Constraining neutron star matter with
laboratory experiments
Crab Pulsar
2005 APS April Meeting Tampa FL
Betty Tsang
The National Superconducting
Cyclotron Laboratory
@Michigan State University
Birth of a Neutron Star
July 4, 1054, China
July 5, 1054, N. America
Outline:
Structure of NS and EOS
Experimental constraints
NS observations (M, R, T)
Nuclei
Heavy Ion Collisions (<O)
Current status:
n/p ratios
isotope distributions
isospin (N/Z) diffusion
Heavy Ion Collisions (>O)
n/p flow
+/- ratios
…
Size & Structure of Neutron Star depends on EOS
Dense neutron matter.
Strong mag. field.
Strange composition
pasta and anti-pasta
phases; kaon/pion
condensed core …
EOS influence
R,M relationship
maximum mass.
Free Fermi gas EOS:
mass < 0.7 M
cooling rate.
core structure
D. Page
What is known about the EOS of symmetric matter
E(, d) = E(, d=0) + Esym(,d) d2
Pressure (MeV/fm3)
Danielewicz, Lacy, Lynch, Science 298,1592 (2002)
d = (n - p)/(n + p)
Not well
constrained
• Relevant for
supernovae - what
about neutron stars?
B = aV A  a S A
2/3
2
Z ( Z  1)
(
A

2
Z
)
+ d  aC
 a sym
1/ 3
A
A
(a sym A  a sym A
Proton Number Z
V
S
2/3
( A  2Z ) 2
)
A2
Inclusion of surface
terms in symmetry
Neutron Number N
Parity violating e- scattering: Rn(208Pb)
JLAB (2005)
Heavy ion collisions :
Access to high density nuclear matter
Danielewicz, Lacy, Lynch, Science 298,1592 (2002)
Results from Au+Au flow
(E/A~1-8 GeV) measurements
include constraints in
momentum dependence of the
mean field and NN crosssections
R. Lacey
Heavy ion collisions :
Access to low density nuclear matter
E/A<100 MeV; Multifragmentation Scenario
P
T
--Initial compression and energy deposition
-- Expansion – emission of light particles.
-- Cooling – formation of fragments
-- Disassembly
Model Approaches
Dynamical and Statistical
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Sn+Sn; E/A=50 MeV; b=0 fm
Micha Kilburn
REU 2003
BUU: Transport theory based on Boltzmann Equations
Observables in HI collisions
Assume Esym()( /0)g
Heavy Ion Collisions (Ntot/Ztot>1):
Central collisions (isospin fractionation)
n/p ratios; <En>, <Ep>
Bound
matter
Isotope distributions
Peripheral Collisions
Isospin diffusion
The symmetry term affects
the N/Z composition of the
dense region.
Stiff g~2 : N/Zres~Ntot/Ztot
Soft g~0.5: N/Zres<Ntot/Ztot
n/p Experiment 124Sn+124Sn; 112Sn+112Sn; E/A=50 MeV
420-620
80-380
Scattering Chamber
Famiano et al
N-detection – neutron wall
p-detection: Scattering Chamber
WU MicroBall
(b determination)
~6in
central
bˆ  0.2
# of charged particles
3 particle telescopes
(p, d, t, 3He, …)
n-TOF start detector
n/p Double Ratios (central collisions)
Double Ratio
124Sn+124Sn;Y(n)/Y(p)
112Sn+112Sn;Y(n)/Y(p)
minimize
systematic errors
Data, Famiano et al, preliminary
Double Ratio
g~0.5 soft
g~1.1 stiff
BUU: Li, Ko, & Ren PRL 78, 1644, (1997)
Center of mass Energy
There will be
improvements in
both data
(analysis) and
BUU (1997)
calculations.
Observables in HI collisions
Assume Esym()( /0)g
Heavy Ion Collisions (Ntot/Ztot>1):
Central collisions (isospin fractionation)
n/p ratios; <En>, <Ep>
RES
Isotope distributions
Stiff g~2 : N/Zres~Ntot/Ztot
Soft g~0.5: N/Zres<Ntot/Ztot
Isotope Distribution Experiment
MSU, IUCF, WU collaboration
Sn+Sn collisions involving 124Sn, 112Sn at E/A=50 MeV
Miniball + Miniwall
4  multiplicity array
Z identification, A<4
LASSA
Si strip +CsI array
Good E, position,
isotope resolutions
Measured Isotopic yields
T.X Liu et al. PRC 69,014603
Central collisions
P
T
Similar distributions
R21(N,Z)=Y2(N,Z)/ Y1(N,Z)
Isoscaling from Relative Isotope Ratios
R21(N,Z)
=Y2(N,Z)/ Y1(N,Z)
N + Z
e
MB Tsang et al. PRC 64,054615
Isoscaling : R21=Y2/ Y1 eN + Z
Observed in many reactions by many groups.
112Sn+58Ni
and 124Sn+64Ni at 35 AMeV; Central collisions,
CHIMERA-REVERSE experiment
E. Geraci et al., Nucl. Phys. A732 (2004) 173
Shetty et al, PRC68,021602(2003)
Derivation of isoscaling from Grand Canonical ensemble
Yields  term with exponential dependence on n, p


