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The symmetry energy describes how the energy of nuclear matter rises as one goes away from equal numbers of neutrons and protons. This is very important to describe neutron rich matter in astrophysics. This article reviews our knowledge of the symmetry energy from theoretical calculations, nuclear structure measurements, heavy ion collisions, and astronomical observations. We then present a roadmap to make progress in areas of relevance to the symmetry energy that promotes collaboration between the astrophysics and the nuclear physics communities.

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A new microscopic simulation method of heavy-ion collisions is formulated by incorporating the twonucleon collision process into the antisymmetrized version of molecular dynamics. This method can describe quantum-mechanical features such as shell effects. The fragment mass distribution of the ,2 C+ ,2 C reaction at 28.7 MeV/nucleon is shown to be reproduced very well by this new method combined with the treatment of statistical cascade decays of excited fragments, which verifies the usefulness of the new method. PACS numbers: 25.70.Pq, 24.10.Cn, 24.60.DrThe study of fragment formation is indispensable for the understanding of heavy-ion reaction mechanisms. "Quantum" molecular dynamics (QMD) [1] and the Landau-Vlasov method combined with the percolation analysis [2] are representative practical methods of microscopic simulation for the description of fragment formation. These two methods are, however, largely of classical nature and, for example, they can describe shell effects neither of the colliding individual nuclei nor in the reaction process. The antisymmetrized version of molecular dynamics [3-5], which Feldmeier called fermionic molecular dynamics, treats explicitly the wave function of the total system and hence is able to describe quantummechanical effects such as shell effects. However, until now the two-nucleon collision process has not been incorporated into the framework, which has made this framework insufficient for the description of fragment formation.The present authors have succeeded in incorporating two-nucleon collisions into the antisymmetrized version of molecular dynamics. This means the construction of a new microscopic simulation framework of the heavy-ion reaction. Hereafter we call this new simulation framework simply AMD. The aims of this paper are first to explain this new framework of AMD and second to show an example of applications of AMD to fragment formation which verifies the usefulness of AMD.In AMD, the wave function of the ^l-nucleon system \(Z)>: