  The proton-proton momentum correlation function from different rapidity
regions are systematically investigated for the Au + Au collisions at different
impact parameters and different energies from 400$A$ MeV to 1500$A$ MeV in the
framework of the isospin-dependent quantum molecular dynamics model
complemented by the $Lednick\acute{y}$ and $Lyuboshitz$ analytical method. In
particular, in-medium nucleon-nucleon cross section dependence of the
correlation function is brought into focus, while the impact parameter and
energy dependence of the momentum correlation function are also explored. The
sizes of the emission source are extracted by fitting the momentum correlation
functions using the Gaussian source method. We find that the in-medium
nucleon-nucleon cross section obviously influence the proton-proton momentum
correlation function which is from the whole rapidity or projectile/target
rapidity region at smaller impact parameters, but there is no effect on the
mid-rapidity proton-proton momentum correlation function, which indicates that
the emission mechanism differs between projectile/target rapidity and
mid-rapidity protons.
