THOMAS-FERMI THEORY OF THE BREATHING MODE AND NUCLEAR INCOMPRESSIBILITY

A Thomas-Fermi theory with a linear scaling assumption is proposed for the breathing mode of nuclear collective motion. It leads to a genera l result K-A = (K(rho, delta)) + K-GD - 2E(C)/A a which states that th e incompressibility K-A of a finite nucleus A mainly equals the nuclea r matter incompressibility K(rho, delta) averaged over the nucleon den sity distribution p(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 gi ven by the Thomas-Fermi statistical model with a Seyler-Blanchard-type interaction is employed to calculate the nuclear matter incompressibi lity K(rho, delta) and a localized approximation of the Seyler-Blancha rd-type interaction, which is shown to be similar to the Skyrme-type i nteraction, is developed to calculate the value of K-GD.K-GD and - 2E( C)/A contribute about 20 - 10 % and 1 - 5 %, respectively, to the nucl ear incompressibility K-A, from the light to the heavy nuclei. The she ll and the even-odd effects are discussed by a scaling model which sho ws that these effects can be neglected for medium and heavy nuclei, Th e anharmonic effect is shown to he significant only for Light nuclei. The leptodermous expansion of K-A is obtained and the contribution fro m the curvature term proportional to A(-2/3) is discussed. The calcula ted isoscalar giant monopole resonance energy E-M for a variety of nuc lei are shown to be in agreement with experimental measurements.