0 0.5 1 1.5 2
Li et al., PRL 78 (1997) 1644
Vasy
(MeV
)
/ o
NeutronProton
u =
stiff
soft
Esym=12.7(r/ro)2/3 + 19(r/ro)gi
124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Double Ratiominimize systematic errors
Two observables: n/p ratios and isospin diffusion
E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A
Esym=12.7(r/ro)2/3 + 19(r/ro)gi
124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Double Ratiominimize systematic errors
Two observables: n/p ratios and isospin diffusion
• S() 12.3·(ρ/ρ0)2/3 + 17.6·
(ρ/ρ0) γi
• IQMD calculations were performed for i=0.35-2.0.
• Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used.
Zhang et.al.,Phys. Lett. B 664 (2008) 145
E/A (,) = E/A (,0) + d2S()d = (n- p)/ (n+ p) = (N-Z)/A
124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Double Ratiominimize systematic errors
Two observables: n/p ratios and isospin diffusion
0.4gi 1.05
• S() 12.3·(ρ/ρ0)2/3 + 17.6·
(ρ/ρ0) γi
• IQMD calculations were performed for i=0.35-2.0.
• Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used.
Zhang et.al.,Phys. Lett. B 664 (2008) 145
Isospin Diffusion Projectile
Target
124Sn
112Sn
mixed 124Sn+112Snn-rich 124Sn+124Snp-rich 112Sn+112Sn
mixed 124Sn+112Snn-rich 124Sn+124Snp-rich 112Sn+112Sn
( ) / 2( ) 2 AB AA BB
i ABAA BB
R
Ri= 1 no diffusion; Ri= 0 equilibrationExtent of diffuseness reflects strength of SE
0.4gi 1
0.45gi 0.95
Consistent constraints from the 2
analysis of isospin diffusion data
S(r)=12.5(r/ro)2/3 +17.6 (r/ro)gi
Projectile
Target
124Sn
112Sn
Deg
ree
of is
ospi
n di
ffus
ion
...183
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0
0
BsymB
osym
KLSE
0
00
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B
symsym
B
EL P
Symmetry energy constraints from HIC
arXiv:1204.0466S(r)=12.5(r/ro)2/3 +17.6 (r/ro)gi
0.4gi 1
Consistent with previous isospin diffusion constraints Chen, Li et al., Phys. Rev. Lett. 94 (2005) 032701
Giant Dipole ResonanceCollective oscillation of neutrons against protons
Consistency in Symmetry Energy Constraints
Trippa et al., PRC 77, 061304(R) (2008)
Tsang et al, PRL 102,122701 (2009)
Danielewicz & Lee, NPA818, 36 (2009)
Isobaric Analog States aa(A)
P. Moller et al, PRL 108,052501 (2012)
FRDM-2011a. s~0.57 MeV
Extrapolation from 208Pb radius to pressure in n-star
Typel & Brown, PRC 64, 027302 (2001) Steiner et al., Phys. Rep. 411, 325 (2005)
=L/3r00
symE
P( =0.1 r fm) (MeV/fm3)
An experimental overview of the symmetry energy around nuclear matter density
Experimental Observables:• Heavy Ion Collisionsn/p ratiosIsospin diffusions
• Mass model (FRDM)• Isobaric Analog States (IAS)• Giant dipole Resonance (GDR)
208Pb skin measurements• PREX• antiprotonic atom systematics• 208Pb(p,p)• 208Pb(p,p’) –dipole polarizability• Dipole Pygmy Resonance (DPR)
Summary and Outlook
Introduction
18
dRnp = 0.21±0.06 fm L=67±12.1 MeVSo=33±1.1 MeV
Laboratory experiments to measure the 208Pb neutron skin
Pb(p,p)
Zenihiro et al., PRC82, 044611 (2010)
Pb skin thickness from dipole polarizability
Pb(p,p’) Ebeam=295 MeV
dRnp = 0.156+0.025-0.021 fmTheoretical uncertainties underpredicted ?
