constraining the eos and symmetry energy from hi collisions
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Constraining the EoS and Symmetry Energy from HI collisions. Statement of the problem Demonstration: symmetric matter EOS Laboratory constraints on the symmetry energy from nuclear collisions Summary and outlook . - PowerPoint PPT PresentationTRANSCRIPT
Constraining the EoS and Symmetry Energy from HI collisions
Constraining the EoS and Symmetry Energy from HI collisions
• Statement of the problem
• Demonstration: symmetric matter EOS
• Laboratory constraints on the symmetry energy from nuclear collisions
• Summary and outlook
• Statement of the problem
• Demonstration: symmetric matter EOS
• Laboratory constraints on the symmetry energy from nuclear collisions
• Summary and outlook
William Lynch, Yingxun Zhang, Dan Coupland, Pawel Danielewicz, Micheal Famiano, Zhuxia Li, Betty Tsang
William Lynch, Yingxun Zhang, Dan Coupland, Pawel Danielewicz, Micheal Famiano, Zhuxia Li, Betty Tsang
• The density dependence of symmetry energy is largely unconstrained.
• What is “stiff” or “soft” is density dependent
• The density dependence of symmetry energy is largely unconstrained.
• What is “stiff” or “soft” is density dependent
EOS: symmetric matter and neutron matterEOS: symmetric matter and neutron matter
E/A (,) = E/A (,0) + 2S()
= (n- p)/ (n+ p) = (N-Z)/A
E/A (,) = E/A (,0) + 2S()
= (n- p)/ (n+ p) = (N-Z)/A
Brown, Phys. Rev. Lett. 85, 5296 (2001)
a/s
2 A/EP
Neutron matter EOS
-20
0
20
40
60
80
100
120
0 1 2 3 4
symmetric matter
NL3Bog1:e/aBog2:e/aK=300, m*/m=70Akmal_corr.
E/A
( M
eV)
/0
Need for probes sensitive to higher densities(Why the monopole is not sufficient and Knm is somewhat irrelevant.)
Need for probes sensitive to higher densities(Why the monopole is not sufficient and Knm is somewhat irrelevant.)
• If the EoS is expanded in a Taylor series about 0, the incompressibility, Knm provides the term proportional to (-0)2. Higher order terms influence the EoS at sub-saturation and supra-saturation densities.
• The solid black, dashed brown and dashed blue EoS’s all have Knm=300 MeV.
• If the EoS is expanded in a Taylor series about 0, the incompressibility, Knm provides the term proportional to (-0)2. Higher order terms influence the EoS at sub-saturation and supra-saturation densities.
• The solid black, dashed brown and dashed blue EoS’s all have Knm=300 MeV.
-20
0
20
40
60
80
100
120
0 1 2 3 4
symmetric matter
NL3Bog1:e/aBog2:e/aK=300, m*/m=70Akmal_corr.
E/A
( M
eV)
/0
-20
0
20
40
60
80
100
120
0 1 2 3 4
symmetric matter
NL3Bog1:e/aBog2:e/aK=300, m*/m=70Akmal_corr.
E/A
( M
eV)
/0
• The curvature Knm of the EOS about 0 can be probed by collective monopole vibrations, i.e. Giant Monopole Resonance.
• The curvature Knm of the EOS about 0 can be probed by collective monopole vibrations, i.e. Giant Monopole Resonance.
• To probe the EoS at 30, you need to compress matter to 30.
• To probe the EoS at 30, you need to compress matter to 30.
Constraining the EOS at high densities by nuclear collisionsConstraining the EOS at high densities by nuclear collisions
• Two observable consequences of the high pressures that are formed:
– Nucleons deflected sideways in the reaction plane.
– Nucleons are “squeezed out” above and below the reaction plane. .
• Two observable consequences of the high pressures that are formed:
– Nucleons deflected sideways in the reaction plane.
– Nucleons are “squeezed out” above and below the reaction plane. .
pressure contours
density contours
Au+Au collisions E/A = 1 GeV)Au+Au collisions E/A = 1 GeV)
1
10
100
1 1.5 2 2.5 3 3.5 4 4.5 5
Symmetric Matter
GMR (K=240)Flow Experiment
P (
MeV
)/fm
-3)
/0
1
1 0
1 0 0
1 1 .5 2 2 .5 3 3 .5 4 4 .5 5
sy m m etr ic m atter
R M F :N L 3A k m alF e rm i g asF lo w E x p e rim en tF S U A uG M R E x p e rim en t
P(M
eV/f
m-3
)
/0
1
1 0
1 0 0
1 1 .5 2 2 .5 3 3 .5 4 4 .5 5
E O S _ D D
R M F :N L 3A k m alF e rm i g asF lo w E x p e rim en tK ao n E x p e rim en tF S U A uG M R E x p erim en t
P(M
eV/f
m-3
)
/0
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
Danielew
icz et al., Scie
nce
298,1
59
2 (2
002).
