  The Galactic Center Excess (GCE), one of the most remarkable discoveries by
Fermi-LAT, has prompted extensive exploration over the past decade, often
attributed to dark matter or millisecond pulsars. This work proposes a novel
interpretation on the origin of the GCE, focusing on the observed spectral
shape. Protons are accelerated at the Galactic center and collide with the
neutron cluster on the surface of the non-rotating neutron stars. Due to the
gluon condensation in nucleons, these collisions produce a large number of
mesons, which have reached to the saturation state and subsequently generate
the broken power law in the gamma ray spectra. We explained the spectral shape
of GCE using the gluon condensation and an assumption of existing the
non-rotating neutron stars at the Galactic center. This example of the gluon
condensation mechanism not only expands the applications of the hadronic
scenario in the cosmic gamma ray spectra but also provides a new evidence of
the gluon condensation.
