Stability and instability of a hot and dilute nuclear droplet - I. Adiabatic isoscalar modes

The diabatic approach to dissipative collective nuclear motion is reformula ted in the local-density approximation in order to treat the normal modes o f a spherical nuclear droplet analytically. In a first application the adia batic isoscalar modes are studied and results for the eigenvalues of compre ssional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers a nd for soft and stiff equations of state. Wp find that the region of bulk i nstabilities (spinodal regime) is substantially smaller for nuclear droplet s than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with similar growth rates. The surface modes have a l arger spinodal region, reaching out to densities and temperatures way beyon d the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and fragment-mass d istributions (in particular the power-law behavior) are consistent with the instability properties of all expanding nuclear droplet, and hence with a dynamical fragmentation process within the spinodal regime of hulk and surf ace modes (spinodal decomposition).