A Dynamical Macroscopic Description of Isoscalar Giant Multipole States in Terms of the Displacement Potential

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Abstract
In the framework of the time-dependent Hartree-Fock theory, an equation of motion for the displacement potential describing isoscalar giant multipole states is derived and solved analytically on the assumption of the square-well density-distribution. For multipolarity L≥1, resultant eigenmodes are found to be mixtures of the ‘Tassie mode’ and two kinds of longitudinal elastic waves with real and imaginary wave numbers. For L = 0, the present description leads to the result essentially equivalent to the one given by Holzwarth, Eckart et al. and also by Serr et al. We derive boundary conditions at the surface which determine the mixing ratios as well as the eigenfrequency. Properties of eigenmodes are discussed and compared with those obtained from a self-consistent RPA calculation for L = 0 and 2. It is indicated that the present description well reproduces basic features of isoscalar giant monopole and quadrupole states given by RPA.