  The universal analytical approach was developed to describe the process of
particle slow extraction from a synchrotron using adiabatic crossing the
betatron resonance of the third order. The obtained formulas make it possible
to calculate the time diagrams for the current of the extracted beam ('spill
profile'), taking into account the chromaticity, particle momentum spread and
synchrotron oscillations. On this basis, a method for monochromatization of
extracted beam is indicated. The theory is compared with some results obtained
in the experiment on crossing the third-order resonance at the VEPP-4M storage
ring.
