The National Superconducting Cyclotron Laboratory
@Michigan State University
Betty Tsang
Constraining neutron star matter with laboratory experiments
2005 APS April Meeting Tampa FL
Cra
b P
ulsa
r
Birth of a Neutron StarJuly 4, 1054, China
July 5, 1054, N. America
Outline:Structure of NS and EOSExperimental constraints
NS observations (M, R, T)Nuclei
Heavy Ion Collisions (<O)Current status:
n/p ratiosisotope distributionsisospin (N/Z) diffusion
Heavy Ion Collisions (>O) n/p flow+/- ratios…
Size & Structure of Neutron Star depends on EOS
D. Page
Dense neutron matter. Strong mag. field.Strange composition pasta and anti-pasta phases; kaon/pion condensed core …
EOS influence R,M relationshipmaximum mass. Free Fermi gas EOS:
mass < 0.7 Mcooling rate.core structure
What is known about the EOS of symmetric matterEsym(
= (n - p)/(n + p)
Not well constrained
• Relevant for supernovae - what about neutron stars?
Danielewicz, Lacy, Lynch, Science 298,1592 (2002)
Pres
sure
(MeV
/fm3 )
Parity violating e- scattering: Rn(208Pb)JLAB (2005)
Inclusion of surface terms in symmetry
2
23/2 )2()(
AZAAaAa SV
symsym
Neutron Number N
Prot
on N
umbe
r Z
3/2AaAaB SV 3/1
)1(AZZaC
AZAasym
2)2(
Heavy ion collisions : Access to high density nuclear matter
Results from Au+Au flow (E/A~1-8 GeV) measurements include constraints in momentum dependence of the mean field and NN cross-sections
R. Lacey
Danielewicz, Lacy, Lynch, Science 298,1592 (2002)
Pres
sure
(MeV
/fm3 )
P TE/A<100 MeV; Multifragmentation Scenario
--Initial compression and energy deposition-- Expansion – emission of light particles.-- Cooling – formation of fragments-- Disassembly
Model ApproachesDynamical and Statistical
Heavy ion collisions : Access to low density nuclear matter
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Micha KilburnREU 2003Sn+Sn; E/A=50 MeV; b=0 fm
BUU: Transport theory based on Boltzmann Equations
Heavy Ion Collisions (Ntot/Ztot>1):
Central collisions (isospin fractionation)Bound matter
Observables in HI collisions Assume Esym(( 0
n/p ratios; <En>, <Ep>
Isotope distributions
Peripheral Collisions
Isospin diffusionThe symmetry term affects the N/Z composition of the dense region.Stiff ~2 : N/Zres~Ntot/Ztot
Soft ~0.5: N/Zres<Ntot/Ztot
80-380
420-620
Neu
tron
Wal
l
Neu
tron
Wal
l
n/p Experiment 124Sn+124Sn; 112Sn+112Sn; E/A=50 MeV
Scattering Chamber
Famiano et al
Beam
N-detection – neutron wall
p-detection: Scattering Chamber
3 particle telescopes(p, d, t, 3He, …)
n-TOF start detectorWU MicroBall(b determination)
~6in
beam
2.0ˆ b
# of charged particles
central
Impa
ct p
aram
eter
~1.1 stiff
BUU: Li, Ko, & Ren PRL 78, 1644, (1997)
Data, Famiano et al, preliminaryData, Famiano et al, preliminary~0.5 soft
~1.1 stiff
BUU: Li, Ko, & Ren PRL 78, 1644, (1997)
Data, Famiano et al, preliminary
n/p Double Ratios (central collisions)
There will be improvements in both data (analysis) and BUU (1997) calculations.
124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Dou
ble
Rat
io
Double Ratiominimize systematic errors
Center of mass Energy
Observables in HI collisions Assume Esym(( 0
n/p ratios; <En>, <Ep>
Isotope distributions
Heavy Ion Collisions (Ntot/Ztot>1):
Central collisions (isospin fractionation)RES
Stiff ~2 : N/Zres~Ntot/Ztot
Soft ~0.5: N/Zres<Ntot/Ztot
Isotope Distribution ExperimentMSU, IUCF, WU collaboration
Sn+Sn collisions involving 124Sn, 112Sn at E/A=50 MeV
Miniball + Miniwall4 multiplicity arrayZ identification, A<4
LASSASi strip +CsI array Good E, position,isotope resolutions
Measured Isotopic yieldsT.X Liu et al. PRC 69,014603
P TCentral collisions
Similar distributionsR21(N,Z)=Y2(N,Z)/ Y1(N,Z)
Isoscaling from Relative Isotope Ratios
ZNe
MB Tsang et al. PRC 64,054615
R21(N,Z)=Y2(N,Z)/ Y1(N,Z)
112Sn+58Ni and 124Sn+64Ni at 35 AMeV; Central collisions, CHIMERA- REVERSE experiment
E. Geraci et al., Nucl. Phys. A732 (2004) 173
Isoscaling : Observed in many reactions by many groups.
