  The adjoint equation was introduced in the early days of neutron transport
and its solution, the neutron importance, has ben used for several applications
in neutronics. The work presents at first a critical review of the adjoint
neutron transport equation. Afterwards, the adjont model is constructed for a
reference physical situation, for which an analytical approach is viable, i.e.
an infinite homogeneous scattering medium. This problem leads to an equation
that is the adjoint of the slowing-down equation that is well-known in nuclear
reactor physics. A general closed-form analytical solution to such adjoint
equation is obtained by a procedure that can be used also to derive the
classical Placzek functions. This solution constitutes a benchmark for any
statistical or numerical approach to the adjoint equation. A sampling technique
to evaluate the adjoint flux for the transport equation is then proposed and
physically interpreted as a transport model for pseudo-particles. This can be
done by introducing appropriate kernels describing the transfer of the
pseudo-particles in phase space. This technique allows estimating the
importance function by a standard Monte Carlo approach. The sampling scheme is
validated by comparison with the analytical results previously obtained.