• Note: analysis required additional constraints on m* and NN.
• Flow confirms the softening of the EOS at high density.
• Constraints from kaon production are consistent with the flow constraints and bridge gap to GMR constraints.
• Note: analysis required additional constraints on m* and NN.
• Flow confirms the softening of the EOS at high density.
• Constraints from kaon production are consistent with the flow constraints and bridge gap to GMR constraints.
Constraints from collective flow on EOS at >2 0.Constraints from collective flow on EOS at >2 0.
E/A (, ) = E/A (,0) + 2S() = (n- p)/ (n+ p) = (N-Z)/A1
• The symmetry energy dominates the uncertainty in the n-matter EOS.
• Both laboratory and astronomical constraints on the density dependence of the symmetry energy at supra-saturation density are urgently needed.
• The symmetry energy dominates the uncertainty in the n-matter EOS.
• Both laboratory and astronomical constraints on the density dependence of the symmetry energy at supra-saturation density are urgently needed.
Danielew
icz et al., Scie
nce
298,1
59
2 (2
002).
Probes of the symmetry energyProbes of the symmetry energy
• To maximize sensitivity, reduce systematic errors:
– Vary isospin of detected particle
– Vary isospin asymmetry =(N-Z)/A of reaction.
• Low densities (<0):
– Neutron/proton spectra and flows
– Isospin diffusion
• High densities (20) :
– Neutron/proton spectra and flows + vs. - production
• To maximize sensitivity, reduce systematic errors:
– Vary isospin of detected particle
– Vary isospin asymmetry =(N-Z)/A of reaction.
• Low densities (<0):
– Neutron/proton spectra and flows
– Isospin diffusion
• High densities (20) :
– Neutron/proton spectra and flows + vs. - production
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/AE/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
symmetry energy<0
<0
Why choose to measure Isospin Diffusion, n/p flows and pion production?
Why choose to measure Isospin Diffusion, n/p flows and pion production?
• Supra-saturation and sub-saturation densities are only achieved momentarily
• Theoretical description must follow the reaction dynamics self-consistently from contact to detection.
• Theoretical tool: transport theory:
– The most accurately predicted observables are those that can be calculated from i.e. flows and other average properties of the events that are not sensitive to fluctuations.
• Isospin diffusion and n/p ratios:
– Depends on quantities that can be more accurately calculated in BUU or QMD transport theory.
– May be less sensitive to uncertainties in (1) the production mechanism for complex fragments and (2) secondary decay.
• Supra-saturation and sub-saturation densities are only achieved momentarily
• Theoretical description must follow the reaction dynamics self-consistently from contact to detection.
• Theoretical tool: transport theory:
– The most accurately predicted observables are those that can be calculated from i.e. flows and other average properties of the events that are not sensitive to fluctuations.
• Isospin diffusion and n/p ratios:
– Depends on quantities that can be more accurately calculated in BUU or QMD transport theory.
– May be less sensitive to uncertainties in (1) the production mechanism for complex fragments and (2) secondary decay.
),,( tprf
Measurement of n/p spectral ratios: At E/A = 50 MeV, it probes the pressure due to asymmetry term at 0.
Measurement of n/p spectral ratios: At E/A = 50 MeV, it probes the pressure due to asymmetry term at 0.
• Expulsion of neutrons from bound neutron-rich system by symmetry energy. At E/A=50 MeV, 0 is the relevant domain.
• Has been probed by direct measurements of n vs. proton emission rates in central Sn+Sn collisions.
• Expulsion of neutrons from bound neutron-rich system by symmetry energy. At E/A=50 MeV, 0 is the relevant domain.
• Has been probed by direct measurements of n vs. proton emission rates in central Sn+Sn collisions.
•Double ratio removes the sensitivity to neutron efficiency and energy calibration. •Double ratio removes the sensitivity to neutron efficiency and energy calibration.
soft symmetry energyBao-An Li et al., PRL 78, 1644 (1997).
stiff symmetry energy
• Collide projectiles and targets of differing isospin asymmetry
• Probe the asymmetry =(N-Z)/(N+Z) of the projectile spectator during the collision.
