  We show that scanning gate microscopy can be used for probing
electron-electron interactions inside a nanostructure. We assume a simple model
made of two non-interacting strips attached to an interacting nanosystem. In
one of the strips, the electrostatic potential can be locally varied by a
charged tip. This change induces corrections upon the nanosystem Hartree-Fock
self-energies which enhance the fringes spaced by half the Fermi wavelength in
the images giving the quantum conductance as a function of the tip position.
