  Two-particle scattering probabilities in tunneling scenarios with exchange
interaction are analyzed with quasi-particle wave packets. Two initial
one-particle wave packets (with opposite central momentums) are spatially
localized at each side of a barrier. After impinging upon a tunneling barrier,
each wave packet splits into transmitted and reflected components. When the
initial two-particle anti-symmetrical state is defined as a Slater determinant
any type of (normalizable) one-particle wave packet, it is shown that the
probability of detecting two (identically injected) electrons at the same side
of the barrier is different from zero in very common (single or double barrier)
scenarios. In some particular scenarios, the transmitted and reflected
components become orthogonal and the mentioned probabilities reproduce those
values associated to distinguishable particles. These unexpected non-zero
probabilities are still present when non-separable Coulomb interaction or
non-symmetrical potentials are considered. On the other hand, for initial wave
packets close to Hamiltonian eigenstates, the usual zero two-particle
probability for electrons at the same side of the barrier found in the
literature is recovered. The generalization to many-particle scattering
probabilities with quasi-particle wave packets for low and high phase-space
density are also analyzed. The far-reaching consequences of these non-zero
probabilities in the accurate evaluation of quantum noise in mesoscopic systems
are briefly indicated.
