The National Superconducting Cyclotron State University Betty Tsang Constraining neutron star matter with laboratory experiments 2005 APS April Meeting Tampa FL Crab Pulsar

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 D. Page  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

What is known about the EOS of symmetric matter  E sym (    = (  n -  p )/(  n +  p ) Not well constrained Relevant for supernovae - what about neutron stars? Danielewicz, Lacy, Lynch, Science 298,1592 (2002) Pressure (MeV/fm 3 )

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

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) Pressure (MeV/fm 3 )

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 Heavy ion collisions : Access to low density nuclear matter

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Micha Kilburn REU 2003 Sn+Sn; E/A=50 MeV; b=0 fm BUU: Transport theory based on Boltzmann Equations

Heavy Ion Collisions ( N tot /Z tot >1) : Central collisions (isospin fractionation) Bound matter Observables in HI collisions Assume E sym (  (   0   n/p ratios;, Isotope distributions Peripheral Collisions Isospin diffusion The symmetry term affects the N/Z composition of the dense region. Stiff  ~2 : N/Z res ~N tot /Z tot Soft  ~0.5: N/Z res <N tot /Z tot

Neutron Wall n/p Experiment 124 Sn+ 124 Sn; 112 Sn+ 112 Sn; E/A=50 MeV Scattering Chamber Famiano et al Beam

N-detection – neutron wall

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

 ~1.1 stiff BUU: Li, Ko, & Ren PRL 78, 1644, (1997) Data, 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. 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) Double Ratio minimize systematic errors Center of mass Energy

Observables in HI collisions Assume E sym (  (   0   n/p ratios;, Isotope distributions Heavy Ion Collisions ( N tot /Z tot >1) : Central collisions (isospin fractionation) RES Stiff  ~2 : N/Z res ~N tot /Z tot Soft  ~0.5: N/Z res <N tot /Z tot

Isotope Distribution Experiment MSU, IUCF, WU collaboration Sn+Sn collisions involving 124 Sn, 112 Sn 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, PT Central collisions Similar distributions R 21 (N,Z)=Y 2 (N,Z)/ Y 1 (N,Z)

Isoscaling from Relative Isotope Ratios MB Tsang et al. PRC 64, R 21 (N,Z) =Y 2 (N,Z)/ Y 1 (N,Z)

Isoscaling : Observed in many reactions by many groups. R 21 =Y 2 / Y 1 Shetty et al, PRC68,021602(2003)

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

Density dependence of symmetry energy Isoscaling slope Tsang et al, PRL, 86, 5023 (2001) Central collisions of 124 Sn+ 124 Sn & 112 Sn+ 112 Sn at E/A=50 MeV Need a model to relate  with . Data – isotope yields Y 2 / Y 1 =C  =isoscaling slope Assume E(  )=23.4(  /  o )  in a statistical model using rate equations to describe fragment emissions. EES  ~

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? 112 Sn 124 Sn  ( 112 Sn residue) <  ( 124 Sn residue)

x AB =x AA  R i = 1. x AB =x BB  R i = -1. x AB =experimental or theoretical isospin observable for system AB Rami et al., PRL, 84, 1120 (2000) Isospin Transport Ratio  =2C sym  (1-  )/T;  = (N-Z)/(N+Z) Experimental: x AB =  Theoretical : x AB =  No isospin diffusion between symmetric systems Isospin diffusion occurs only in asymmetric systems A+B 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  b=>0.8 Y/y beam >0.7

Experimental Results RiRi b=>0.8 Y/y beam >0.7

 RR RR  Constraints on symmetry term in EOS from isospin diffusion Assume E sym (  (   0    E sym (      n -  p  n +  p  Tsang et al., PRL 92, (2004) Chen et al., PRL 94, (2005)  ~ BUU+m*: Transport theory based on Boltzmann Equations & include momentum dependence in mean field. 112,124 Sn+ 112,124 Sn E/A=50 MeV Peripheral collisions

NS properties? Steiner: nucl-th for 1.4 M ⃝ R NS >12 km Experimental constraints on symmetry energy using heavy ion collisions  0 = ;  sym ~ C(     Isotope distributions:  ~ (simplistic calculations) Isospin (N/Z) diffusion:  ~ Can expect significant improvements in these constraints Expt : n/p ratios – preliminary, n/p flow, PP correlations Theory: Better transport calculations. 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