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We calculate the energy spectrum and the one-photon El and M1 decays of charmonium and bquarkonium including their first-order relativistic corrections, within the context of the Buchmiiller-Tye potential. Results seem to suggest that the confining potential is predominantly scalar since this assumption gives good agreement for spectra and for El decay rates of crand gives reasonable results for bb7 For M1 decays discrepancies persist unless the quarks have large anomalous moments, but the resolution of such discrepancies can probably be achieved by other means. As an interesting by-product of our investigations we find that for the nonrelativistically inhibited El decay T"+X!+~ of the bbsystem, some rates are enhanced by a huge factor by firstorder relativistic effects. When more data are available these decays should provide an additional testing ground for models of relativistic corrections.

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Exotic dark matter together with the vacuum energy (associated with the cosmological constant) seem to dominate the Universe. Thus its direct detection is central to particle physics and cosmology. Supersymmetry provides a natural dark matter candidate, the lightest supersymmetric particle (LSP). One essential ingredient in obtaining the direct detection rates is the density and the velocity distribution of the LSP in our vicinity. In the present paper we study simultaneously density profiles and velocity distributions in the context of the Eddington approach. In such an approach, unlike the commonly assumed Maxwell-Boltzmann (M-B) distribution, the upper bound of the velocity arises naturally from the potential.PACS numbers: 95.35.+d, 12.60.Jv