  Recently, two coincidence detection techniques, the coincidence
angle-resolved photoemission spectroscopy (cARPES) and the coincidence
inelastic neutron scattering (cINS), have been proposed to detect directly the
two-body correlations of strongly correlated electrons in particle-particle
channel or two-spin channel. In the original proposals, a coincidence detector
is introduced for the coincidence detection of two photoelectric processes or
two neutron-scattering processes. In this article, we present a {\it
post-experiment} coincidence counting method for the proposed coincidence
detection techniques without a coincidence detector. It requires a {\it pulse}
photon or neutron source. Consider one incident multiphoton or multineutron
pulse that causes many photoelectric or neutron-scattering processes within one
time window. $I_{d_1}^{(1)}$ and $I_{d_2}^{(1)}$ record the numbers of the
emitted photoelectrons or the scattered neutrons which arrive at two detectors
$D_1$ and $D_2$, respectively. The coincidence counting is defined by
$I_d^{(2)}=I_{d_1}^{(1)} \times I_{d_2}^{(1)}$, which records the coincidence
probability of two photoelectric processes or two neutron-scattering processes
within this time window. Therefore, $I_d^{(2)}$ involves the two-body
correlations of the target electrons. The previously proposed cARPES and cINS
can be implemented upon the {\it pulse}-resolved angle-resolved photoemission
spectroscopy (ARPES) and inelastic neutron scattering (INS) experimental
apparatuses with pulse sources.
