Nuclear symmetry energy effects on liquid-gas phase transition in hot asymmetric nuclear matter Bharat K. Sharma and Subrata Pal Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India The liquid-gas phase transition in hot asymmetric nuclear matter is investigated within relativis- tic mean-field model using the density dependence of nuclear symmetry energy constrained from the measured neutron skin thickness of finite nuclei. We find symmetry energy has a significant influence on several features of liquid-gas phase transition. The boundary and area of the liquid-gas coexistence region, the maximal isospin asymmetry and the critical values of pressure and isospin asymmetry all of which systematically increase with increasing softness in the density dependence of symmetry energy. The critical temperature below which the liquid-gas mixed phase exists is found higher for a softer symmetry energy. PACS numbers: 21.65.+f,25.75.+r,64.10.+h The possible occurrence of liquid-gas phase (LGP) transition in intermediate energy heavy ion collisions us- ing neutron-rich stable and future radioactive beams pro- vides a rather unique tool to probe hot and dense phases of highly asymmetric nuclear matter. Collisions exper- iments [1, 2] with stable heavy nuclei at intermediate energy do indicate theoretically predicted [3] features of liquid-gas phase transition where the hot and compressed nucleus produced expands and fragments into several in- termediate mass fragments (high-density liquid phase) and light particles and nucleons (low-density gas phase). available experimental data. Thus to understand better the features of LGP transition in hot asymmetric nu- clear matter, it is imperative to employ the asymmetric nuclear EOS that has been constrained from analysis of skin thickness data of several nuclei [17] or from isospin diffusion/scaling data [12, 20]. Such an investigation is particularly useful as future experiments with radioac- tive ion beams with large neutron-proton asymmetries can be used to explore [24, 25] symmetry energy effects on liquid-gas phase transition. In this letter, we study the effects of constrained sym- metry energy [17] on the thermodynamic properties of LGP in hot neutron-rich nuclear matter within relativis- tic mean field (RMF) models [26]. For this purpose we use two accurately calibrated models: NL3 [27] and FSUGold [28], that was obtained by fitting the model parameters to certain ground state properties of finite nuclei. The interaction Lagrangian density in the non- linear RMF model is given by [17, 25] The early theoretical studies of the thermodynamic properties of liquid-gas phase transition [4–7] are mostly confined to symmetric nuclear matter that employed the quite well predicted [8–10] behavior of the symmetric nu- clear matter equation of state (EOS). One of the major ingredients in studies of asymmetric nuclear matter re- quire knowledge of the density dependence of symme- try energy E$_{sym}$ ( ρ ) [11–13]. Unfortunately, the model predictions of E$_{sym}$ ( ρ ) even for nuclear matter at zero temperature are extremely diverse [14]. Only at the nu- clear saturation density ρ$_{0}$ ≈ 0 . 16 fm − 3 the value of E ( ρ$_{0}$, T $^{= 0) = 32}$± 4 MeV has been well constrained. Recently some progress has been achieved by consis- tently constraining the symmetry energy of cold neutron- rich matter near normal matter density from analysis of isospin diffusion [11–13] and isoscaling [15] data in inter- mediate energy heavy ion collisions and from the study of neutron skin thickness of several nuclei [16, 17]. While knowledge of symmetry energy E$_{sym}$ ( ρ, T ) at finite tem- perature in particular has received little attention [18–20] that is crucial for a proper understanding of the features of LGP transition in hot asymmetric nuclear matter. In fact, new qualitative features are expected when an asymmetric nuclear system with two conserved charges, baryon number and third component of isospin, under- goes a LGP change which has been suggested to be of second order [21]. Most previous studies of LGP tran- sition [21–23] relied on model predictions of symmetry energy E$_{sym}$ ( ρ, T ) with no or minimal contact with the which includes a isospin doublet nucleon field ( ψ ) in- teracting via exchange of isoscalar-scalar sigma ( φ ), isoscalar-vector omega ( V $^{µ}$), isovector-vector rho ( b $^{µ}$) meson fields and the photon ( A $^{µ}$) field. The nonlinear sigma meson couplings ( κ, λ ) soften the symmetric nu- clear matter EOS at around ρ$_{0}$ , while its high density part is softened by the self-interactions ( ζ ) for the omega meson field. For the original NL3 set with ζ = Λ$_{v}$ = 0, the sat- uration of symmetric nuclear matter occurs at a Fermi momentum of k$_{F}$ = 1 . 30 fm − 1 with a binding energy B/A ≈ 16 . 3 MeV and an incompressibility of K$_{0}$ = 271 MeV. The original FSUGold [28], with two additional couplings ζ = 0 . 06 and Λ$_{v}$ = 0 . 03, with K$_{0}$ = 230 MeV produces a soft symmetric and asymmetric nuclear mat- L = ψ [ g$_{s}$φ − ( g$_{v}$V$_{µ}$ + g$_{ρ}$ 2 τ · b µ + e 2 (1 + τ$_{3}$ ) A$_{µ}$ ) γ µ ] ψ − κ 3! ( g$_{s}$φ ) 3 − λ 4! ( g$_{s}$φ ) 4 + ζ 4! g 4 v ( V$_{µ}$V $^{µ}$) 2 +Λ$_{v}$ ( g 2 ρ b µ · b $^{µ}$) ( g 2 $_{v}$V$_{µ}$ V $^{µ}$) (1) arXiv:1001.2374v1 [nucl-th] 14 Jan 2010