  We study collision of two atoms with formation of Feshbach resonance at
combined interaction with the external magnetic field and laser radiation. In
cases of one- and two-photon resonances of laser radiation with two discrete
vibrational molecular levels, we show that Feshbach resonances appear at
interaction of external magnetic field with dressed states formed via
Autler-Townes effect. In addition, in case of one-photon resonance the lower
vibrational molecular state is coupled by laser radiation with the continuum of
the elastic channel and forms laser-induced Feshbach resonance via both
Autler-Townes effect and LICS mechanism. We study the combined process of
formation of Feshbach resonances; this enables the control of Feshbach
resonance by varying the magnetic field and intensity and frequency of laser
radiation. We obtain the cross-sections of elastic and inelastic scattering and
show that quenching of resonance occurs at the energy equal to that of the
systems ground state. Dependence of the cross-sections on the magnetic field
and laser intensity is examined in detail. In all considered cases, the
scattering length is obtained depending on the magnetic and laser fields are
studied. In the absence of magnetic interaction if the hyperfine substates of
the quasibound state in the closed channel and those of individual colliding
atoms in the open channel are the same, Feshbach resonances may arise via weak
interaction between nuclear and electronic motions, which leads to transitions
between electronic states. The obtained results can be employed in new studies
of collisions of cold atoms, e.g., of alkali metal atoms and for interpretation
of new experiments in BECs.