Tamii et al., PRL107, 062502 (2011)
p+n
p
E
OE
p
polarizability
p+
p+
p+
J.Piekarewicz et al., arXiv:1201.3807
Reinhard & Nazarewicz ,PRC81, 051303 (R) (2010)
Summary of Pb skin thickness and symmetry energy constraints
Diverse experiments but consistent results
arXiv:1204.0466
See references inarXiv:1204.0466
Importance of 3n force in the EoS of pure n-matter
Challenge I: constraints from neutron star observations
arXiv:1204.0466 Steiner PRL108, 081102 (2012)
Challenge II: Constraints at very low density
Symmetry energy at r<0.05ro, T<10 MeV is dominated by correlations and cluster formation
J.B. Natowitz et al, PRL 104 (2010) 202501
Esy
m(n
)/E
sym
(n0)
Isospin Observables:Neutron/proton and t/3He and light isotopes energy spectra
• flow– px vs. y (v1)– Elliptic flow (v2)– Disappearance of flow (balance energy)• π+/π- spectra• π+/π- flow
Challenge III: Constraints at supra-normal densitieswith Heavy Ion Collisions
RIBF, FRIB, KoRIA
International Collaboration
ASY-EOS experiment @GSI, May 2011Au+Au @ 400 AMeV
96Zr+96Zr @ 400 AMeV 96Ru+96Ru @ 400 AMeV
~ 5x107 Events for each system
Beam Line
Shadow Bar
TofWall
Land(not splitted)
target
ChimeraKrakow array
MicroBall
Russotto & Lemmon
SAMURAI-TPC will be installed inside the SAMURAI dipole magnet in RIKEN
TPC chamber
Field Cage
Electronics and pad plane
Voltage step down
Outer enclosure
AT/TPC @ MSU
arXiv:1204.0466
NSCL/HiRA group
Acknowledgement:
A Time projection chamber is being built in the US to measure p+/p- & light charge particles in RIKEN
Nuclear Symmetry Energy (NuSym) collaboration http://groups.nscl.msu.edu/hira/sep.htm
Determination of the Equation of State of Asymmetric Nuclear Matter
MSU: B. Tsang & W. Lynch, G. Westfall, P. Danielewicz, E. Brown, A. SteinerTexas A&M University : Sherry Yennello, Alan McIntoshWestern Michigan University : Michael Famiano RIKEN, JP: TadaAki Isobe, Atsushi Taketani, Hiroshi SakuraiKyoto University: Tetsuya Murakami Tohoku University: Akira Ono GSI, Germany: Wolfgang Trautmann , Yvonne LeifelsDaresbury Laboratory, UK: Roy Lemmon INFN LNS, Italy: Giuseppe Verde, Paulo RussottoGANIL, France: Abdou ChbihiCIAE, PU, CAS, China: Yingxun Zhang, Zhuxia Li, Fei Lu, Y.G. Ma, W. TianKorea University, Korea: Byungsik Hong
Summary
Consistent Symmetry Energy constraints for 0.3<r/ro<1 using different experimental techniques and theories.
Importance of 3n force in the EoS of pure n-matter at high density.
arXiv:1204.0466
...183
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0
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osym
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B
sym PE
LB
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0
Extracting the 208Pb skin thickness from HIC
Typel & Brown, PRC 64, 027302 (2001)Steiner et al., Phys. Rep. 411, 325 (2005)
0.16-0.27 fm
arXiv:1204.0466
Laboratory experiments to measure the 208Pb neutron skin
208Pb
Existence of a neutron skin3% 1% measurementPREXII approved (2013-2014)
Phys Rev Let. 108, 112502 (2012)
Neutron Number N
Pro
ton
Nu
mb
er Z
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZAasym
2)2(
Symmetry Energy in Nuclei
Inclusion of surface terms in symmetry
2
23/2 )2()(
A
ZAAaAa SV
symsym
Hu
bb
le S
T
Crab Pulsar
)( 3/2AaAa SV
symsym
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZACsym
2)2(
Csym=22.4 MeV
)/
(3/1
2
A
baa
Fitting of Empirical Binding Energies
Ambiquities in the volume and surface terms of asym
Finite nuclei infinite nuclear matter
Souza et al., PRC 78, 014605 (2008)
Symmetry coefficient from Isobaric Analog States aa(A)
micaCSV EA
ZNa
A
ZaAaAaE
2
3/1
23/2 )(
Charge invariance: invariance of nuclear interactions under rotations in n-p space
Corrections for microscopic effects + deformation
So = 31.5 MeV; L = 75.6 – 107.1 MeVSo = 33.5 MeV; L = 80.4 – 113.9 MeV
Danielewicz & Lee, NPA818, 36 (2009)
Finite Range Droplet Model (FRDM) – Peter Moller
So = 32.5 ± 0.5 MeV; L = 70 ± 15 MeV
Sophisticated mass model by adding improvementsFRDM-2011a includes symmetry energy in the fit
P. Moller et al, PRL 108,052501 (2012)
Correlation analysis of Pb skin thickness
Reinhard & Nazarewicz ,PRC81, 051303 (R) (2010)
dRnp (208Pb)= 0.20±0.02 fm L=65.1±15.5 MeVSo=32.3±1.3 MeV
Klimkiewicz et al., PRC 76, 051603(R) (2007)Wieland et al., PRL102, 092502 (2009)Carbonne et al., PRC 81, 041301 (2010)
Skin thickness from Pygmy Dipole Resonance
Collective oscillation of neutron skin against the Core dRnp
dRnp = 0.16±(0.02)stat±(0.04)syst±(0.05)theo
Systematics of anti-protonic atoms
Large experimental and theoretical uncertaintiesNeed better quality data & theory
Antiproton probe the extreme tail of nuclei.
