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We have studied the two-center effect (TCE) in ion-atom ionization by measuring the energy and angular distributions of the double-differential cross sections (DDCSs) (d2σ/dεdΩ) of the low-energy electrons emitted in a collision of He atoms with 2.5 MeV/nucleon C6+ ions. The electrons with energies between 0.1 and 300 eV were detected for 13 different emission angles between 15° and 160°. From the measured DDCSs we have deduced the single differential cross sections such as dσ/dΩ and dσ/dε and the total cross section. The data have been compared with the continuum distorted wave eikonal initial state calculations with H-like and Hartree-Fock-Slater wave functions for the initial and final state of the electron and first Born calculations. The forward-backward asymmetry parameter also has been deduced to study the TCE in detail. In the following paper [Lokesh C. Tribedi et al., Phys. Rev. A 58, 3626 (1998)] we have explored the collision dynamics by deducing the momentum distributions of the electron, the recoil ion, and the projectile.