Nuclear matter Properties and Neutron Star Phenomenology Using the Finite Range Simple Effective Interaction

The saturation properties of symmetric and asymmetric nuclear matter have been computed using the finite range simple effective interaction with Yukawa form factor. The results of higher-order derivatives of the energy per particle and the symmetry energy computed at saturation, namely, Q0, Ksym, Kτ, Qsym, are compared with the corresponding values extracted from studies involving theory, experiment and astrophysical observations. The overall uncertainty in the values of these quantities, which results from a wide spectrum of studies described in earlier literature, lies in the ranges −1200≲Q0≲400 MeV, −400≲Ksym≲100 MeV, −840≲Kτ≲−126 MeV and −200≲Qsym≲800 MeV, respectively. The ability of the equations of state computed with this simple effective interaction in predicting the threshold mass for prompt collapse in binary neutron star merger and gravitational redshift has been examined in terms of the compactness of the neutron star and the incompressibility at the central density of the maximum mass star. The correlations existing between neutron star properties and the nuclear matter saturation properties have been analyzed and compared with the predictions of other model calculations.


Introduction
The Simple Efffective Interaction (SEI) The finite range simple effective interaction was initially proposed by Behera and collaborators and has the following explicit form for a Yukawa finite range form factor (SEI-Y), where a zero-range spin-orbit (SO) interaction depending on a strength parameter W0 is taken to deal with finite nuclei.The SEI in Eq.(??) has 12 parameters in total, namely, α, γ, b, x0, x3, t0, t3, W , B, H, and M plus the spin-orbit strength parameter W0, which enters in the description of finite nuclei.
Nine of these twelve parameters are fitted to reproduce empirical constraints and microscopical results in nuclear nd neutron matter.
Introduction SEI in asymmetric nuclear matter

Fitting protocol
• The symmetric nuclear matter (SNM) requires only the following three combinations of the strength parameters, which together with γ, b and α constitute the six parameters for the SNM.For a given value of the exponent γ, which characterizes as the stiffness parameter and determines the incompressibil • It is demanded that he nuclear mean-field in symmetric nuclear matter at saturation vanished for a kinetic energy of incident nucleaon of 300 MeV.This constraint allows to determine, for a given value of γ, the strength of the excahnege energy, εex , and the range of the form factor α.
• The parameter b is determined to avoid the supra-luminous behaviour.
• The two remaining parameters, ε0 and εγ are obtained from given saturation conditions.(density nd energy per baryon) • The splitting of the exchange strength is decided to be ε l ex = 2ε ul ex /3, which ensures that the entropy in pure neutron matter does not exceed that of symmetric nuclear matter.
• The splitting of the parameters ε0 and εγ is decided from the value oif the symmetry energy and its slope.
• The characteristic slope of the symmetry energy is fixed from the condition that the asymmetric contribution to the nucleonic part of the energy density in charge neutral beta-stable stellaar matter npeµ is maximal.
• One of the two free parameters, x0, is fixed from the spin-up and spin-down splitting of the effective mass in polatized neutron matter.
• Finally the parameter t0 and the spin-orbit strength W0 are determined from calculations in finite nuclei.