  A microscopic analysis of the optical potentials (OPs) and cross sections of
quasielastic scattering of $^{12,14}$Be on $^{12}$C at 56 MeV/nucleon and on
protons at energy near 700 MeV is carried out. For lower energy scattering the
real part of the OP is calculated by using of double-folding procedure
accounting for the anti-symmetrization effects, while the imaginary part is
obtained on the base of the high-energy approximation (HEA). The HEA is also
applied to the calculations of both real and imaginary OPs when solving the
relativistic equation for the high-energy proton-nucleus elastic scattering.
The neutron and proton density distributions computed in different microscopic
models for $^{12}$Be and $^{14}$Be are used. In the present hybrid model of the
optical potential the only free parameters are the depths of the real and
imaginary parts of OP obtained by fitting the experimental data. The role of
the inelastic scattering channel to the first excited $2^{+}$ and $3^{-}$
states in $^{12}$C when calculating the quasielastic cross sections, as well as
the modified density of the $^{12}$C target accounting for the surface effects
are studied. In addition, the cluster model, in which $^{14}$Be consists of a
$2n$-halo and the $^{12}$Be core, is applied to calculate the cross sections of
diffraction breakup and stripping reactions in $^{14}$Be+$^{12}$C scattering
and longitudinal momentum distributions of $^{12}$Be fragments at energy of 56
MeV/nucleon. A good agreement of the theoretical results with the available
experimental data of both quasielstic scattering and breakup processes is
obtained.
