We present a calculation of the radiative capture cross section p(n, γ)d in the low-energy range, where the M 1 reaction channel dominates. Employing the LENPIC nucleon-nucleon interaction up to the fifth order (N4LO) that is regularized by the semi-local coordinate space regulators, we obtain the initial and final state wave functions, and evaluate the phase shifts of the scattering state and deuteron properties. We derive the transition operator from the chiral effective field theory up to the next-to-next-to leading order (N2LO), where we also regularize the transition operator using regulators consistent with those of the interactions. We compute the capture cross sections and the results show a converging pattern with the chiral-order expansion of the nucleon-nucleon interaction, where the regulator dependence of the results is weak when higher-order nucleon-nucleon interactions are employed. We quantify the uncertainties of the cross-section results due to the chiralorder truncation. The chirally complete and consistent cross-section results are performed up to N2LO and they compare well with the experiments and other theoretical predictions.

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We present a calculation of the radiative capture cross section p(n, γ)d in the low-energy range, where the M 1 reaction channel dominates. Employing the LENPIC nucleon-nucleon interaction up to the fifth order (N4LO) that is regularized by the semi-local coordinate space regulators, we obtain the initial and final state wave functions, and evaluate the phase shifts of the scattering state and deuteron properties. We derive the transition operator from the chiral effective field theory up to the next-to-next-to leading order (N2LO), where we also regularize the transition operator using regulators consistent with those of the interactions. We compute the capture cross sections and the results show a converging pattern with the chiral-order expansion of the nucleon-nucleon interaction, where the regulator dependence of the results is weak when higher-order nucleon-nucleon interactions are employed. We quantify the uncertainties of the cross-section results due to the chiralorder truncation. The chirally complete and consistent cross-section results are performed up to N2LO and they compare well with the experiments and other theoretical predictions.

We investigate the use of the sinc collocation and harmonic oscillator bases for solving a two-particle system bound by a Gaussian potential described by the radial Schrödinger equation. We analyze the properties of the bound state wave functions by investigating where the basis-state wave functions break down and relate the breakdowns to the infrared and ultraviolet scales for both bases. We propose a correction for the asymptotic infrared region, the long range tails of the wave functions. We compare the calculated bound state eigenvalues and mean square radii obtained within the two bases. From the trends in the numerical results, we identify the advantages and disadvantages of the two bases. We find that the sinc basis performs better in our implementation for accurately computing both the deeply-and weakly-bound states whereas the harmonic oscillator basis is more convenient since the basis-state wave functions are orthogonal and maintain the same mathematical structure in both position and momentum space. These mathematical properties of the harmonic oscillator basis are especially advantageous in problems where one employs both position and momentum space. The main disadvantage of the harmonic oscillator basis as illustrated in this work is the large basis space size required to obtain accurate results simultaneously for deeply-and weakly-bound states. The main disadvantage of the sinc basis could be the numerical challenges for its implementation in a many-body application.