• The use of the isospin transport ratio Ri() isolates the diffusion effects:
• Useful limits for Ri for 124Sn+112Sn collisions:
– Ri =±1: no diffusion
– Ri 0: Isospin equilibrium
• Collide projectiles and targets of differing isospin asymmetry
• Probe the asymmetry =(N-Z)/(N+Z) of the projectile spectator during the collision.
• The use of the isospin transport ratio Ri() isolates the diffusion effects:
• Useful limits for Ri for 124Sn+112Sn collisions:
– Ri =±1: no diffusion
– Ri 0: Isospin equilibrium
Isospin diffusion in peripheral collisions, also probes symmetry energy at <0.
Isospin diffusion in peripheral collisions, also probes symmetry energy at <0.
rich.prot_bothrich.neut_both
rich.prot_bothrich.neut_bothi
2/)(2)(R
P
N
mixed 124Sn+112Sn
n-rich 124Sn+124Sn
p-rich 112Sn+112Sn
mixed 124Sn+112Sn
n-rich 124Sn+124Sn
p-rich 112Sn+112Sn
Systems{Example:
neutron-rich projectile
proton-rich target
measure asymmetry after collision
What influences isospin diffusion?What influences isospin diffusion?
• Isospin diffusion equation:
• Naive expectations:
– D increases with S()
– D decreases with np
• We tested this by performing extensive BUU and QMD calculations with S() for the form:
– S() = 12.5·(ρ/ρ0)2/3 + Sint· (ρ/ρ0) γi
• Results:
– Diffusion sensitive to S(0.4ρ0)
– Diffusion increases with Sint and decreases with i
– Diffusion increases with np
– Diffusion decreases when mean fields are momentum dependent and neck fragments emerge.
– Diffusion decreases with cluster production.
• Isospin diffusion equation:
• Naive expectations:
– D increases with S()
– D decreases with np
• We tested this by performing extensive BUU and QMD calculations with S() for the form:
– S() = 12.5·(ρ/ρ0)2/3 + Sint· (ρ/ρ0) γi
• Results:
– Diffusion sensitive to S(0.4ρ0)
– Diffusion increases with Sint and decreases with i
– Diffusion increases with np
– Diffusion decreases when mean fields are momentum dependent and neck fragments emerge.
– Diffusion decreases with cluster production.
Djj pn
Djj pn
DDjj pn
DDjj pn
Sensitivity to symmetry energySensitivity to symmetry energy
Stronger density dependence
Weaker density dependence
Lijun Shi, thesis
richotonrichNeutron
richotonrichNeutroniR
Pr
Pr 2/)(2)(
• The asymmetry of the spectators can change due to diffusion, but it also can changed due to pre-equilibrium emission.
• The use of the isospin transport ratio Ri() isolates the diffusion effects:
• The asymmetry of the spectators can change due to diffusion, but it also can changed due to pre-equilibrium emission.
• The use of the isospin transport ratio Ri() isolates the diffusion effects:
Tsang et al., PRL92, 062701 (2004)
Probing the asymmetry of the SpectatorsProbing the asymmetry of the Spectators
• The main effect of changing the asymmetry of the projectile spectator remnant is to shift the isotopic distributions of the products of its decay
• The main effect of changing the asymmetry of the projectile spectator remnant is to shift the isotopic distributions of the products of its decay
• This can be described by the isoscaling parameters and :
• This can be described by the isoscaling parameters and :
)ZNexp(C
Z,NY
Z,NY
1
2
Tsang et. al.,PRL 92, 062701 (2004)
no diffusion
Liu et al.PRC 76, 034603 (2007).
Determining Ri()Determining Ri()
• In statistical theory, certain observables depend linearly on :
• Calculations confirm this• Experiments confirm this
• In statistical theory, certain observables depend linearly on :
• Calculations confirm this• Experiments confirm this
• Consider the ratio Ri(X), where X = , X7 or some other observable:
• If X depends linearly on 2:
• Then by direct substitution:
• Consider the ratio Ri(X), where X = , X7 or some other observable:
• If X depends linearly on 2:
• Then by direct substitution:
richotonPrrichNeutron
richotonPrrichNeutroni XX
2/)XX(X2)X(R
baX 2
2ii RXR
)ZNexp(C
Z,NY
Z,NY
1
2
richotonrichNeutron
richotonrichNeutroniR
Pr
Pr 2/)(2)(
richotonrichNeutron
richotonrichNeutroniR
Pr
Pr 2/)(2)(
dcBeY/LiYln X
,ba
277
7
2
Probing the asymmetry of the SpectatorsProbing the asymmetry of the Spectators
• The main effect of changing the asymmetry of the projectile spectator remnant is to shift the isotopic distributions of the products of its decay
• The main effect of changing the asymmetry of the projectile spectator remnant is to shift the isotopic distributions of the products of its decay
• This can be described by the isoscaling parameters and :
• This can be described by the isoscaling parameters and :
)ZNexp(C
Z,NY
Z,NY
1
2
Tsang et. al.,PRL 92, 062701 (2004)1.0
0.33
-0.33
-1.0
Ri()
Liu et al.PRC 76, 034603 (2007).
