New insight into thend→3Hγprocess at thermal energy with pionless effective field theory

Abstract

We take a new look at the neutron radiative capture by a deuteron at thermal energy with the pionless effective field theory [EFT($\ensuremath{\pi}\phantom{\rule{-0.5em}{0ex}}/$)] approach. We present in detail the calculation of $nd\ensuremath{\rightarrow}$ ${}^{3}\mathrm{H}\ensuremath{\gamma}$ 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 $nd\ensuremath{\rightarrow}$ ${}^{3}\mathrm{H}\ensuremath{\gamma}$ 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\ensuremath{\rightarrow}$${}^{3}\mathrm{H}\ensuremath{\gamma}$ up to $\text{next-to-next-to-leading}\phantom{\rule{4.pt}{0ex}}\text{order}\phantom{\rule{4.pt}{0ex}}{\text{(N}}^{2}\text{LO)}$ with the results of the previous model-dependent theoretical calculations and experimental data. The more acceptable results for cross section ${\ensuremath{\sigma}}_{\mathrm{tot}}^{(2)}=0.297\phantom{\rule{0.28em}{0ex}}(\text{LO})+0.124\phantom{\rule{0.28em}{0ex}}(\text{NLO})+0.048\phantom{\rule{0.28em}{0ex}}({\text{N}}^{2}\text{LO})=[0.469\ifmmode\pm\else\textpm\fi{}0.033]\phantom{\rule{0.222222em}{0ex}}\text{mb}$ show order by order convergence and cutoff independence. No three-body currents are needed to renormalize observables up to ${\text{N}}^{2}\text{LO}$ in this process.