  The recent discovery of two heavy fermion materials PuCoGa_{5} and
NpPd_{5}Al_{2} which transform directly from Curie paramagnets into
superconductors, reveals a new class of superconductor where local moments
quench directly into a superconducting condensate. A powerful tool in the
description of heavy fermion metals is the large N expansion, which expands the
physics in powers of 1/N about a solvable limit where particles carry a large
number (N) of spin components. As it stands, this method is unable to jointly
describe the spin quenching and superconductivity which develop in PuCoGa_{5}
and NpPd_{5}Al_{2}. Here, we solve this problem with a new class of large N
expansion that employs the symplectic symmetry of spin to protect the odd
time-reversal parity of spin and sustain Cooper pairs as well-defined singlets.
With this method we show that when a lattice of magnetic ions exchange spin
with their metallic environment in two distinct symmetry channels, they are
able to simultaneously satisfy both channels by forming a condensate of
composite pairs between between local moments and electrons. In the tetragonal
crystalline environment relevant to PuCoGa_{5} and NpPd_{5}Al_{2} the lattice
structure selects a natural pair of spin exchange channels, giving rise to the
prediction of a unique anisotropic paired state with g-wave symmetry. This
pairing mechanism predicts a large upturn in the NMR relaxation rate above
T_{c}, a strong enhancement of Andreev reflection in tunneling measurements and
an enhanced superconducting transition temperature T_{c} in Pu doped
Np_{1-x}Pu_{x}Pd_{5}Al_{2}.
