Exploring symmetry energy with emitted neutrons and protons using the Quantum Molecular Dynamics Model

Emissions of free neutrons and protons from the central collisions of Sn+Sn and Sn+Sn reactions are simulated using the Improved Quantum Molecular Dynamics model with two different density dependence of the symmetry energy in the nuclear equation of state. The constructed double ratios of the neutron to proton ratios of the two reaction systems are found to be sensitive to the symmetry terms in the EOS. The effect of cluster formation is examined and found to affect the double ratios mainly in the low energy region. In order to extract better information on symmetry energy with transport models, it is therefore important to have accurate data in the high energy region which also is affected minimally by sequential decays. Information about the Equation of State (EOS) of asymmetric matter improves our understanding of the properties of neutron star such as stellar radii and moments of inertia, maximum masses [1-3], crustal vibration frequencies [4], and neutron star cooling rates [3,5], which are currently being investigated with ground-based and satellite observations. Recent observations of neutron stars with the XMM-Newton X-ray telescope have been interpreted as requiring an unusually repulsive equation of state for neutron matter [6]. It is important to determine whether such interpretations are supported by laboratory measurements. Measurements of isoscalar collective vibrations, collective flow and kaon production in energetic nucleus-nucleus collisions have constrained the equation of state for symmetric matter for densities ranging from normal saturation density to five times saturation density [7-9]. On the other hand, the extrapolation of the EOS to neutron–rich matter depends on the density dependence of the nuclear symmetry energy, which has comparatively few experimental constraints [10]. In the past decade, different probes in reaction experiments have been found to be sensitive to the symmetry energy term in the equation of state. These probes exploit the difference in the interactions of protons and neutrons either as free nucleons or as bound isotopes. They include isoscaling [11-13], isospin diffusion [14], neutron to proton (n/p) ratios (Rn/p) [15,16], neutron and proton flow [17], π/π ratios and π/π flow [18, 19]. In principle, the neutron to proton ratios [15, 20] have a more straight forward link to the symmetry energy than the other probes. However, experimentally, detection of neutrons is more difficult than detection of protons. Experimentally neutrons and protons are usually measured by two different detection systems. To remove the sensitivity to the different efficiencies in the proton and neutron detection systems, the double ratio DR(n/p)=Rn/p(A)/Rn/p(B) is constructed from the experimental measurements. Rn/p(A)/ Rn/p(B) = . . . . . . . . / ) ( / ) ( / ) ( / ) (