Limits of EoS Applicability in Neutron Stars and Supernovae: Physics Workshop Discussion

1. Workshop on the Physics of Nucleons and Nuclei 16-17 October 2006 SURA, Washington DC Limits of applicability of the currently available EoS at high density matter in neutron stars and core-collapse supernovae: Discussion comments J.R.Stone Oxford University, Oxford, United KIngdom Physics Division, ORNL, Oak Ridge TN Department of Chemistry and Biochemistry, University of Maryland, College Park, MD

2. 1. Seek reduction of the number of variable parameters of the baryon-baryon interaction in medium and convergence of different nuclear and particle physics models to the most essential physics, important in nuclei and high density matter. 2. Recognition of the true limits of the applicability of the current models for EoS at high density. At what density and temperature the baryons start to loose their identity as composite particles and the mixed-phase and pure quark-based models are essential? Relativistic effects? 3. How sensitive are present experimental data on finite nuclei and astrophysical objects made of uniform baryon matter to the physics underlying our models? Is there any way we could identify individual model parameters (or a group of parameters) to a particular observable (or a class of observables) and thus control its (their) modelling?

3. Does extrapolation matter? What happens at densities higher then 3 x n0? (n0 = 0.16 fm-3) Interaction ncmax[fm-3] R [km] Mg/Ms APR 1.14 10.01 2.20 SkM* 1.66 8.95 1.62 SLy4 1.21 9.96 2.04

4. Dirac- Brueckner-Hartree-Fock Groningen, Bonn A, DD pheno. Hofmann et al, PRC 64, 025804 Brueckner-Hartree-Fock Nijmegen potential Vidana et al, PRC 62,035801 B e t a s t a b l e m a t t t e r

5. Relativistic quark-qluon coupling model: P.Guichon et al. NX attractive: 7 X hypernuclear events: UX ~ -28 MeV at n=n0 quasi-free production of X: UX ~ -18 MeV NL attractive: L hypernuclei A=3-209: UL~ -30 MeV at n=n0 NS ? : S- atoms: repulsive +S He hypernucleus bound by isospin forces

6. Menezes and Providencia, PRC 68, 035804 (2003) T=20 MeV T=0 MeV MIT bag + Non-linear Walecka RMF with GL interaction full baryon octet Mmax ~ 1.4-1.6 Msolar Nambu-Jona-Lasinio + Non-linear Walecka RMF with GL interactiom full baryon octet Mmax ~ 1.8-1.9 Msolar

7. DB DB Sk RMF Sk AV14 E sat (MeV) nsat(fm-3) K [MeV] DB(BA ) -15.59 0.185 290 DB(BC) -12.26 0.155 185 RMF -15.75 0.193 540 Li et al., PRC 45, 2782 (1992)

8. Calculated neutron skin in 208Pb for 87 Skyrme models in comparison with experimental data Experimental data on neutron skins from proton scattering are model dependent! Clark et al. PRC 67, 054605 (2003) Most precise data (1.5%) from atomic parity violation measurement in electron scattering at JLAB expected in about 2 years Horowicz et al. PRC63, 025501 (2001)

9. Relative magnitude of the skin effect: not isospin dependent Surface effects – shape of the last occupied orbital at Fermi surface? Z N N-Z 40 82 42 28 50 22 50 82 32 20 28 8 82 126 44 { Work in Progress! (2004)

10. Mass: 1.2 – 2.2 Solar Radius: The Sun: 670 000 km NS : 10 – 14 km

11. W. G. Neutron, JRS – 3D temperature dependent HF+BCS calculation of nuclear matter (with the Skyrme interaction as yet…) Assumption: nuclear matter is modeled as an infinite sequence of unit cells with periodic boundary conditions. Transition to uniform matter as a function of density and temperature: r=0.04,0.08,0.12 fm-3 left to right T=0 MeV (top) T=5 MeV (bottom) Minimization of the total free energy as a function of the number of particles in the unit cell