The broadening of spectral lines due to dipole-dipole interactions with ground-state atoms of the same element is calculated with the impact and classical path approximations. Summation over all contributing intermediate states accounts for the multiplicity of the levels involved and results in a width proportional to the geometrical mean of absorption and emission oscillator strengths. Higher multipole interactions are shown to be almost always negligible, and for Lyman-$\ensuremath{\alpha}$ the iterated solution of the time-dependent Schr\"odinger equation describing the collisions is extended to fourth order. Estimated errors of its calculated width and of the widths of other lines are about 5% in the validity regime of the impact approximation, apart from any uncertainties in oscillator strengths and statistical weight factors.