NONLINEAR LIQUID-DROP MODEL - CNOIDAL WAVES

By introducing in the hydrodynamic model, i.e. in the hydrodynamic equ ations and the corresponding boundary conditions, the higher-order ter ms in the deviation of the shape, we obtain to second order the Kortew eg de Vries equation (KdV). The same equation is obtained by introduci ng in the liquid drop model (LDM), i.e. in the kinetic, surface and Co ulomb terms, the higher terms to second order. The KdV equation has cn oidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary wav es. The solitons could describe the preformation of clusters on the nu clear surface. We apply this nonlinear LDM to the alpha formation in h eavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear sur face. By introducing the shell effects we choose this minimum to be de generated with the ground state. The spectroscopic factor is given by the ratio of the square amplitudes in the two minima.