Many-body expansion for light nuclear systems

We extend the many-body expansion (MBE), previously applied to hydrogen bonded and molecular systems, to the light nuclear systems 3H and 3He 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 2H nucleus is calculated with this model at -2.312 MeV, which is within 4% of the experimental value of -2.225 MeV. The application of the MBE yields results for the three-body term in the 3H nucleus that is comparable with previous estimates, while it is reported for the first time for the nucleus of 3He. The energies of 3H and 3He that include the sum of the one-and two-body terms with the model are -6.97 +/- 0.21 MeV and -6.19 +/- 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 -1.51 +/- 0.21 MeV and -1.53 +/- 0.21 MeV, respectively. The MBE for the 3H and 3He 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 similar to 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.