Particle creation in an oscillating spherical cavity

We study the creation of massless scalar particles from the quantum vacuum due to the dynamical Casimir effect by spherical shell with oscillating rad ius. In the case of a small amplitude of the oscillation, to solve the infi nite set of coupled differential equations for the instantaneous basis expa nsion coefficients we use the method based on the time dependent perturbati on 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 par ametric resonance and non-resonance cases.