  A new method to calculate cross sections for $(p,pn)$ and $(p,2p)$ reactions
measured under inverse kinematics conditions is proposed. The method uses the
prior form of the scattering transition amplitude, and replaces the exact
three-body wave function appearing in this expression by an expansion in terms
of $p$-$n$ or $p$-$p$ states, covering the physically relevant excitation
energies and partial waves. A procedure of discretization, similar to that used
in continuum-discretized coupled-channels calculations, is applied in order to
make this expansion finite and numerically tractable. The proposed formalism is
non-relativistic but several relativistic kinematical corrections are applied
to extend its applicability to energies of current interest. The underlying
optical potentials for the entrance and exit channels are generated
microscopically, by folding an effective density-dependent G-matrix with the
density of the composite nucleus. Numerical calculations for
$^{12}$C($p$,$2p$), $^{12}$C($p$,$pn$) and $^{23}$O($p$,$pn$) at
$\sim$400~MeV/nucleon are presented to illustrate the method. The role of
final-state interactions and Pauli principle between the outgoing nucleons is
also discussed.
