  Abbreviated Abstract: We study correlated states in a circular and
linear-chain configuration of identical two-level atoms containing the energy
of a single quasi-resonant photon in the form of a collective excitation, where
the collective behaviour is mediated by exchange of transverse photons between
the atoms. For a circular configuration of atoms the effective Hamiltonian on
the radiationless subspace of the system can be diagonalized analytically. In
this case, the radiationless energy eigenstates carry a $\mathbb{Z}_N$ quantum
number $p=0,1, ..., N$ which is analogous to the angular momentum quantum
number $l= 0, 1, ...$, carried by particles propagating in a central potential,
such as a hydrogen-like system. Just as the hydrogen s-states are the only
electronic wave functions which can occupy the central region of the Coulomb
potential, the quasi-particle corresponding to a collective excitation of the
circular atomic sample can occupy the central atom only for vanishing
$\mathbb{Z}_N$ quantum number $p$. For large numbers of atoms in a maximally
subradiant state, a critical interatomic distance of $\lambda/2$ emerges both
in the linear-chain and the circular configuration of atoms. The spontaneous
decay rate of the linear configuration exhibits a jump-like "critical"
behaviour for next-neighbour distances close to a half-wavelength. Furthermore,
both the linear-chain and the circular configuration exhibit exponential photon
trapping once the next-neighbour distance becomes less than a half-wavelength,
with the suppression of spontaneous decay being particularly pronounced in the
circular system. In this way, circular configurations containing sufficiently
many atoms may be natural candidates for {\it single-photon traps}.
