We study kaonic deuterium, the bound K − d state A Kd . Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K − d scattering for arbitrary relative momenta. Near threshold our formula reduces to the wellknown DGBT formula. The S-wave amplitude of K − d scattering near threshold is defined by the resonances Λ(1405), Σ(1750) and a smooth elastic background, and the inelastic channels K − d → N Y and K − d → N Y π, where Y = Σ ± , Σ 0 and Λ 0 , where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K − d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A Kd → N Y and experimental data on the rates of the N Y -pair production in the reactions K − d → N Y . We obtain Γ 1s = (630 ± 100) eV. For the shift of the energy level of the ground state of kaonic deuterium we predict ǫ 1s = (353 ± 60) eV.
We analyse the continuum-state and bound-state β − -decay rates of the neutron. For the calculation of theoretical values of the decay rates we use the new value for the axial coupling constant gA = 1.2750(9), obtained recently by H. Abele (Progr. Part. Nucl. Phys., 60, 1 (2008)) from the fit of the experimental data on the neutron spin-electron correlation coefficient of the electron energy spectrum of the continuum-state β − -decay of the neutron. We take into account the contribution of radiative corrections and the scalar and tensor weak couplings. We define correlation coefficients of the electron energy spectrum in terms of axial, scalar and tensor coupling constants. Using recent precise experimental data for the lifetime of the neutron and correlation coefficients we estimate the scalar and tensor weak coupling constants. The bound-state β − -decay rates of the neutron we calculate as functions of axial, scalar and tensor weak coupling constants. We show that dominantly the neutron decays into hydrogen in the hyperfine states with total angular momentum F = 0. The calculated angular distributions of the probabilities of the bound-state β − -decays of the polarised neutron can be used for the experimental measurements of the bound-state β − -decays into the hyperfine states with a total angular momentum F = 1. PACS: 12.15.Ff, 13.15.+g, 23.40.Bw, 26.65.+t
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