  This is the second in a series of two papers (I and II) on the problem of
decoherence in weak localization. In paper I, we discussed how the Pauli
principle could be incorporated into an influence functional approach for
calculating the Cooperon propagator and the magnetoconductivity. In the present
paper II, we check and confirm the results so obtained by diagrammatically
setting up a Bethe-Salpeter equation for the Cooperon, which includes
self-energy and vertex terms on an equal footing and is free from both infrared
and ultraviolet divergencies. We then approximately solve this Bethe-Salpeter
equation by the Ansatz C(t) = C^0 (t) e^{-F(t)}, where the decay function F(t)
determines the decoherence rate. We show that in order to obtain a
divergence-free expression for the decay function F(t), it is sufficient to
calculate C^1 (t), the Cooperon in the position-time representation to first
order in the interaction. Paper II is independent of paper I and can be read
without detailed knowledge of the latter.
