Mid-range nucleon-nucleon interaction in the linear sigma model

Abstract

The mid-range attraction between two nucleons is described by correlated two-pion exchange in the linear σ model. In contrast to previous work, chiral symmetry is incorporated dynamically, rather than by enforcing chiral constraints by hand. The input chiral σ mass is a free parameter, but the range and strength of the nucleon-nucleon (NN) attraction are insensitive to its value, which can be taken to be very large. A large σ mass reduces the strength of the nonlinear σ-meson interactions. The resulting strong NN attraction and small many-nucleon forces qualitatively reproduce the scalar dynamics in the Walecka model. To describe correlated two-pion exchange, the s-wave ππ phase shift is computed by summing the tree-level amplitude using the lowest-order Padé approximant. Unitarity and dispersion relations then determine the s-wave N N → ππ amplitude in the pseudophysical and physical regions. This amplitude contains important ππ rescattering effects and respects chiral symmetry. Unitarity and dispersion relations are then used again to calculate the spectral function for the scalar-isoscalar part of the NN interaction. The result can be approximated by a light scalar meson with a broadly distributed mass, which is consistent with the earlier results of Durso, Jackson and Verwest; moreover, the computed mass distribution is insensitive to the input σ mass, as long as it is large ( ⪆1 GeV ). Finally, nuclear matter properties are calculated in a Hartree approximation with the model scalar-isoscalar interaction and an elementary ω meson.