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## NUCLEAR MATTER

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**Specific and non-trivial relations**among different fields NUCLEAR STRUCTURE QCD HADRON PHYSICS MANY-BODY SYSTEMS NUCLEAR MATTER NUCLEARPHYSICS ASTROPHYSICS HEAVY ION REACTIONS M. Baldo**M. Baldo**G.F. Burgio L.G. Cao M. Di Toro G. Giansiracusa V. Greco U. Lombardo C. Maieron O. Nicotra H.J. Schultze X.R. Zhou I. Bombaci A. Fabrocini G. Lugones S, Fantoni A. Ilarionov K.E. Schmidt Catania Pisa Trieste A. Drago F. Frontera G. Pagliara I. Parenti O. Benhar V. Ferrari L. Gualtieri S. Marassi Roma Ferrara CT51 LS31 MI31 OG51 PI31 PI32 P. Avogadro P.F. Bortignon R.A. Broglia G. Colo’ P. Donati G. Gori F. Ramponi P.M. Pizzochero E. Vigezzi Iniziative specifiche INFN A. Lavagno Milano Torino**The structure and the properties of a compact star**(“NS”) are determined by the equation of state (EOS) of dense hadronic matter. matter’s constituents Mmax R M(R), … EOS interactions Mmax = (1.4 – 2.5) M Oppenheimer-Volkoff mass “stiff” EOS M “stiff” EOS Pressure “soft” “soft” density R**BBG**Variational M. Baldo, G. Giansiracusa, U. Lombardo, H.Q. Song, PLB 473(2000)1 A. Akmal, V.R. Pandharipande, D.G. Ravenhall, PRC58(1998)1804**X.R.Zhou, G.F. Burgio, U. Lombardo, H.-J. Schultze, W. Zuo,**PRC69(2004)18801**-stable nuclear matter**if neutrino-free matter • Equilibrium with respect to the weak interaction processes • Charge neutrality To be solved for any given value of the total baryon number density nB**Composition of asymmetric and beta-stable**matterincludinghyperons • Composition of stellar matter i)Chemical equilibrium among the different baryonic species ii) Charge neutrality iii) Baryon number conservation**Baryon chemical potentials in dense hyperonic matter**n + e- - + e I. Vidaña, Ph.D. thesis (2001)**BHF**GM3 GM3 EOS:Glendenning, Moszkowski, PRL 67(1991) Relativistic Mean Field Theory of hadrons interacting via meson exchange**H.J. Schulze, A. Polls, A. Ramos, I. Vidana PRC 73, 058801**(2006)**Quark Matter in Neutron Stars**QCD Ultra-Relativistic Heavy Ion Collisions Quark-deconfinement phase transition The core of the most massive Neutron Stars is one of the best candidates in the Universe where such a deconfined phase of quark matter can be found 2SC**“Neutron Stars”**“traditional” Neutron Stars Hadronic Stars Hyperon Stars Hybrid Stars Quark Stars Strange Stars**IncludingQuarkmatter**• Since we have no theory which describes both confined and • deconfined phases, one uses two separate EOS for baryon • and quark matter assuming a first order phase transition. • Baryon EOS. • Quark matter EOS. MIT bag model • Nambu-Jona Lasinio • Color dielectric model**G.F. Burgio, M Baldo, P.K.Saku, H.-J. Schultze**Phys. Rev. C66(2002)25802 Density-dependent Bag constant The value of B is constrained in symmetric matter from reaction experiments, suggesting that transition to quark matter does not occur before 1 GeV/fm3 Symmetric matter β-stable matter**Hybrid star composition**Mass-radius relation**Effective bag constant**Color dielectric model C. Maieron, M. Baldo, G.F. Burgio, H.J. Schulze, PRD70(2004)43010**Color and flavour-conserving transition from a hadronic to**a superconducting quark star No transition Transition to a hybrid star Transition to a strange star G. Lugones, I. Bombaci, Phys. Rev. D72(2005)65021**Densities of u,d,s quark are the same in the two phases**Pairing between u and d, u andd quarks (same chemical potential) Bag constant Free quarks, electrons Pairing Paired phase favoured for large gaps, which compensate the locking of chemical potential**A. Lavagno, G. Pagliara, EPJ A27(2006)289**M. Baldo, M. Buballa, G.F. Burgio, F.Neumann, M. Oertel, H.J. Schultze, PLB 562(2003)153**A closer look at the quark phase transition:quantum**nucleation theory I.M. Lifshitz and Y. Kagan, 1972; K. Iida and K. Sato, 1998 QM drop Quantum fluctuations of a virtual drop of quark matter in hadron matter R Hadronic Matter U(R) U(R) = (4/3) R3 nQ* (Q* - H ) + 4 R2 E Z. Berezhiani, I. Bombaci, A. Drago, F, Frontera, A. Lavagno, Apj 586(2003)1250 R- R+ R**Tuniv**Tuniv ~ 41017s**The critical mass of metastable Hadronic Stars**Def.: Mcr = MHS(=1yr) HS with MHS < Mcr are metastable with = 1 yr The critical mass Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars HS with MHS > Mcr are very unlikely to be observed**Hadronic Stars:nucleons + hyperons**I.Bombaci, I. Parenti, I. Vidaña, APJ 614(2004)314**What changes in a**protoneutron star? Temperature, neutrino trapping (Nicotra) O. Nicotra, M. Baldo, G.F. Burgio, H.