Variational Monte Carlo calculations ofH3andHe4with a relativistic Hamiltonian

The two-nucleon phase shifts and deuteron properties are fitted using relativistic, (${\mathit{m}}^2$+${\mathit{p}}^2$ ${)}^{1/2}$, kinetic-energy operators to obtain realistic models of v${\mathrm{̃}}_{\mathit{i}\mathit{j}}$, the two-nucleon interaction in the frame in which the total momentum ${\mathbf{P}}_{\mathit{i}\mathit{j}}$ of the interacting pair is zero. The relativistic Hamiltonian ${\mathit{H}}_{\mathit{R}}$ contains the relativistic kinetic energy, v${\mathrm{̃}}_{\mathit{i}\mathit{j}}$, and δ${\mathit{v}}_{\mathit{i}\mathit{j}}$(${\mathbf{P}}_{\mathit{i}\mathit{j}}$) which describes the dependence of the interaction on the total momentum of the pair. The δ${\mathit{v}}_{\mathit{i}\mathit{j}}$(${\mathbf{P}}_{\mathit{i}\mathit{j}}$) are obtained from the v${\mathrm{̃}}_{\mathit{i}\mathit{j}}$ using relativistic mechanics. The ground states of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are calculated using the ${\mathit{H}}_{\mathit{R}}$ with the variational Monte Carlo method, and the results are compared with those obtained using the nonrelativistic ${\mathit{H}}_{\mathrm{NR}}$. Results of calculations including the three-nucleon interaction are also reported. The relativistic effects reduce the binding energies of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ by ∼0.34 and 2.02 MeV, and they do not change the momentum distribution of the nucleons in these nuclei significantly.