  New corrections to the equation of motion and total collapsing time of an
empty spherical cavity immersed in an infinite incompressible medium are
proposed on the assumption of a non-uniform density. The dimensionless number
quantifying the corrections with respect to the standard Rayleigh results
(coined the $\Delta$-factor) is fully independent of other possible
contributions like surface tension and viscous terms. The $\Delta$-factor
effect advocated here can be seen as a direct consequence of a mass-shell
non-trivial solution to the continuity equation. The consistency of the
corrections with respect to the Bernoulli theorem and some physical
consequences in the framework of the Rayleigh-Plesset equation are also
discussed.
