We calculate the scattering lenths A(K-,3He) and A(K-,4He) using the multiple scattering approach and different parameters sets for the elementary a(Kbar,N). Within the zero-range approximation, we find for both systems loosely bound states with binding energies in the range 2-7 MeV and widths 11-18 MeV. It is demonstrated that the existence of deeply bound K-,4He states, which have been predicted in literature, can be tested by measuring the reaction dd -> 4He K-K+ at COSY.
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