  The energy of Skyrmions is calculated with the help of a technique based on
the excitonic representation: the basic set of one-exciton states is used for
the perturbation-theory formalism instead of the basic set of one-particle
states. We use the approach, at which a skyrmion-type excitation (at zero Lande
factor) is considered as a smooth non-uniform rotation in the 3D spin space.
The result within the framework of an excitonically diagonalized part of the
Coulomb Hamiltonian can be obtained by any ratio $r_{\tiny C}=(e^2/\epsilon
{}l_B)/\hbar \omega_c $ [where $e^2/\epsilon {}l_B$ is the typical Coulomb
energy (${}l_B$ being the magnetic length); $\omega_c$ is the cyclotron
frequency], and the Landau-level mixing is thereby taken into account. In
parallel with this, the result is also found exactly, to second order in terms
of the $r_{\tiny C}$ (if supposing $r_{\tiny C}$ to be small) with use of the
total Hamiltonian. When extrapolated to the region $r_{\tiny C}\sim 1$, our
calculations show that the skyrmion gap becomes substantially reduced in
comparison with the Hartree-Fock calculations. This fact brings the theory
essentially closer to the available experimental data.
