We establish a formal connection between the particle-particle (pp) random
phase approximation (RPA) and the ladder channel of the coupled cluster doubles
(CCD) equations. The relationship between RPA and CCD is best understood within
a Bogoliubov quasiparticle (qp) RPA formalism. This work is a follow-up to our
previous formal proof on the connection between particle-hole (ph) RPA and
ring-CCD. Whereas RPA is a quasibosonic approximation, CC theory is a correct
bosonization in the sense that the wavefunction and Hilbert space are exactly
fermionic. Coupled cluster theory achieves this goal by interacting the ph
(ring) and pp (ladder) diagrams via a third channel that we here call
"crossed-ring" whose presence allows for full fermionic antisymmetry.
Additionally, coupled cluster incorporates what we call "mosaic" terms which
can be absorbed into defining a new effective one-body Hamiltonian. The
inclusion of these mosaic terms seems to be quite important. The pp-RPA an d
qp-RPA equations are textbook material in nuclear structure physics but are
largely unknown in quantum chemistry, where particle number fluctuations and
Bogoliubov determinants are rarely used. We believe that the ideas and
connections discussed in this paper may help design improved ways of
incorporating RPA correlation into density functionals based on a CC
perspective