R21=Y2/ Y1ZNe
Shetty et al, PRC68,021602(2003)
Yields term with exponential dependence on n, p
),(),(),(
)/exp(12
),(/),(exp),(*
int
int
ZNfZNYZNY
TEJZwhere
ZNZTZNBZNZNY
HOTCOLD
iii
pnHOT
feeding correction
Derivation of isoscaling from Grand Canonical ensemble
2/)(
/)(
/)1)((2
21
1,1,1,1
21
ooo
sym
AZN
TCslopes are related to symmetry energy source asymmetry
Reproduced by all statistical and dynamical multifragmentation models
B(Z,N)/kTA
uA
AA
Nn
Zp kTm
ANNZGYYNZY e22
))(,(),()1(
23
22/31
Saha Equation
BE and Zint terms cancel for constant T Ratios of Y (N,Z) from 2 systems observe isoscaling
TT pn /,/
TZTNCZNYZNY
ZNR //
1
221
pne),(),(
,
Density dependence of symmetry energyIs
osca
ling
slop
e
Tsang et al, PRL, 86, 5023 (2001)
Central collisions of 124Sn+ 124Sn & 112Sn+ 112Sn at E/A=50 MeV
Need a model to relate with .
Data – isotope yieldsY2/ Y1=C ZNe
=isoscaling slope
Assume E()=23.4(/o) in a statistical model using rate equations to describe fragment emissions.
EES
~0.5-0.85
Observables in HI collisions Peripheral Collisions
Isospin diffusion
Symmetry energy will act as a driving force to transport the n or p from projectile to target or vice versa via the neck region.
N/Z Diffusion?Coulomb?Pre-equilibrium?Theoretical observable?
112Sn 124Sn
(112Sn residue) < (124Sn residue)
xAB=xAA Ri = 1.xAB=xBB Ri = -1.xAB=experimental or theoretical isospin observable for system AB
Rami et al., PRL, 84, 1120 (2000)
BBAA
BBAAABi xx
xxxR
2
Isospin Transport Ratio
=2Csym(1-)/T; = (N-Z)/(N+Z)
Experimental: xAB= Theoretical : xAB=
No isospin diffusion between symmetric systems 124
124112
112
Isospin diffusion occurs only in asymmetric systems A+B
124112
Non-isospin diffusion effects same for A in A+B & A+A ;same for B in B+A & B+B
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
~0.5
Lijun Shi
~1.1
Lijun Shi
~0.5
Tsang et al., PRL92(2004)Lijun Shi
~1.1
~0.5
Experimental Results
112124
124112 0.44
0.13
124124 0.57
112112 0.0
b=>0.8Y/ybeam>0.7
Experimental Results
112124
124112 0.47
-0.45
124124 1.0
112112 -1.0
Ri
b=>0.8Y/ybeam>0.7
R
R
Constraints on symmetry term in EOS from isospin diffusion
Assume Esym(( 0
Esym(n-pn+p
Ts an g et a l., P RL 92 , 0 6 27 0 1( 20 0 4)
Ch e n e t al ., PR
L 9 4, 0 32 7 01 (2 00 5 )
~0.6-1.6
BUU+m*: Transport theory based on Boltzmann Equations & includemomentum dependence in mean field.
112,124Sn+ 112,124SnE/A=50 MeVPeripheral collisions
NS properties?Steiner: nucl-th0410066 for 1.4 M ⃝
RNS>12 km
Experimental constraints on symmetry energyusing heavy ion collisions
0=0.3-1.0; sym ~ C(
Isotope distributions: ~0.5-0.85 (simplistic calculations)Isospin (N/Z) diffusion: ~0.6-1.5 Can expect significant improvements in these constraintsExpt : n/p ratios – preliminary, n/p flow, PP correlationsTheory: Better transport calculations
.
Experiments at Rare Isotope Accelerator can provide constraints at higher densities (~O -2O)
Acknowledgements
Theorists: W. Friedman (Wisconsin, Madison)P. Danielewicz (MSU), S. Das Gupta (McGill, Canada), A. Ono (Tokohu, Japan), L. Shi (MSU), M. Kilburn (MSU)
Experimentalists: HiRA collaborationMichigan State UniversityT.X. Liu (thesis), M. Famiano (n/p expt), W.G. Lynch, W.P. Tan, G. Verde, A. Wagner, H.S. XuWashington UniversityL.G. Sobotka, R.J. CharityInidiana UniversityR. deSouza, S. Hudan, V. E. Viola
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