Data from 26 nuclei: 40Ca to 238U
Strong correlation between dRnp and asymmetry d.
A. Trzcinska et al, PRL 87, 082501 (2001); M. Centelles et al, PRL 102, 122502 (2009); B.A. Brown et al., PRC 76, 034305 (2007); B. Klos et al., PRC76, 014311 (2007)
dR
np
=( - )/d N Z A
Constraining the EoS using Heavy Ion collisions
pressure contours
density contours
Au+Au collisions E/A = 1 GeV)Au+Au collisions E/A = 1 GeV)
E/A (,) = E/A (,0) + d2S(); d = (n- p)/ (n+ p) = (N-Z)/A
Two observable due to the high pressures formed in the overlap region:– Nucleons are “squeezed out” above and below the reaction plane. – Nucleons deflected sideways in the reaction plane. –
Sid
ewar
d F
lowin plane
out of plane
Determination of symmetric matter EOS from nucleus-nucleus collisions
The curves represent calculations with parameterized Skyrme mean fields
They are adjusted to find the pressure that replicates the observed flow.
Danielewicz et al., Science 298,1592 (2002).
The boundaries represent the range of pressures obtained for the mean fields that reproduce the data.
They also reflect the uncertainties from the input parameters in the model.
1
10
100
1 1.5 2 2.5 3 3.5 4 4.5 5
symmetric matter
RMF:NL3Fermi gasBogutaAkmalK=210 MeVK=300 MeVexperiment
P (
MeV
/fm3 )
/0
NSCL experiments 05049 & 09042Density dependence of the symmetry energy
with emitted neutrons and protons& Investigation of transport model parameters
(May & October, 2009 )
facility ProbeBeam
EnergyTravel (k) $
year density
MSU n, p,t,3He 50-140 0 2009 <ro
GSI n, p, t, 3He 400 25 2010/2011 2.5 ro
MSU iso-diffusion 50 0 2011 <ro
RIKEN iso-diffusion 50 25 2012 <ro
MSU p+,p- 140 0 2014-2015 1-1.5 ro
RIKEN n,p,t, 3He,p+,p- 200-300 85 2013-2014 2ro
GSI n, p, t, 3He 800 25 2014 2-3ro
FRIB n, p,t,3He, p+,p- 200 0 2018- 2-2.5 ro
FAIR K+/K- 800-1000 ? 2018 3ro
GSI S394, May 2011
NSCL experiment 07038 Precision Measurements of
Isospin Diffusion, June 2011)
arXiv:1204.0466
Definition of Symmetry Energy
E/A (,) = E/A (,0) + d2S(); d = (n- p)/ (n+ p) = (N-Z)/A
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZAasym
2)2(
-20
-10
0
10
20
30
0 0.1 0.2 0.3 0.4 0.5 0.6
EOS for Asymmetric Matter
Soft (=0, K=200 MeV)asy-soft, =1/3 (Colonna)asy-stiff, =1/3 (PAL)
E/A
(M
eV)
(fm-3)
=(n-
p)/(
n+
p)
Challenges: Constraints on the density dependence of symmetry energy at supra normal density
Fourpi experiments are not optimized to measure symmetry energyNeed better experiments (ASYEOS & SAMURAI/TPC collaborations)
Xiao et al., PRL102, 062502 (2009)Russotto et al., PL B697 (2011) 471
How to obtain the information about EoS using heavy ion collisions?
Experiments:
Accelerator: Projectile, target, energy
Detectors: Information of emitted particles – identity, spatial info, energy, yields construct observables
Models
Input: Projectile, target, energy.
Simulate the collisions with the appropriate physics
Success depends on the comparisons of observables.
