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We investigate the Ruderman-Kittel-Kasuya-Yosida oscillations of theitinerant carrier spin density in a system where those oscillations appear onlydue to a finite distribution of a localized spin. The system represents ahalf-infinite one-dimensional quantum wire with a magnetic impurity located atits edge. In contrast to the conventional model of a point-like exchangeinteraction the itinerant carrier spin density oscillations in this systemexist. We {\it analytically} demonstrate that when the radius of the exchangeinteraction is less than the wave length of the itinerant carriers living onthe Fermi surface, the long range behavior of the oscillations is identical tothe one taking place in the zero radius limit of the same exchange interactionbut for an infinite one-dimensional quantum wire where, in comparison with theoriginal half-infinite system, the mass of the itinerant carriers is {\itstrongly} modified by the exchange interaction radius. On the basis of ouranalysis we make a suggestion on directionality of surfaceRuderman-Kittel-Kasuya-Yosida interaction shown in recent experiments: webelieve that in general the anisotropy of the Ruderman-Kittel-Kasuya-Yosidainteraction could result not only from the anisotropy of the {\it Fermisurface} of itinerant carriers but also from the anisotropy of the {\it spincarrying atomic orbitals} of magnetic impurities.

Mass modification of itinerant carriers in RKKY oscillations induced by finite range exchange interactions