  In this paper, we study the entanglement property of a 4-particle system. In
this system, two initially entangled electrons A and C are scattered by two
uncorrelated positrons B and D, respectively. We calculate the entanglements
among the particles both before and after the double QED scattering
($AB\rightarrow AB, CD\rightarrow CD$). We find that the change of entanglement
entropy between subsystems A and B during the scattering processs is
proportional to the total cross section,
$\sigma_{tot}=\sigma_{AB}\times\sigma_{CD}$. Even though there is no direct
interaction between subsystems A and C (or B and D), the scattering process
induces entanglement change among them which is also proportional to
$\sigma_{tot}$. This result shows some kind of entanglement sharing property in
multipartite system. In order to further investigate the entanglement sharing,
we calculate the entanglement monotones which quantify the genuine multipartite
entanglement in a multipartite system. For our chosen scattering process,
$e^+e^-\rightarrow\mu^+\mu^-$, however, we find that the outgoing state is a
W-type 4-partite entangled state which has no genuine 4-partite entanglement.
