  This paper reports the study of a new interferometric configuration to
measure the effect of gravity on positronium. A Mach-Zehnder matter-wave
interferometer has been designed to operate with single-photon transitions and
to transfer high momentum to a 200 eV positronium beam. The work shows the
results and methods used to simulate the interferometer and estimate the
operating parameters and the time needed to perform the experiment. It has been
estimated that within less than one year, the acquisition time is sufficient to
achieve a 10\% accuracy level in measuring positronium gravitational
acceleration, even with a poorly collimated beam, which is significant for
theoretical models describing matter-antimatter symmetry. These results pave
the way for single photon transition large momentum transfer interferometry
with fast atomic beams, which is particularly useful for studies with
antimatter and unstable atoms.
