Elastic collision cross-sections for Xe <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> ions with neutral Xe atoms are calculated using a modified Tang-Toennies ion-atom potential and a semi-classical approximation with phase shifts calculated by the Jeffreys-Wentzel-Kramers-Brillouin approximation. Results are presented for integral and differential cross sections at center-of-mass energies in the 1 meV to 10 eV energy range. The cross sections were then used to calculate the drift velocities and diffusion coefficients of Xe <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> ions in gaseous xenon at atmospheric pressures and reduced electric fields, E/N, in the 3 to 300 Td range (N is the neutral gas number density and 1 Td=10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-17</sup> Vcm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 </sup> ) using Monte Carlo technique. The results obtained are compared and discussed with limited experimental data available from previous studies