  We investigate superradiance and subradiance of indistinguishable atoms with
quantized motional states, starting with an initial total state that factorizes
over the internal and external degrees of freedom of the atoms. Due to the
permutational symmetry of the motional state, the cooperative spontaneous
emission, governed by a recently derived master equation [F. Damanet et al.,
Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates $\gamma$ and
$\gamma_0$ and a single parameter $\Delta_{\mathrm{dd}}$ describing the
dipole-dipole shifts. We solve the dynamics exactly for $N=2$ atoms,
numerically for up to 30 atoms, and obtain the large-$N$-limit by amean-field
approach. We find that there is a critical difference $\gamma_0-\gamma$ that
depends on $N$ beyond which superradiance is lost. We show that exact
non-trivial dark states (i.e. states other than the ground state with vanishing
spontaneous emission) only exist for $\gamma=\gamma_0$, and that those states
(dark when $\gamma=\gamma_0$) are subradiant when $\gamma<\gamma_0$.
