A Thomas-Fermi theory with a linear scaling assumption is proposed for the breathing mode of nuclear collective motion. It leads to a general result K A ϭ͗K(,␦)͘ϩK GD Ϫ2E C /A which states that the incompressibility K A of a finite nucleus A mainly equals the nuclear matter incompressibility K(,␦) averaged over the nucleon density distribution (r) of nucleus A, added to a term K GD contributed from the gradients of nucleon densities, with twice the Coulomb energy per nucleon E C /A subtracted. The nuclear matter equation of state given by the Thomas-Fermi statistical model with a Seyler-Blanchard-type interaction is employed to calculate the nuclear matter incompressibility K(,␦) and a localized approximation of the Seyler-Blanchard-type interaction, which is shown to be similar to the Skyrme-type interaction, is developed to calculate the value of K GD . K GD and Ϫ2E C /A contribute about 20-10 % and 1-5 %, respectively, to the nuclear incompressibility K A , from the light to the heavy nuclei. The shell and the even-odd effects are discussed by a scaling model which shows that these effects can be neglected for medium and heavy nuclei. The anharmonic effect is shown to be significant only for light nuclei. The leptodermous expansion of K A is obtained and the contribution from the curvature term proportional to A Ϫ2/3 is discussed. The calculated isoscalar giant monopole resonance energy E M for a variety of nuclei are shown to be in agreement with experimental measurements.

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess δ. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point (ρc, δc) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of δc is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, δc does not depend sensitively on the choice of the parameter γ in Skyrme interaction.

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Nuclear matter properties are calculated in the relativistic mean field theory by using a number of different parameter sets. The result shows that the volume energy a1 and the symmetry energy J are around the acceptable values 16MeV and 30MeV respectively; the incompressibility K0 is unacceptably high in the linear model, but assumes reasonable value if nonlinear terms are included; the density symmetry L is around 100M eV for most parameter sets, and the symmetry incompressibility Ks has positive sign which is opposite to expectations based on the nonrelativistic model. In almost all parameter sets there exists a critical point (ρc, δc), where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero, falling into ranges 0.014fm −3 < ρc < 0.039fm −3 and 0.74 < δc ≤ 0.95; for a few parameter sets there is no critical point and the pure neutron matter is predicted to be bound. The maximum mass MNS of neutron stars is predicted in the range 2.45M⊙ ≤ MNS ≤ 3.26M⊙, the corresponding neutron star radius RNS is in the range 12.2km≤ RNS ≤ 15.1km.

The isospin dependence, recently observed in reactions at , is discussed within the framework of two simple nuclear multifragmentation models, namely the site percolation and the nucleation-evaporation models. It is shown that both the models are able to discriminate between and reactions. The nucleation-evaporation model succeeds to reproduce nicely the experimental data, but the site percolation model fails in doing that, even if the cluster noncompactive effect is taken into account. The calculations indicate that the data are originated mainly from a single source.