Femtometer toroidal structures in nuclei

Abstract

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.

Classical Skyrmions—static solutions and dynamics

“…The deuteron in the Skyrme model is a rotational state of the B = 2 toroidal Skyrmion, with spin J = 1 and isospin 0. Earlier work established that the axis of rotation is not the axis of symmetry, but an axis orthogonal to this [21,29]. The state with J = 1 and J 3 = 1 is easiest to consider.…”

New Lewis Structures through the application of the Hypertorus Electron Model

“…The deuteron presents three different shapes: a torus, an sphere inside another sphere and two separated spheres [3]. These are the three possible intersections between a three dimensional space, that cut a hypertorus in half [4,5,6].…”

“…These are the three possible intersections between a three dimensional space, that cut a hypertorus in half [4,5,6]. Of course, this definition is not reported in reference [3]. However, this is very important because these are the same shapes observed in every single molecule's laplacian of the electron density.…”

A Measurement of the neutron electric form factor at very large momentum transfer using polaried electrions scattering from a polarized helium-3 target

“…Therefore, the relative densities of protons and neutrons in the 3 He nucleus appear to be a function of initial momentum selected. The ratio of p/n for the choice of initial momenta used for E02-013 has been calculated based on the work of Schiavilla et al [109,110], and its effect on the final value of G n E has been determined.…”