Y ( N , Z ) HOT  exp (  n N +  p Z + B( N , Z ) / T ) Z int ( N , Z )
*
(
)
where
Z
=
2
J
+
1
exp(

E
Saha Equation
 i
int
i /T)
3/ 2

Z N i
A1 A

Y ( Z , N ) = Yp Yn G( Z , N )( N A )
A
Y (N , Z )
= Y (N , Z )
 f (N , Z ) 
COLD
HOT
2
3
2  2 ( A1)
2
feeding
B(Z,N)/kT
 correction
e

m
kT
 u 
BE and Zint terms cancel for constant T
Ratios of Y (N,Z) from 2 systems observe isoscaling
R21 (N , Z ) =
Y2 ( N , Z )
N n / T + Z p / T
 C e
Y1 ( N , Z )
 =  n / T ,  =  p / T
slopes are related to
 symmetry energy
 source asymmetry
 = 2Csym (d1  d 2 )(1  d ) / T
d1 = ( N o,1  Z o,1 ) / Ao,1
d = (d1 + d 2 ) / 2
Reproduced by all statistical and dynamical multifragmentation models
Density dependence of symmetry energy
Central collisions of 124Sn+ 124Sn & 112Sn+ 112Sn at E/A=50 MeV
Isoscaling slope
EES
Data – isotope yields
N + Z
Y2/ Y1=C e
=isoscaling slope
Need a model to relate
 with g.
g~0.5-0.85
Assume E()=23.4(/o)g
in a statistical model using
rate equations to describe
fragment emissions.
Tsang et al, PRL, 86, 5023 (2001)
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.
112Sn
124Sn
N/Z Diffusion?
Coulomb?
Pre-equilibrium?
Theoretical observable?
 (112Sn residue) <  (124Sn residue)
Isospin Transport Ratio
Isospin diffusion occurs only
in asymmetric systems A+B
No isospin diffusion between
symmetric systems
124
112
124
112
124
112
Non-isospin diffusion effects
same for A in A+B & A+A ;same for B in B+A & B+B
2 x AB  x AA  xBB
Ri =
x AA  xBB
xAB=xAA Ri = 1.
xAB=xBB  Ri = -1.
xAB=experimental or
theoretical isospin
observable for system AB
Rami et al., PRL, 84, 1120 (2000)
=2Csymd(1-d)/T;
d = (N-Z)/(N+Z)
Experimental: xAB= 
Theoretical : xAB= d
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
Lijun Shi
g~1.1
g~0.5
g~1.1
g~0.5
Lijun Shi
Tsang et al., PRL92(2004)
Experimental Results

124
124
124
112
112
124
112
112
0.57
0.44
0.13
0.0
b=>0.8
Y/ybeam>0.7
Experimental Results
Ri
124
124
124
112
112
124
112
112
1.0
0.47
-0.45
-1.0
b=>0.8
Y/ybeam>0.7
Constraints on symmetry term in EOS from isospin diffusion
E(, d) = E(, 0) + Esym()d2;
d=(n-p )/(n+p )
Assume Esym()( /0)g
BUU+m*:
Transport theory
based on Boltzmann
Equations & include
momentum
dependence in mean
field.
g~0.6-1.6
112,124Sn+ 112,124Sn
E/A=50 MeV
Peripheral collisions
g
Experimental constraints on symmetry energy
using heavy ion collisions
/0=0.3-1.0; Esym ~ C(/0)g
Isotope distributions: g~0.5-0.85 (simplistic calculations)
Isospin (N/Z) diffusion: g~0.6-1.5
Can expect significant improvements in these constraints
Expt : n/p ratios – preliminary, n/p flow, PP correlations
Theory: Better transport calculations
NS properties?
Steiner: nucl-th0410066 for 1.4 M.⃝
RNS>12 km
Experiments at Rare Isotope Accelerator can provide
constraints at higher densities (~O -2O)
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 collaboration
Michigan State University
T.X. Liu (thesis), M. Famiano (n/p expt), W.G.
Lynch, W.P. Tan, G. Verde, A. Wagner, H.S. Xu
Washington University
L.G. Sobotka, R.J. Charity
Inidiana University
R. deSouza, S. Hudan, V. E. Viola