  We study the existence of bound states in the continuum for a system of n
two-level quantum emitters, coupled with a one-dimensional boson field, in
which a single excitation is shared among different components of the system.
The emitters are fixed and equally spaced. We first consider the approximation
of distant emitters, in which one can find degenerate eigenspaces of bound
states corresponding to resonant values of energy, parametrized by a positive
integer. We then consider the full form of the eigenvalue equation, in which
the effects of the finite spacing and the field dispersion relation become
relevant, yielding also nonperturbative effects. We explicitly solve the cases
n=3 and n=4.
