  We study the subgap Yu-Shiba-Rusinov (YSR) states in the Richardson's model
of a superconductor with a magnetic impurity for different electron pairing
strengths from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime to the
strong-coupling Bose-Einstein-condensate (BEC) regime. We observe that the
effect of the increasing pairing strength on the YSR excitation spectrum as a
function of hybridisation strength and impurity on-site potential is only
quantitative and, in fact, rather weak when the results are appropriately
rescaled. We furthermore show that the problem is analytically solvable in the
deep BEC limit which is equivalent to flat-band superconductivity. This exact
solution can be related to a zero-bandwidth (ZBW) effective BCS mean field
Hamiltonian where the superconductor is described by a single electron level
with onsite pairing. The small difference between the BCS and BEC regimes of
the Richardson's model explains the success of the simple ZBW calculations for
BCS mean-field Hamiltonians. A ZBW model requires only a suitable parameter
rescaling to become useful as a quantitative predictive tool for the full
problem.
