Femtometer Toroidal Structures in Nuclei

The two-nucleon density distributions in states with isospin $T=0$, spin $S$=1 and projection $M_S$=0 and $\pm$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 $M_S$=$\pm$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 $\alpha d$ $L$=2 ($D$-wave) components in $^3$He, $^4$He and $^6$Li. The toroidal distribution has a maximum-density diameter of $\sim$1 fm and a half-maximum density thickness of $\sim$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.