Quantum Monte Carlo studies of relativistic effects in light nuclei

Abstract

Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two-and three-body potentials and their boost corrections. In this work we use the variational Monte Carlo method to study two kinds of relativistic effects in the binding energy of 3 H and 4 He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by ∼ 15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of ∼ 0.4 (1.9) MeV in 3 H ( 4 He) and account for ∼ 37% of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.

Realistic models of pion-exchange three-nucleon interactions

“…The V R contribution in present models is comparable to their ∆ dispersive effect, while the V 2π,P W is much more attractive. Studies of A = 3, 4 nuclei with relativistic Hamiltonians [17] indicate that the boost interaction δv gives the largest relativistic correction, of ∼ 0.4 MeV, to the triton energy. It is included in the present relativistic (H * ) models.…”

“…It increases the triton energy by ∼ 0.4 MeV away from experiment, while the nuclear matter equilibrium E 0 and ρ 0 move to −13.7 MeV at 0.23 fm −3 , which is closer to the empirical density, but farther from the empirical energy. The VMC studies [17] of δv(P ij ) also show that the dominant corrections come from the first and second terms of Eq. (2.8) and that only the first six operator terms (the static terms) of AV18 give substantial contributions.…”

“…[33]. The effects of the δv(P ij ) on the energies of 3 H and 4 He [17] and nuclear matter [3] have been studied for the AV18 model using the variational method. This boost correction gives a repulsive contribution in both cases.…”

Toy model of the nucleon-nucleon potential

“…The most impressive results for solving the problem of underbinding are obtained by applying phenomenological three-nucleon forces adjusted to achieve the correct triton ground state energy [7]. With this addition 4 He is properly bound, while the ground state energies of A = 5 − 8 and the excitation energies of the low-lying states are again too high [8].…”

“…Fully relativistic calculations are extremely complicated and consequently have not yet been carried out. The kinematical corrections, yielding a Hamiltonian with the correct transformation properties up to order (v/c) 2 , produce results that are small and repulsive: approximately 0.3 MeV of repulsion in the triton and almost 2 MeV in the α particle [4] (see, however, [5]). Nonlocal NN potentials, such as the CD Bonn, can improve the result for the binding energy of the triton by some 0.4 MeV, but not more [6].…”