  Experiments on the cuprate superconductors demonstrate that these materials
may be viewed as a stack of Josephson junctions along the c-direction. In this
paper, we present a model which describes this intrinsic Josephson coupling in
terms of incoherent quasiparticle hopping along the c-axis arising from
wave-function overlap, impurity-assisted hopping, and boson-assisted hopping.
We use this model to compute the magnitude and temperature T dependence of the
resulting Josephson critical current j_c (T) for s- and d-wave superconductors.
Contrary to other approaches, d-wave pairing in this model is compatible with
an intrinsic Josephson effect at all hole concentrations and leads to j_c (T)
\propto T at low T. By parameterizing our theory with c-axis resistivity data
from YBCO, we estimate j_c (T) for optimally doped and underdoped members of
this family. Our estimates suggest that further experiments on this compound
would be of great help in elucidating the validity of our model in general and
the pairing symmetry in particular. We also discuss the implications of our
model for LSCO and BSCCO.
