Many-body expansion for light nuclear systems

Abstract

We extend the many-body expansion (MBE), previously applied to hydrogen bonded and molecular systems, to the light nuclear systems $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ by considering the nucleonic degrees of freedom as fundamental in the expansion. The analysis is based on the Pauli nucleonic dynamics (PND) model, a simple antisymmetrized dynamical code, inspired by the sophisticated constrained molecular dynamics (CoMD) model. The total energy of the $^{2}\mathrm{H}$ nucleus is calculated with this model at \ensuremath{-}2.312 MeV, which is within 4% of the experimental value of \ensuremath{-}2.225 MeV. The application of the MBE yields results for the three-body term in the $^{3}\mathrm{H}$ nucleus that is comparable with previous estimates, while it is reported for the first time for the nucleus of $^{3}\mathrm{He}$. The energies of $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ that include the sum of the one- and two-body terms with the model are $\ensuremath{-}6.97\ifmmode\pm\else\textpm\fi{}0.21$ MeV and $\ensuremath{-}6.19\ifmmode\pm\else\textpm\fi{}0.21$ MeV and the three-body terms, estimated from the difference of the sum of the one- and two-body terms from the experimentally measured energies, are $\ensuremath{-}1.51\ifmmode\pm\else\textpm\fi{}0.21$ MeV and $\ensuremath{-}1.53\ifmmode\pm\else\textpm\fi{}0.21$ MeV, respectively. The MBE for the $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ nuclei is qualitatively similar to the one previously reported for the water trimer: the two- and three-body terms are negative with the latter amounting to $\ensuremath{\sim}3%$ of the former. Additionally, the three-body terms correspond to about 16--23% of the total energy of the bound systems, a percentage that is also comparable to the one in the water trimer (17%). In this manner, the MBE analysis can be applied to light nuclear systems following the same protocol as the one that has been previously extensively used for hydrogen bonded molecular systems.