Analysis of the geocoronal He-I 58.4-nm resonance radiation field with rocket borne gas absorption cell photometers has revealed singly scattered photons to attain steadily increasing importance in the radiation signals if photons close to the line center are effectively suppressed. In order quantitatively to intensity in terms of contributions from different scattering orders. In the formulation of these contributions we have used the concept of angle-dependent partial frequency redistribution in comparison with that of complete redistribution. The first and second order intensity contributions are studied in detail here with respect to their spectral profile, to their local and solar zenith angle dependence, and to their height profile. The second and higher order intensity contributions are shown to decrease steeply with increasing distance from the line center, such that for a specific observation a critical wavelength distance can be calculated beyond which only singly scattered photons contribute to the total intensity. The intensity due only to singly scattered photons is proven to be proportional to the helium column density on the line of sight within clearly determinable accuracies. Thus its height profile enables immediate deduction of local atmospheric parameters, as the atmospheric helium density and temperature, even under optically thick conditions.