Theory must predict how reaction evolves from initial contact to final observables
Transport models (BUU, QMD, AMD)Describe dynamical evolution of the collision process
Summary of Pb skin thickness and symmetry energy constraints
arXiv:1204.0466
Hebeler et al., PRL 105, 161102 (2010)
Laboratory experiments to measure the 208Pb neutron skin
208Pb
PREX (Parity Radius experiment) measures Rnp of 208Pb
Why 208Pb? It has excess of neutrons dRnp=<rn
2>1/2 -<rp2>1/2
It is doubly-magicIts first excited state is 2.6 MeV
Expected uncertainty:APV (Parity-violating Asymmetry )~3% dRn ~1%
Ran in Jefferson Lab in Spring 2010.Phys Rev Let. 108, 112502 (2012)
Density dependence of Symmetry Energy E/A (,) = E/A (,0) + d2S(); d = (n- p)/ (n+ p) = (N-Z)/A
1
10
100
1 1.5 2 2.5 3 3.5 4 4.5 5
symmetric matter
RMF:NL3AkmalFermi gasFlow ExperimentKaons ExperimentFSU Au
P (
MeV
/fm
-3)
/0
Danielewicz, Lacey, Lynch, Science 298,1592 (2002)
Pre
ssur
e (M
eV/f
m3 )
1
10
100
1 1.5 2 2.5 3 3.5 4 4.5 5
neutron matter
Akmalav14uvIINL3DDFermi GasExp.+Asy_softExp.+Asy_stiff
P (
MeV
/fm3)
/0
??
...183
2
0
0
0
0
BsymB
osym
KLSE
symmetry energy constraints from IAS
Tsang et al, PRL 102,122701 (2009)
Equation of State (EoS)
-20
-10
0
10
20
30
0 0.1 0.2 0.3 0.4 0.5 0.6
EOS for Asymmetric Matter
Soft (=0, K=200 MeV)asy-soft, =1/3 (Colonna)asy-stiff, =1/3 (PAL)
E/A
(M
eV)
(fm-3)
=(n-
p)/(
n+
p)
Ideal gas: PV=nRT
Definition of Symmetry Energy
E/A (,) = E/A (,0) + d2S(); d = (n- p)/ (n+ p) = (N-Z)/A
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZAasym
2)2(
B.A
. Brow
n, PR
L 85 (2000) 5296
FRDMIAS
Reactions
nuclearstructure
U.S. effort at NSCLActive Target Time Projection Chamber
(MRI)
• Two alternate modes of operation• Fixed Target Mode with target wheel inside chamber:
– 4 tracking of charged particles allows full event characterization– Scientific Program » Constrain Symmetry Energy at >0
• Active Target Mode:– Chamber gas acts as both detector and thick target (H2, D2, 3He, Ne, etc.)
while retaining high resolution and efficiency– Scientific Program » Transfer & Resonance measurements, Astrophysically
relevant cross sections, Fusion, Fission Barriers, Giant Resonances• U.S. collaboration on AT-TPC, U.S. – French GET collaboration on electronics.
S(r)=12.5(r/ro)2/3 +C (r/ro)gi
Symmetry Energy from phenomenological interactionsB
.A. B
rown, P
RL
85 (2000) 5296
...183
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arXiv:1204.0466
Acknowledgement:
NSCL/HiRA group
Giant Dipole Resonance
Collective oscillation of neutrons against protons
Symmetry Energy from Giant dipole Resonsnce
Trippa et al., PRC 77, 061304(R) (2008)
Tsang et al, PRL 102,122701 (2009)
Danielewicz & Lee, NPA818, 36 (2009)
Isobaric Analog States aa(A)
P. Moller et al, PRL 108,052501 (2012)
FRDM-2011a. s~0.57 MeV
...183
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0
BsymB
osym
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B
sym PE
LB
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Mini-summary of symmetry energy constraints from FRDM and IAS
An experimental overview of the symmetry energy around nuclear matter density
Experimental Observables:• Heavy Ion Collisionsn/p ratiosIsospin diffusions
• Giant dipole Resonance (GDR)• Mass model (FRDM)• Isobaric Analog States (IAS)
208Pb skin measurements• PREX• antiprotonic atom systematics• 208Pb(p,p)• 208Pb(p,p’) –dipole polarizability• Dipole Pygmy Resonance (DPR)
Summary and Outlook
Introduction
...183
2
0
0
0
0
BsymB
osym
KLSE
symmetry energy constraints from nuclear masses
Tsang et al, PRL 102,122701 (2009)
Danielewicz & Lee, NPA818, 36 (2009)Isobaric Analog States aa(A) relates the asymmetry term to isospin and energy differences of two IAS
P. Moller et al, PRL 108,052501 (2012)
Sophisticated mass model by adding improvementsFRDM-2011a includes symmetry energy in the fit. s~0.57 MeV