The National Superconducting Cyclotron Laboratory @ Michigan State University

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

Danielewicz, Lacy, Lynch, Science 298,1592 (2002) Not well constrained Pressure (MeV/fm3) • Relevant for supernovae - what about neutron stars? What is known about the EOS of symmetric matterE(, d) = E(, d=0) + Esym(,d) d2 d = (n - p)/(n + p)

Inclusion of surface terms in symmetry Proton Number Z Neutron Number N Parity violating e- scattering: Rn(208Pb) JLAB (2005)

Danielewicz, Lacy, Lynch, Science 298,1592 (2002) Pressure (MeV/fm3) 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

P T Heavy ion collisions : Access to low density nuclear matter E/A<100 MeV; Multifragmentation Scenario --Initial compression and energy deposition -- Expansion – emission of light particles. -- Cooling – formation of fragments -- Disassembly Model Approaches Dynamical and Statistical

Micha Kilburn REU 2003 Sn+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)g n/p ratios; <En>, <Ep> Isotope distributions Peripheral Collisions Isospin diffusion The symmetry term affects the N/Z composition of the dense region. Stiff ~2 : N/Zres~Ntot/Ztot Soft ~0.5: N/Zres<Ntot/Ztot

Neutron Wall 420-620 80-380 Neutron Wall Beam Scattering Chamber n/p Experiment124Sn+124Sn; 112Sn+112Sn; E/A=50 MeV Famiano et al

N-detection – neutron wall

n-TOF start detector WU MicroBall (b determination) central Impact parameter # of charged particles 3 particle telescopes (p, d, t, 3He, …) ~6in p-detection: Scattering Chamber beam

minimize systematic errors Double Ratio Data, Famiano et al, preliminary Data, Famiano et al, preliminary Data, Famiano et al, preliminary g~0.5 soft Double Ratio g~1.1 stiff g~1.1 stiff BUU: Li, Ko, & Ren PRL 78, 1644, (1997) BUU: Li, Ko, & Ren PRL 78, 1644, (1997) Center of mass Energy n/p Double Ratios (central collisions) 124Sn+124Sn;Y(n)/Y(p) 112Sn+112Sn;Y(n)/Y(p) There will be improvements in both data (analysis) and BUU (1997) calculations.

Heavy Ion Collisions (Ntot/Ztot>1): Central collisions (isospin fractionation) RES Observables in HI collisions Assume Esym()(/0)g n/p ratios; <En>, <Ep> Isotope distributions Stiff ~2 : N/Zres~Ntot/Ztot Soft ~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 + Miniwall4  multiplicity arrayZ identification, A<4 LASSASi strip +CsI array Good E, position,isotope resolutions

Central collisions P T Measured Isotopic yields T.X Liu et al. PRC 69,014603 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) MB Tsang et al. PRC 64,054615

Shetty et al, PRC68,021602(2003) R21=Y2/ Y1 Isoscaling :Observed in many reactions by many groups.

Yields  term with exponential dependence on n, p Saha Equation feeding correction Derivation of isoscaling from Grand Canonical ensemble BE and Zint terms cancel for constant T Ratios of Y (N,Z) from 2 systems observe isoscaling slopes are related to  symmetry energy  source asymmetry Reproduced by all statistical and dynamical multifragmentation models

Data – isotope yields Y2/ Y1=C EES a=isoscaling slope Isoscaling slope Assume E()=23.4(/o) in a statistical model using rate equations to describe fragment emissions. Density dependence of symmetry energy Central collisions of 124Sn+ 124Sn & 112Sn+ 112Sn at E/A=50 MeV Need a model to relate a with g. g~0.5-0.85 Tsang et al, PRL, 86, 5023 (2001)

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. 124Sn 112Sn Observables in HI collisions Peripheral Collisions Isospin diffusion N/Z Diffusion? Coulomb? Pre-equilibrium? Theoretical observable? a (112Sn residue) < a (124Sn residue)

Isospin Transport Ratio 124 Isospin diffusion occurs only in asymmetric systems A+B 112 No isospin diffusion between symmetric systems 124 112 124 112 Rami et al., PRL, 84, 1120 (2000) Experimental: xAB=a Theoretical : xAB= d Non-isospin diffusion effects same for A in A+B & A+A ;same for B in B+A & B+B xAB=xAARi = 1. xAB=xBBRi = -1. xAB=experimental or theoretical isospin observable for system AB a=2CsymDd(1-d)/T; d = (N-Z)/(N+Z)

Lijun Shi g~1.1 g~0.5

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