Quantitative valuesQuantitative values
• Reactions:
– 124Sn+112Sn: diffusion
– 124Sn+124Sn: neutron-rich limit
– 112Sn+112Sn: proton-rich limit
• Exchanging the target and projectile allowed the full rapidity dependence to be measured.
• Gates were set on the values for Ri() near beam rapidity.
– Ri() 0.470.05 for 124Sn+112Sn
– Ri() -0.44 0.05 for 112Sn+124Sn
• Obtained similar values for Ri(ln(Y(7Li)/ Y(7Be))
– Allows exploration of dependence on rapidity
• Reactions:
– 124Sn+112Sn: diffusion
– 124Sn+124Sn: neutron-rich limit
– 112Sn+112Sn: proton-rich limit
• Exchanging the target and projectile allowed the full rapidity dependence to be measured.
• Gates were set on the values for Ri() near beam rapidity.
– Ri() 0.470.05 for 124Sn+112Sn
– Ri() -0.44 0.05 for 112Sn+124Sn
• Obtained similar values for Ri(ln(Y(7Li)/ Y(7Be))
– Allows exploration of dependence on rapidity
Liu et al., (2006)
v/vbeam
Liu et al.P
RC
76, 034603 (2007).
richotonrichNeutron
richotonrichNeutroniR
Pr
Pr 2/)(2)(
richotonrichNeutron
richotonrichNeutroniR
Pr
Pr 2/)(2)(
iR
Comparison to QMD calculationsComparison to QMD calculations
• IQMD calculations were performed for i=0.35-2.0, Sint=17.6 MeV.
• Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used. Symmetry energies: S() 12.3·(ρ/ρ0)2/3 + 17.6· (ρ/ρ0) γi
• IQMD calculations were performed for i=0.35-2.0, Sint=17.6 MeV.
• Momentum dependent mean fields with mn*/mn =mp*/mp =0.7 were used. Symmetry energies: S() 12.3·(ρ/ρ0)2/3 + 17.6· (ρ/ρ0) γi
• Experiment samples a range of impact parameters
– b5.8-7.2 fm.
– larger b, smaller i
– smaller b, larger i
• Experiment samples a range of impact parameters
– b5.8-7.2 fm.
– larger b, smaller i
– smaller b, larger i
mirror nuclei
Expansion around 0: Symmetry slope L & curvature Ksym
Symmetry pressure Psym
...183
2
0
0
0
0
BsymB
osym
KLSE sym
B
sym PE
LB
00
33
0
Diffusion is sensitive to S(0.4), which corresponds to a contour in the (S0, L) plane.
Diffusion is sensitive to S(0.4), which corresponds to a contour in the (S0, L) plane.
fits to IASmasses
fits to
ImQMD
CONSTRAINTS
ImQMD fits for
variable S0
ImQMD fits for
variable S0
Bao-An Li et al., Phys.
Rep. 464, 113 (2008).
Bao-An Li et al., Phys.
Rep. 464, 113 (2008).
PDR: A. Klimkiewicz,
PRC 76, 051603 (2007).
PDR: A. Klimkiewicz,
PRC 76, 051603 (2007).
Danielewicz, Lee,
NPA 818, 36 (2009)
Danielewicz, Lee,
NPA 818, 36 (2009)
GDR: Trippa,
PRC77, 061304
GDR: Trippa,
PRC77, 061304
ImQMD fits for
S0=30.1 MeV
ImQMD fits for
S0=30.1 MeV
Tsang et al., PRL 102, 122701 (2009).
9
10
11
12
13
14
15
16
1 2 3 4 5 6 7 8
Lattimer and PrakashBeta-equilibrated matter
Astrophys.J. 550 (2001) 426
R (
km)
P(n/n0=1.0) (MeV/fm3)
Friedman, and Pandharipande
M=1.4Msun
9
10
11
12
13
14
15
16
0 10 20 30 40 50 60
Lattimer and PrakashBeta-equilibrated matter
Astrophys.J. 550 (2001) 426
R (
km)
P(n/n0=2.0) (MeV/fm3)
Friedman, and Pandharipande
M=1.4Msun
Why probe higher densities?Example: EoS neutron star radius
Why probe higher densities?Example: EoS neutron star radius
• The neutron star radius is not strongly correlated with the symmetry pressure at saturation density. – This portends difficulties in
uniquely constraining neutron star radii for constraints at subsaturation density.
