  We study the creation of massless scalar particles from the quantum vacuum
due to the dynamical Casimir effect by spherical shell with oscillating radius.
In the case of a small amplitude of the oscillation, to solve the infinite set
of coupled differential equations for the instantaneous basis expansion
coefficients we use the method based on the time-dependent perturbation theory
of the quantum mechanics. To the first order of the amplitude we derive the
expressions for the number of the created particles for both parametric
resonance and non-resonance cases.
