  There is compelling evidence from inelastic-neutron-scattering and tunneling
experiments that the heavy-fermion superconductor UPd$_2$Al$_3$ can be
understood as a dual system consisting of magnetic excitons, arising from
crystal-field-split U$^{4+}$ levels, coupled to delocalised f-electrons. We
have computed the superconducting transition temperature and the mass
renormalisation arising from a dual model with maximal spin anisotropy using a
strong-coupling approach. We find an instability to two possible
opposite-spin-pairing states with even- or odd-parity gap functions. Each has a
line node perpendicular to the c-direction, in agreement with NMR
relaxation-rate, specific-heat and thermal-conductivity measurements. In
addition, both have total spin component $S_z$=0, compatible with the
observation of a pronounced Knight shift and $H_{c2}$ Pauli limiting. For
parameter values appropriate to UPd$_2$Al$_3$, we determine the dependence of
the superconducting transition temperature $T_c$ on a phenomenological coupling
constant $g$ and we investigate the associated mass enhancement and its
anisotropy.
