Nonlinear Approach in Nuclear Dynamics

摘要

Attention is focused on the various approaches that use the concept of nonlinear dispersive waves (solitons) in nonrelativistic nuclear physics. THe problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is shown that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Raleigh-Taylor type) instability, with the dispersion terms in the evolution equations. The both instabilities may compensate each other and lead to stable solutions (solitons). A static scission configuration in cold ternary fission is considered in the framework of mean field approach. We suggest to use to inverse mean field method to solve single-particle Schrodinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system in the approximation of reflectless single-particle potentials. The solution-like solutions of the Korteweg-de Vries equation are using to describe collective excitations of nuclei observed in inelastic alpha-article and proton scattering. The analogy between fragmentation into pats of nuclei and buckyballs has led us to the idea of light nuclei as quasi-crystals. We establish that the quasi-crystalline structure can be formed when the distance between the alpha-particles is comparable with the length of the De Broglia wave of the alpha-particle. Applying this model to the scattering of alpha-particles we obtain that the form factor of the clusterized nucleus can be factorized into the formfactor of the cluster and the density of clusters in the nucleus. It gives possibility to study the distribution of clusters in nuclei and to resolve what kind of distribution we are dealing with: a surface or volume one.