Within an isospin- and momentum-dependent hadronic transport model, it is shown that the recent FOPI data on the pi;{-}/pi;{+} ratio in central heavy-ion collisions at SIS/GSI energies [Willy Reisdorf, Nucl. Phys. A 781, 459 (2007)10.1016/j.nuclphysa.2006.10.085] provide circumstantial evidence suggesting a rather soft nuclear symmetry energy E_{sym}(rho) at rho> or =2rho_{0} compared to the Akmal-Pandharipande-Ravenhall prediction. Some astrophysical implications and the need for further experimental confirmations are discussed.

Using an isospin-and momentum-dependent transport model we study near-threshold pion production in heavy-ion collisions induced by radioactive beams at the planned rare isotope accelerator (RIA). We revisit the question of probing the high-density behavior of nuclear symmetry energy E sym (ρ) using the π − /π + ratio. It is found that both the total and differential π − /π + ratios remain sensitive to the E sym (ρ) when the momentumdependence of both the isoscalar and isovector potentials are consistently taken into account. Moreover, the multiplicity and spectrum of π − mesons are found more sensitive to the E sym (ρ) than those of π + mesons. Finally, effects of the Coulomb potential on the pion spectra and π − /π + ratio are also discussed.

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It is generally considered that an atomic nucleus is always compact. Based on the isospindependent Boltzmann nuclear transport model, here I show that large block nuclear matter or excited nuclear matter may both be hollow. And the size of inner bubble in these matter is affected by the charge number of nuclear matter. Existence of hollow nuclear matter may have many implications in nuclear or atomic physics or astrophysics as well as some practical applications.