Variational Monte Carlo Calculations of $^3$H and $^4$He with a relativistic Hamiltonian - II

Abstract

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