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The reaction pp -> K+ + (Lambda p) was measured at Tp=1.953 GeV and Theta = 0 deg with a high missing mass resolution in order to study the Lambda p final state interaction. The large final state enhancement near the Lambda p threshold can be describ ed using the standard Jost-function approach. The singlet and triplet scattering lengths and effective ranges are deduced by fitting simultaneously the Lambda p invariant mass spectrum and the total cross section data of the free Lambda p scattering.
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