Calibration of nuclear matter parameters in an effective chiral model T. K. Jha 1,2* 1 Theoretical Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad, India - 380 009 2 Physics Group, Birla Institute of Technology and Science - Pilani, Goa Campus, India - 403 726. Introduction Recently, there have been some efforts to generate new parameters of the model [1] to extend its applicability to nuclear matter studies. With similar motivation, here we evaluate the parameters of an effective sigma model [2] and analyze the equation of state so obtained. This shall enable us to study and correlate some fundamental properties of matter such as nucleon effective mass and nuclear incompressibility, both of which are not precisely known. Nuclear equation of state is the primary input that goes in the de- termination of the structural properties of the neutron star, such as the mass and the radius. The extreme of densities prevailing in the core of these stars render stable exotics in the form of hyperons and quarks, the composition and concentration of which are EoS dependant. In the present work, we look into these aspects and analyze the correlations between properties such as nucleon effective mass (m ⋆ ), the nuclear incompressibility (K), and the resulting equation of state of dense matter. The Model and the Methodology The present model embodies dynamically generated mass of the vector meson, which also plays role in regulating the the nucleon ef- fective mass, in addition to the higher orders of the scalar field interaction. The effective Lagrangian of the model includes the pseudo- scalar meson π, the scalar meson σ, the vector meson ω and the iso-vector ρ-meson. The in- teraction of the scalar and the pseudoscalar mesons with the vector boson generates a dy- * Electronic address: tkjha@bits-goa.ac.in namical mass for the vector bosons through spontaneous breaking of the chiral symmetry and the scalar field attain a vacuum expecta- tion value σ 0 . Then the mass of the nucleon (m), the scalar (m σ ) and the vector meson mass (m ω ), are related to the scalar conden- sate. The meson field equations are solved self- consistently at a fixed baryon density and the corresponding energy density and pres- sure is calculated. however, we need to evalu- ate the parameters of the model (the coupling constants C σ , C ω , C ρ and the higher order scalar field constants B and C) that satisfy nuclear matter saturation properties. To eval- uate them, we follow the standard procedure of calibrating the parameters with respect to the known properties at saturation density. At the standard state ρ B = ρ 0 =0.153fm -3 , the nuclear matter saturation density for sym- metric nuclear matter, the energy per particle is e(ρ 0 )= ε/ρ 0 -m= a 1 ≈ -16 MeV. Fur- ther, the equilibrium condition requires that P (ρ 0 , 0) = 0 i.e., ε = ε k + ε σ + ε ω = -16MeV (1) P = -ε + ρ B ∂ε ∂ρ B = 1 3 ε k - 1 3 m ⋆ ρ S - ε σ + ε ω =0. (2) With the aforesaid methodology, we evalu- ate the nuclear matter parameters at different saturation density in the mean field approach. The parameters with variation in saturation density would project the correlations be- tween the fundamental properties of matter Proceedings of the International Symposium on Nuclear Physics (2009) 628