A closed variant of the Born approximation for calculating differential scattering cross sections in ion-atom collisions is developed. An expression in terms of the matrix elements J_(ij) with respect to the single-electron states of the atom is found for the matrix element describing the target atom in the formula for the differential cross section. The matrix elements J_(ij) are averaged over the relative orientation of the momentum transferred in the collision and the symmetry axis of the electronic orbitals of the target atom, using the single-electron Rutaan-Hartree-Fock wave functions. The algebraic representation of the matrix elements J_(ij) makes it possible to perform calculations for atoms with any value of Z. The model developed is used to calculate the cross sections σ_Σ and characteristic scattering angles θ_c for the process of electron loss by H~- ions with energy E = 0.1-100 MeV in targets consisting of atoms with Z = 2-54. It is shown that σ_Σ ∝ E~(-1) and θ_c ∝ E~(-1/2) for all Z, and for fixed E the behavior of σ_Σ(Z) and θ_c(Z) is determined by the order of filling of the electronic shells of the target atoms (the ionization potential). The computational results are analyzed and compared with the experimental data and the results of other calculations.
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