Isospin effects on intermediate mass fragments at intermediate energy-heavy ion collisions

In this study, we investigated the isospin properties of intermediate mass fragments (IMFs) for the central collisions of 112,124\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{112,124}$$\end{document}Sn+112,124\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{112,124}$$\end{document}Sn at a beam energy of 50 MeV per nucleon using an improved quantum molecular dynamics model (ImQMD) coupled with a sequential decay model (GEMINI). Three observables were analyzed: (1) the average center-of-mass kinetic energy per nucleon ⟨Ec.m./A⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle E_\text {c.m.}\big/A\rangle$$\end{document} of fragments as a function of their charge number Z; (2) the average neutron number to proton number ratio (⟨N⟩/Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle N\rangle \big/Z$$\end{document}) of fragments with a given charge number Z as a function of their center-of-mass kinetic energy per nucleon (Ec.m./A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_\text {c.m.}\big/A$$\end{document}); and (3) the average total neutron number to total proton number ratio (∑N/∑Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum N\big/\sum Z$$\end{document}) and double ratio (DR(N/Z)) of IMFs with Z = 3–8 as a function of their center-of-mass kinetic energy per nucleon Ec.m./A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_\text {c.m.}\big/A$$\end{document}. Our calculations revealed that the sensitivity of the isospin properties of IMFs relative to the stiffness of the symmetry energy remains even after sequential decay. By comparing the calculations of ∑N/∑Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum N\big/\sum Z$$\end{document} and DR(N/Z) with the data, it was found that the soft symmetry energy, i.e., γ=0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma =0.5$$\end{document}, is favored.