Symmetry energy for asymmetric nuclear matter at subsaturation densities was investigated in the framework of an isospin-dependent quantum molecular dynamics model. A single ratio of neutrons and protons is compared with the experimental data of Famiano et al. [Phys. Rev. Lett. 97, 052701 (2006)] We have also performed a comparison for the double ratio with experimental as well as different theoretical results of Boltzmann-Uehling-Uhlenbeck in 1997, Isospin-dependent Boltzmann-Uehling-Uhlenbeck in 2004, Boltzmann-Nordeim-Vlasov, and Improved Quantum Molecular Dynamics models. It is found that the double ratio predicts the softness of symmetry energy, which is a little underestimated in the single ratio. Furthermore, the study of the single ratio is extended for different kinds of fragments, while the double ratio is extended for different neutron-rich isotopes of Sn.

The symmetry energy at sub-and supra-saturation densities has great importance for understanding the exact nature of asymmetric nuclear matter as well as neutron stars, but it is poorly known, especially at supra-saturation densities. We will demonstrate here whether or not the neutron-toproton ratios from different kinds of fragments can determine the supra-saturation behavior of the symmetry energy. For this purpose, a series of Sn isotopes were simulated at different incident energies using the isospin quantum molecular dynamics (IQMD) model with either a soft or a stiff symmetry energy. It is found that the single neutron-to-proton ratio from free nucleons as well as Light Charged particles (LCPs) is sensitive to the symmetry energy, incident energy, and isospin asymmetry of the system. However, with the double neutron-to-proton ratio, this is true only for the free nucleons. It is possible to study the high-density behavior of symmetry energy by using the neutron-to-proton ratio from free nucleons.

The phase space obtained using Isospin Quantum Molecular Dynamical (IQMD) Model is analyzed by applying the binding energy cut in the most commonly and widely used secondary cluster recognization algorithm. In addition, for the present study, the energy contribution from momentum dependent and symmetry potentials is also included during the calculation of total binding energy, which was absent in clusterization algorithms used earlier.The stability of fragments and isospin effects are explored by using the new clusterization algorithm. The findings are summarized as follow: (1) It identifies the fragments at quite early time. (2) It is more sensitive for free nucleons and light charged particles compared to intermediate mass fragments, which results in the enhanced (reduced) production of free nucleons (LCPs). (3) It has affected the yield of isospin sensitive observables neutrons (n), protons (p), 3 H, 3 He and single ratio [R(n/p)] to a greater extent in mid-rapidity and low kinetic energy region. In conclusion, the induction of binding energy cut in the clusterization algorithm is found to play a crucial role in the study of isospin physics. This study will give another direction for the determination of symmetry energy in heavy-ion collisions at intermediate energies.