  Since the eta meson is a short-lived neutral particle, it is not possible to
investigate its structure via classical methods of particle scattering. To
learn about its quark wave function, one studies those decay processes of this
meson in which a pair of photons is produced, where at least one of them is
virtual. The virtual photons have a non-zero mass and convert into
lepton-antilepton pairs. Therefore, information about the quarks' spatial
distribution inside the meson can be extracted from the lepton-antilepton
invariant mass distributions by comparing the empirical results with QED
predictions, which are based on the assumption that the meson is a point-like
particle. The deviation from the expected behavior in the leptonic mass
spectrum exposes the inner structure of the meson. This deviation is
characterized by a form factor. The corresponding data were collected for the
pd --> 3He eta reaction at a proton beam momentum of 1.69 GeV/c. The experiment
was performed using the WASA-at-COSY detector in November 2008. 525 +/- 26
events of the eta --> g e+ e- decay channel were reconstructed. The analysis
chain led to the determination of the value of the slope parameter, bp, equal
to (2.27 +/- 0.73stat. +/- 0.46sys.) GeV^{-2}, where the systematical
uncertainty should be treated as an upper limit only. The estimation of the
charge radius of the eta meson has been made resulting with the value of <
r(eta)^2 >^(1/2) = (0.68 +/- 0.02) fm.
