Differential and total cross sections for the ionization of water molecule by electron impact

A theoretical approach is presented to calculate multiply differential and total cross sections of the ionization of H2O molecule in the vapour phase. The wave function of the target is described by molecular orbitals consisting of a linear combination of slater type atomic orbitals centered on the heaviest atom which is the oxygen atom in this case. The calculations are carried out in the first Born approximation where the projectile is described by a plane wave while the ejected electron is described by a coulomb wave taking into account its interaction with the residual ion. The spherical average over the Euler solid angle due to the randomly oriented gaseous target molecule is carried out analytically using the rotation matrix properties. The differential and total cross sections are thus evaluated without any special difficulty and compared with experiments and distorted wave calculations. Fair agreements are observed.