  A perturbation decaying to 0 at infinity and not too irregular at 0
introduces at most a discrete set of eigenvalues into the spectral gaps of a
one-dimensional Dirac operator on the half-line. We show that the number of
these eigenvalues in a compact subset of a gap in the essential spectrum is
given by a quasi-semiclassical asymptotic formula in the slow-decay limit,
which for power-decaying perturbations is equivalent to the large-coupling
limit. This asymptotic behaviour elucidates the origin of the dense point
spectrum observed in spherically symmetric, radially periodic three-dimensional
Dirac operators.
