  Luminosity is the key quantity characterizing the performance of charged
particle colliders. Precise luminosity determination is an important task in
collider physics. Part of this task is the proper calibration of detectors
dedicated for luminosity measurements. The wide-used experi-mental method of
calibration is the van-der-Meer scan, which is the beam separation scan
performed at specifically optimized beam conditions. This work is devoted to
modeling this scan with the q-Gaussian distribution of particles in colliding
beams. Because of its properties, the Q-Gaussian distribution is believed to
describe the density closer to reality than regular Gaussian-based models. In
this work, the q-Gaussian model is applied for van-der-Meer scan modeling, and
the benefits of this model for luminosity calibration task are demonstrated.
