Abstract
This paper is devoted to a relativistic calculation of muon capture in deuterium. The important effect of hyperfine structure is treated relativistically. The aim of this work is a determination of neutron-neutron scattering length and effective range. We use vertex functions to describe the proton-neutron-deuteron vertex and the Omnès method to compute the final-state interaction. It is shown that an accuracy of 2.5% in spectrum and capture rate must allow a determination of r os and a s with an accuracy of, respectively, ±0.2 fm and ±0.7 fm.
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