-J. Schultze, astro-ph/0608021 Can one make a hydrodynamical description of the hadronic -> quark transition? (Parenti) A. Drago, A. Lavagno, I. Parenti, astro-ph/0512652 Can the deconfinement process be associated with gamma-ray bursts? (Pagliara) A.Drago, G. Pagliara, I. Parenti astro-ph/0608224**A. Drago, A. Lavagno. G. Pagliara, Nucl. Phys. B138(2005)522**M. Alford, M. Braby, M. Paris, S. Reddy, APJ 629(2005)969**Can we approach the quark phase transition**with neutron-rich heavy-ion beams? 132Sn+132Sn 1GeV A 300 MeV A M. Di Toro, A. Drago, T. Gaitanos, V. Greco, A. Lavagno, NPA 775(2006)102**A signature of strange stars in gravitational waves**If the quark phese is described withIn the bag model, the frequency of the fundamental mode depends on the value of the bag constant B O. Benhar, V. Ferrari, L. Gualtieri, S. Marassi, astro-ph/0603464**Summary of the analysis**on quark NS content • The transition to quark matter in NS looks likely, • but the amount of quark matter and the transition density • depend on the quark matter model. • If the “observed” high NS masses (about 2 solar mass) • have to be reproduced, additional repulsion is needed • with respect to “naive” quark models . 3. Further constraints can come from other observational data (cooling, glitches …….)**Schematic cross section of a Neutron Star**outer crustnuclei, e- drip = 4.3 1011 g/cm3 inner crustnuclei, n, e- ~1.5 1014 g/cm3 Nuclear matter layern, p, e- , - exotic core (a) hyperonic matter (b) kaon condensate (c) quark matter M 1.4 M R 10 km**Superfluidity (homogeneous matter)**In most calculations, 1S0 pairing is neutron matter Is strongly suppressed by medium effects A recent calculation based on Quantum Montecarlo yields a nuch smaller reduction of the gaps A. Fabrocini, S. Fantoni, A. Yu Ilarionov, K.E: Schmidt, PRL 95(2005)192501**Pairing interaction in neutron and nuclear matter and**exchange of p.h. excitations n n nn n n n n density exc spin exc p p p n n n n isospin exc spin-isospin exc**antiscreening**Vind>Vdir screening Vind<Vdir L.G. Cao, U. Lombardo, P. Schuck, nucl-th/0608005**nk**Z k Z=1 free Fermi gas Z<1 correlated Fermi system Gap Equation**Comparison with finite nuclei: attractive contributions from**surface vibrations prevail 120Sn Pairing gap due to exchange of density+spin fluctuations Pairing gap due to exchange of of density density fluctuations only G. Gori, F. Ramponi, F. Barranco,R.A. Broglia, P.F. Bortignon ,G. Colo, E. Vigezzi, PRC72(2005)11302**The inner crust: coexistence of finite nuclei with a sea of**free neutrons J. Negele, D. Vautherin Nucl. Phys. A207 (1974) 298**eF=13.5MeV**Uniform Matter eF=13.5MeV Finite size effects on the pairing field Potential in the Wigner cell Pairing gap in uniform neutron matter Pairing gap in the Wigner cell The difference is small but affects specific heat and the cooling process P.M. Pizzochero, F. Barranco, E. Vigezzi, R.A. Broglia, APJ 569(2002)381**Spatial description of (non-local) pairing gap**The range of the force is small compared to the coherence length, but not compared to the diffusivity of the nuclear potential K = 0.25 fm -1 kF(R) K = 2.25 fm -1 R(fm) R(fm) R(fm) The local-density approximation overstimates the decrease of the pairing gap in the interior of the nucleus.**Going beyond mean field: including the effects of**polarization (exchange of vibrations) and of finite nuclei at the same time Spin modes Induced pairing interaction Density modes RPA response G. Gori, F. Ramponi, F. Barranco,R.A. Broglia, G. Colo, D. Sarchi,E. Vigezzi, NPA731(2004)401**Argonne (bare and uniform case)**Gogny (bare and uniform case) With the adopted interaction, screening suppresses the pairing gap very strongly for kF >0.7 fm-1 Screening + nucleus Screening, uniform case However, the presence of the nucleus increases the gap by about 50%**New calculation of the optimal properties of the**WIgner-Seitz cell including pairing Without pairing With pairing: smoothing of shell effects M. Baldo, U. Lombardo, E.E: Saperstein, S.V. Tolokonnikov, Nucl. Phys. A736(2004)241