Isospin asymmetry is a measure of the imbalance between the numbers of neutrons and protons in finite nuclei and/or infinite nuclear matter. How do neutrons and protons interact among themselves in extremely isospin asymmetric systems, such as, neutron stars? How does the equation of state, i.e., a relationship among energy, density and temperature, change as a function of isospin asymmetry in neutron-rich nuclear matter? Answers to these questions have significant astrophysical ramifications for the structure of neutron stars and the dynamics of supernova explosions. However, astrophysical observations are too limited to answer these questions. Fortunately and interestingly, these questions can be studied experimentally by using nuclear reactions induced by short-lived isotope beams at the planned Rare Isotope Accelerator (RIA) in the USA and other competing facilities abroad. The physics associated with these experiments is currently one of the major thrusts and at the foremost front of nuclear sciences. In particular, with high energy neutron-rich beams at RIA, a transient state of nuclear matter with appreciable isospin asymmetry and compression of more than twice the saturation density of normal nuclear matter can be created. RIA will thus provide a unique opportunity to explore the nature of nucleonic matter under extreme conditions of isospin asymmetry and density. To facilitate the success of the experimental research on the isospin dependence of the in-medium nuclear effective interactions and the nuclear equation of state, I shall carry out theoretical studies on several issues important for planning experiments and interpreting data by investigating novel properties of neutron-rich matter and their manifestations in nuclear reactions induced by rare isotope beams. The major foci of my work will be on developing new models for nuclear reactions induced by radioactive beams; identifying the role of isospin degree of freedom in the reaction dynamics; determining experimental observables that can be used to extract critical information about the isospin dependence of the in-medium nuclear effective interactions; and constraining the equation of state of isospin asymmetric nuclear matter.
