  Differential cross sections for electron collisions with the O$_2$ molecule
in its ground ${X}^{3}\Sigma_g^-$ state, as well as excited ${a}^{1}\Delta_g$
and ${b}^{1}\Sigma_g^+$ states are calculated. As previously, the fixed-bond
R-matrix method based on state-averaged complete active space SCF orbitals is
employed. In additions to elastic scattering of electron with the O$_2$
${X}^{3}\Sigma_g^-$, ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states, electron
impact excitation from the ${X}^{3}\Sigma_g^-$ state to the ${a}^{1}\Delta_g$
and ${b}^{1}\Sigma_g^+$ states as well as '6 eV states' of
${c}^{1}\Sigma_u^{-}$, ${A'}^{3}\Delta_u$ and ${A}^{3}\Sigma_u^{+}$ states is
studied. Differential cross sections for excitation to the '6 eV states' have
not been calculated previously. Electron impact excitation to the
${b}^{1}\Sigma_g^+$ state from the metastable ${a}^{1}\Delta_g$ state is also
studied. For electron impact excitation from the O$_2$ ${X}^{3}\Sigma_g^-$
state to the ${b}^{1}\Sigma_g^+$ state, our results agree better with the
experimental measurements than previous theoretical calculations. Our cross
sections show angular behaviour similar to the experimental ones for
transitions from the ${X}^{3}\Sigma_g^-$ state to the '6 eV states', although
the calculated cross sections are up to a factor two larger at large scattering
angles. For the excitation from the ${a}^{1}\Delta_g$ state to the
${b}^{1}\Sigma_g^+$ state, our results marginally agree with the experimental
data except for the forward scattering direction.
