A statistical investigation of the location of onset of intermediate and gyrating ion populations in the Earth's foreshock is presented based on Fixed Voltage Analyzer data from ISEE 1. This study reveals the existence of a spatial boundary for intermediate and gyrating ion populations that coincides with the reported ULF wave boundary. This boundary position in the Earth's foreshock depends strongly upon the magnetic cone angle &#x03B8;<i>_BX</i> and appears well defined for relatively large cone angles, though not for small cone angles. As reported in a previous study of the ULF wave boundary, the position of the intermediate-gyrating ion boundary is not compatible with a fixed growth rate of the waves resulting from the interaction between a uniform beam and the ambient plasma. The present work examines the momentum associated with protons which travel along this boundary, and we show that the variation of the boundary position (or equivalently, the associated particle momentum) with the cone angle is related to classical acceleration mechanisms at the bow shock surface. The same functional behavior as a function of the cone angle is obtained for the momentum predicted by an acceleration model and for the particle momentum associated with the boundary. However, the model predicts systematically larger values of the momentum than the observation related values by a constant amount; we suggest that this difference may be due to some momentum exchange between the incident solar-wind population and the backstreaming particles through a wave-particle interaction resulting from a beam plasma instability.<br><br><b>Key words. </b>Intermediate ion boundary · Statistical investigation · Earth's foreshock · ISEE 1 spacecraft