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 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.