  A new effect is presented, which changes the emittance during colliding-beam
operation in circular colliders. If the initial transverse distribution is
Gaussian, the collision probability is much higher for particles in the core of
the beam than in the tails. When small-amplitude particles are removed, the
remaining ones therefore have a larger transverse emittance. This effect,
called core depletion, may cause a decrease in luminosity. An approximate
analytic model is developed to study the effect and benchmarked against a
multiparticle tracking simulation. Finally, the time evolution of the intensity
and emittances of a Pb bunch in the Large Hadron Collider (LHC) at CERN is
calculated, taking into account also other processes than collisions. The
results show that integrated luminosity drops by 3--4% if core depletion is
taken into account. It is also found that core depletion causes the transverse
emittance to be larger when more experiments are active. This observation could
be checked against experimental data once the LHC is operational.
