Based on the liquid drop model, by including nonlinear terms in the hydrodynamic equations, we show that stable solitons can exist on the nuclear surface of 208 Pb or dose to it, this being the most rigid double magic spherical nucleus. The shell effects related with this nucleus lead to a new minimum in the total potential energy. In order to connect this minimum with the cluster decays, which are spontaneous decays, we choose the corresponding energy to be degenerate with the ground state minimum. A new coexistence model consisting of the usual shell model and a cluster-like model describing a soliton moving on the nuclear surface is obtained. The corresponding amplitudes describe excellently the experimental spectroscopic factors for cluster decays.

Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated . Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discused. A finite-difference differential generalized Korteweg-de Vries equation is shown to describe the three-dimensional motion of the fluid surface and the limit of long and shallow channels one reobtains the well known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial condition is introduced on a graphical-algebraic basis. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear physics since, up to an overall scale, these systems display liquid free surface behavior.Comment: 14 pages RevTex, 5 figures in p

The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such "rotons" were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to drop-like systems from cluster formation to stellar models, including hyperdeformed nuclei and fission. 47.55.Dz, 24.10.Nz, 97.60.Jd Typeset using REVT E X 1

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The characteristic alpha-particle spectra from the decay of intermediate states in α+ 28 Si (32 S) to the silicon ground state have been measured during the bombardment of thick targets. The α-spectra were measured in backward angles for the determination of the spins of the states formed in elastic alpha scattering. The level spectra have been investigated in terms of a nonlinear Lagrangean which gives a quantum analogue to the classical large amplitude collective motion in nuclei, succesfully used for the evaluation of the preformation factor in alpha and cluster decays. The corresponding Hamiltonian becomes diagonal with a spectrum similar to a sum of harmonic oscillator spectra. In this way new quantum numbers are introduced. The present model not only reproduces the observed levels but predicts also positions and spins of other levels of the quasimolecular spectra. Both even and odd parities are reproduced using the same parameters.