第9届QCD相变和重离子碰撞物理研讨会，杭州 BEC-BCS crossover and the liquid-gas phase transition in hot and dense nuclear matter 金猛 华中师范大学 2011.7.18-21 各位老师，各位评委：大家下午好！ 我申报的项目是“。。。”

outline Background 2.Pair correlations: BEC and BCS 3.The method beyond mean field 4.Summary and perspectives

The study on the properties of hot and dense nuclear matter is a very important aspect of nuclear physics The equation of states (EoS), pairing instability, nucleon correlations Low energy heavy-ion collision Neutron star

Cooper pair or bound state Interacting Fermion system Interaction strength Strong: bound state Bose-Einstein condensation (BEC) Weak: Cooper pair Superconductivity, superfluidity (BCS) Interacting Fermions Quarks Color superconductivity Nucleons Nucleon superfluidity Cold atoms Superfluidity Electrons Superconductivity

Nucleon interaction nonrelativistic, effective interaction, Gogny force the single particle properties, low T nuclear matter

Mean field theory Hartree, Hartree-Fock, Hartree-Fock-Bogliubov

Beyond mean field approximation 1. Brueckner-Bethe-Goldstone (G-matrix) can give a better saturation point, but not satisfy Hugenholtz van Hove (HvH) theorem (including the rearrangement term can improve the result) 2. Generalized Beth-Uhlenbeck approach (T-matrix) can study the different components of nuclear density, Mott effect to the production of deuteron. M.Schmidt, G.Roepke and H.Schulz, Ann. Phys. 202(90)57 3. Nozières-Schmitt-Rink (NSR) approach (T-matrix) P. Nozeieres and S.Schmitt-Rink, J. low temp. phys. 59(84)195 4. Selfconsistent Green’s function (SCGF) method (T-matrix) introducing the spectral function and calculating the correlation effect selfconsistently. The thermodynamic consistency is also fulfilled in this approach A.Rios et al, Phys. Rev. C 78(08)044314; V.Soma and P.Bozek, Phys.Rev.C 80(09)025803

Nozieres-Schmitt-Rink (NSR) J. low temp. phys. 59(84)195

BEC-BCS crossover For the separable interaction, the T-matrix can be solved analytically Thouless criterion: Ann. Phys.10(60)553 The threshold for superfluidity defined as the pole of the two-particle T-matrix In the weak coupling limit, this gives the same result for Tc as the BCS theory

T.Alm, A. Schnell, G. Roepke and H. Stein, ZPA 351(1995)295 Tc=7MeV 1、At low density (the strong coupling region), the critical temperature coincides with that for the BEC in Boson gas, 2、at high density (the weak coupling region), the critical temperature coincides with that for the BCS instability in Fermion gas, 3、In the middle density region, the critical temperature is determined from the Thouless criterion

NSR approach based on the Hartree-Fock

Introducing the phase shift, M. Jin, M.Urban,P.Schuck, PRC 82(2010)024911 Introducing the phase shift, The result is same as that obtained from the optical theorem in the electron-hole system, R.Zimmermann and H. Stolz, Phys. Stat. Sol(b) 131(1985)151

Equation of state The liquid-gas phase transition still exist with the same critical temperature as mean field result. Tc=15.9MeV

The contribution of the nucleon correlation The nucleon correlation is important when the density is below the saturation density of nuclear matter

BEC-BCS crossover within MNSR Tc=4.5MeV Compared to the NSR result, the critical temperature for the BEC-BCS crossover becomes lower

Liquid-gas phase transition The boundary of the liquid-gas phase transition can be determined by the equilibrium condition

Phase diagram The S-type region is covered by the unstable region of the liquid-gas phase transition 2. When we decrease the T below the Tc of the BEC-BCS crossover there is a pole in the T-matrix. We need to introduce the pairing gap if we want to go inside the phase boundary of the BEC-BCS crossover

Summary and perspectives With the NSR, one can treat the bound states and the Cooper pairing together in nuclear matter. We develop the Nozieres Schmitt-Rink approach based on the Hartree-Fock approximation, from which we can consider the correlation between nucleons. We need to introduce the pairing gap to go down below the BEC-BCS crossover boundary. We plan to apply our method to study the n-p, p-p and n-n pairing in the asymmetric nuclear matter, pure neutron matter etc..

Thank you !