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 ${\mathbf{P}}_{ij}=0$ rest frame, and the ``boost interaction'' $\delta v({\mathbf{P}}_{ij})$ which depends upon the total momentum ${\mathbf{P}}_{ij}$ and vanishes in the rest frame. The $\delta v$ can be regarded as a sum of four terms: $\delta v_{RE}$, $\delta v_{LC}$, $\delta v_{TP}$ and $\delta v_{QM}$; the first three originate from the relativistic energy-momentum relation, Lorentz contraction and Thomas precession, while the last is purely quantum. The contributions of $\delta v_{RE}$ and $\delta v_{LC}$ 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 $\delta v_{TP}$ and $\delta v_{QM}$. These are found to be rather small.

Comments: 7 pages, P-94-09-079