The two-nucleon density distributions in states with isospin T = 0, spin S=1 and projection M S =0 and ±1 are studied in 2 H, 3,4 He, 6,7 Li and 16 O. The equidensity surfaces for M S =0 distributions are found to be toroidal in shape, while those of M S =±1 have dumbbell shapes at large density. The dumbbell shapes are generated by rotating tori. The toroidal shapes indicate that the tensor correlations have near maximal strength at r < 2 fm in all these nuclei. They provide new insights and simple explanations of the structure and electromagnetic form factors of the deuteron, the quasi-deuteron model, and the dp, dd and αd L=2 (D-wave) components in 3 He, 4 He and 6 Li. The toroidal distribution has a maximum-density diameter of ∼1 fm and a halfmaximum density thickness of ∼0.9 fm. Many realistic models of nuclear forces predict these values, which are supported by the observed electromagnetic form factors of the deuteron, and also predicted by classical Skyrme effective Lagrangians, related to QCD in the limit of infinite colors. Due to the rather small size of this structure, it could have a revealing relation to certain aspects of QCD. Experiments to probe this structure and its effects in nuclei are suggested. Pair distribution functions in other T, S channels are also discussed; those in T, S = 1, 1 have anisotropies expected from one-pion exchange interactions. The tensor correlations in T, S = 0, 1 states are found to deplete the number of T, S = 1, 0 pairs in nuclei and cause a reduction in nuclear binding energies via many-body effects.

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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.

The off-shell aspects of the one-pion-exchange potential (OPEP) are discussed. Relativistic Hamiltonians containing relativistic kinetic energy, relativistic OPEP with various off-shell behaviors and Argonne v 18 short-range parameterization are used to study the deuteron properties. The OPEP off-shell behaviors depend on whether a pseudovector or pseudoscalar pion-nucleon coupling is used and are characterized by a parameter µ. We study potentials having µ=−1, 0 and +1 and we find that they are nearly unitarily equivalent.We also find that a nonrelativistic Hamiltonian containing local potentials and nonrelativistic kinetic energy provides a good approximation to a Hamiltonian containing a relativistic OPEP based on pseudovector pion-nucleon coupling and relativistic kinetic energy.