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We take a new look at the neutron radiative capture by a deuteron at thermal energy with the pionless effective field theory (EFT(π /)) approach. We present in detail the calculation of nd → 3 Hγ amplitudes for incoming doublet and quartet channels leading to the formation of a triton fully in the projection method based on the cluster-configuration space approach. In the present work, we consider all possible one-body and two-body photon interaction diagrams. In fact, additional diagrams that make significant changes in the results of the calculation of the total cross section in the nd → 3 Hγ process are included in this study. The properly normalized triton wave function is calculated and taken into consideration. We compare the cross section of the dominant magnetic M1-transition of nd → 3 Hγ up to next-to-next-to-leading order N 2 LO with the results of the previous model-dependent theoretical calculations and experimental data. The more acceptable results for cross section σ (2) tot = 0.297 (LO) + 0.124 (NLO) + 0.048 (N 2 LO) = [0.469 ± 0.033] mb show order by order convergence and cutoff independence. No three-body currents are needed to renormalize observables up to N 2 LO in this process.

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The effect of muonic molecules complex [Formula: see text] forming with different spin states (J = 0, 1) in various decay channels on the cycling rate, the effective sticking coefficient, and the neutron yield per muon stopped in mixture was studied. It was shown that the error of the relative neutron yield is decreased in the optimum physical condition of the deuterium in the mixture by considering the effect of various decay channels of the muonic molecule complex.

The nonleptonic weak interaction in the few-nucleon system at very low energies is studied with the calculation of the photon circular polarization in the pd → 3 Heγ reaction (P pd γ ). For very low energies, one may treat the pion as heavy and integrate it out from the QCD symmetry-based model-independent effective field theory, leaving only short-range strong interactions which are introduced in term of pionless effective field theory formulation. We investigate a complete set of the parity-violating electromagnetic transitions in the pd → 3 Heγ process. In this paper the interferences of strong, electromagnetic, Coulomb, and parity-violating weak interactions are presented with the calculation of a full set of appropriate diagrams at the leading order. We have obtained energy-dependent P pd γ results as a function of the laboratory energy values 0.5 E Lab 3 MeV in terms of the low-energy coupling constants. The contributions of the initial Sand P -wave proton-deuteron systems have been considered to make the final 3 He ground state in this energy region.