Monopole vibrations of nuclei and effective interactions

Abstract

The link between the bulk characteristics of nuclei and the structure of collective monopole excitations has been analysed in the framework of the hyperspherical model. The model is fully microscopic, involves all particles on equal footing, eliminates centre-of-mass motion exactly and treats dynamically the hyperradiusϱ, the natural collective variable for compressional oscillations. New effective Gaussian interactions constructed here describe not only reasonably well ground state characteristics of doubly magic nuclei from¹⁶O to²⁰⁸Pb, but they make possible to choose an appropriate compressibility coefficient of nuclear matterK _∞, as well. Further, a simplified model with harmonic oscillator approximation is suggested, which provides a natural missing bridge between microscopic and macroscopic descriptions of breathing. This approximation yields microscopically all pertinent relations of hydrodynamics showing thus the role and especially limits of a description based on the harmonic oscillator. Finally, the relation betweenK _∞ and breathing excitation has been illustrated and discussed.