The tensor force in nuclear saturation

Abstract

One-term separable potentials in the 3S-3D channel are constructed which fit the following low-energy nucleon-nucleon data: the triplet effective range and scattering length, deuteron binding energy and quadrupole moment. They also yield 3D1 phase shifts which have the correct sign. These potentials differ, however, in the amount of deuteron D-state probability, PD, which they predict, where PD ranges from 1 % to 9 %. Binding energy calculations of infinite nuclear matter and 4He are performed in order to test the effect of the tensor force on nuclear saturation properties. It is found that the larger the D-state probability, the smaller the energy per particle and saturation density. Detailed comparisons with local potentials in nuclear matter are also presented. In nuclear matter no single-particle potential in intermediate states is used; in 4He, U(r) = case12Mω2r2 − fω, where f is varied such that the absolute value of the diagram with a single potential insertion in a particle line is minimized. It is found in 4He that f= 0.75 and that this result is almost independent of both the potential employed and of ω. Furthermore, for 0 ≦ f ≦ 1.5, the total energy is independent of f.