• chiral effective field theory
• muon capture on deuteron

The subject of this work is the theoretical study of the reaction d(µ−,nn)νµ. It is one of the few weak nuclear reactions involving light nuclei, accessible experimentally, whose capture rate can be calculated using ab-initio procedures. Furthermore, it is closely related to the pp weak capture, an astrophysical reaction of paramount interest, not accessible experimentally.
The main part of this thesis is the calculation of the
capture rate in the doublet hyperfine state, restricted to the S-wave two-neutron
scattering state, and provide a robust estimate for the theoretical uncertainty. New local potentials and consistent currents recently derived in Chiral Effective Field Theory, expressed in coordinate-space, are used. We have first of all test the ab-initio methods used to calculate the deuteron and
nn scattering wave function implementing, besides the variational method already used in literature, the Numerov method. Then, we have investigated the theoretical uncertainty arising from the uncertainty in the single-nucleon axial form factor
and from the chiral order convergence of the weak nuclear current. By using four different models for the nuclear interaction and relative currents, we have estimated also the uncertainty arising from model-dependence.
Our final result, summarized as Γ = 253.2 (5.7) s−1, is in agreement with the results present in the literature. Moreover, we have found
a perfect agreement between the results obtained within the variational and
the Numerov methods.