• The neutron star radius is not strongly correlated with the symmetry pressure at saturation density. – This portends difficulties in
uniquely constraining neutron star radii for constraints at subsaturation density.
• The correlation between the pressure at twice saturation density and the neutron star radius is much stronger.
– additional measurements at supra-saturation density will lead to stronger constraints.
• The correlation between the pressure at twice saturation density and the neutron star radius is much stronger.
– additional measurements at supra-saturation density will lead to stronger constraints.
Would be advisable to have multiple probes that can sample different densities Would be advisable to have multiple probes that can sample different densities
L
High density probe: pion productionHigh density probe: pion production
• Larger values for n/ p at high density for the soft asymmetry term (x=0) causes stronger emission of negative pions for the soft asymmetry term (x=0) than for the stiff one (x=-1).
- /+ means Y(-)/Y(+)
– In delta resonance model, Y(-)/Y(+)(n,/p)2
– In equilibrium,
(+)-(-)=2( p-n)
• The density dependence of the asymmetry term changes ratio by about 10% for neutron rich system.
• Larger values for n/ p at high density for the soft asymmetry term (x=0) causes stronger emission of negative pions for the soft asymmetry term (x=0) than for the stiff one (x=-1).
- /+ means Y(-)/Y(+)
– In delta resonance model, Y(-)/Y(+)(n,/p)2
– In equilibrium,
(+)-(-)=2( p-n)
• The density dependence of the asymmetry term changes ratio by about 10% for neutron rich system.
soft
stiff
Li et al., arXiv:nucl-th/0312026 (2003).
stiff
soft
• This can be explored with stable or rare isotope beams at the MSU/FRIB and RIKEN/RIBF.
– Sensitivity to S() occurs primarily near threshold in A+A
• This can be explored with stable or rare isotope beams at the MSU/FRIB and RIKEN/RIBF.
– Sensitivity to S() occurs primarily near threshold in A+A
t (fm/c)
Y
Y
Au+Au
Preliminary results puzzlingPreliminary results puzzling
?
MSU
Riken
GSI
FRIBS(
) M
eV
Isospin diffusion, n-p flow
Pion production
Future determination of the EoS of neutron-rich matter
Future determination of the EoS of neutron-rich matter
Xiao, et al., arX
iv:0808.0186 (2008)
Reisdorf, et al., N
PA
781 (2007) 459.
Double ratio: pion productionDouble ratio: pion production
• Double ratio involves comparison between neutron rich 132Sn+124Sn and neutron deficient 112Sn+112Sn reactions.
• Double ratio maximizes sensitivity to asymmetry term.
– Largely removes sensitivity to difference between - and + acceptances.
• Double ratio involves comparison between neutron rich 132Sn+124Sn and neutron deficient 112Sn+112Sn reactions.
• Double ratio maximizes sensitivity to asymmetry term.
– Largely removes sensitivity to difference between - and + acceptances.
112112112112
124132124132
112112124132/
Y/Y
Y/Y
SnSn/SnSnR
Yong et al., Phys. Rev. C 73, 034603 (2006)
soft
stiff
Summary and OutlookSummary and Outlook
• Heavy ion collisions provide unique possibilities to probe the EOS of dense asymmetric matter.
• A number of promising observables to probe the density dependence of the symmetry energy in HI collisions have been identified.
– Isospin diffusion, isotope ratios, and n/p spectral ratios provide some constraints at 0, .
– + vs. - production, neutron/proton spectra and flows may provide constraints at 20 and above.
• The availability of fast stable and rare isotope beams at a variety of energies will allow constraints on the symmetry energy at a range of densities.
– Experimental programs are being developed to do such measurements at MSU/FRIB, RIKEN/RIBF and GSI/FAIR
• Heavy ion collisions provide unique possibilities to probe the EOS of dense asymmetric matter.
• A number of promising observables to probe the density dependence of the symmetry energy in HI collisions have been identified.
– Isospin diffusion, isotope ratios, and n/p spectral ratios provide some constraints at 0, .
– + vs. - production, neutron/proton spectra and flows may provide constraints at 20 and above.
• The availability of fast stable and rare isotope beams at a variety of energies will allow constraints on the symmetry energy at a range of densities.
– Experimental programs are being developed to do such measurements at MSU/FRIB, RIKEN/RIBF and GSI/FAIR