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In the spirit of recent work of Lamm, Malchiodi and Micallef in the settingof harmonic maps, we identify Yang-Mills connections obtained by approximationswith respect to the Yang-Mills {\alpha}-energy. More specifically, we show thatfor the SU(2) Hopf fibration over the four sphere, for sufficiently small{\alpha} values the SO(4) invariant ADHM instanton is the unique{\alpha}-critical point which has Yang-Mills {\alpha}-energy lower than aspecific threshold.

Limits of Yang-Mills {\alpha}-connections