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