A New Nonlinear Liquid Drop Model. Clusters as Solitons on The Nuclear Surface

TL;DR

This paper develops a nonlinear liquid drop model incorporating higher order shape deviations, leading to the KdV equation, which describes solitons as clusters on nuclear surfaces, applied to alpha formation in heavy nuclei.

Contribution

It introduces a nonlinear extension of the liquid drop model that predicts soliton-like clusters on nuclear surfaces, linking hydrodynamic and liquid drop approaches.

Findings

Identification of solitons as clusters on nuclear surfaces.

Additional energy minimum corresponding to cluster formation.

Application to alpha formation in heavy nuclei.

Abstract

By introducing in the hydrodynamic model, i.e. in the hydrodynamic equations and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equation (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by the ratio of the square amplitudes in the two minima.