  The newly discovered iron pnictide superconductors apparently present an
unusual case of interband-channel pairing superconductivity. Here we show that,
in the limit where the pairing occurs within the interband channel, several
surprising effects occur quite naturally and generally: different
density-of-states on the two bands lead to several unusual properties,
including a gap ratio which behaves inversely to the ratio of
density-of-states; the weak-coupling limit of the Eliashberg and the BCS
theory, commonly taken as equivalent, in fact predict qualitatively different
dependence of the $\Delta_{1}/\Delta_{2}$ and $\Delta/T_{c}$ ratios on coupling
constants. We show analytically that these effects follow directly from the
interband character of superconductivity. Our results show that in the
interband-only pairing model the maximal gap ratio is $\sqrt{N_{2}/N_{1}}$ as
strong-coupling effects act only to reduce this ratio. This suggests that if
the large experimentally reported gap ratios (up to a factor 2) are correct,
the pairing mechanism must include more intraband interaction than is usually
assumed.
