Variational Monte Carlo calculations ofH3andHe4with a relativistic Hamiltonian

In relativistic Hamiltonians the two-nucleon interaction is expressed as a sum of v${\mathrm{̃}}_{\mathit{i}\mathit{j}}$, the interaction in the ${\mathbf{P}}_{\mathit{i}\mathit{j}}$=0 rest frame, and the ‘‘boost interaction’’ δv(${\mathbf{P}}_{\mathit{i}\mathit{j}}$) which depends upon the total momentum ${\mathbf{P}}_{\mathit{i}\mathit{j}}$ and vanishes in the rest frame. The δv can be regarded as a sum of four terms: δ${\mathit{v}}_{\mathrm{RE}}$, δ${\mathit{v}}_{\mathrm{LC}}$, δ${\mathit{v}}_{\mathrm{TP}}$, and δ${\mathit{v}}_{\mathrm{QM}}$; the first three originate from the relativistic energy-momentum relation, Lorentz contraction, and Thomas precession, while the last is purely quantum. The contributions of δ${\mathit{v}}_{\mathrm{RE}}$ and δ${\mathit{v}}_{\mathrm{LC}}$ have been previously calculated with the variational Monte Carlo method for ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. In this paper we report the results of similar calculations for the contributions of δ${\mathit{v}}_{\mathrm{TP}}$ and δ${\mathit{v}}_{\mathrm{QM}}$. These are found to be rather small.