Tatsuro Sawada

Three-nucleon interactions and nuclear matter

Abstract We derive the three-nucleon potentials due to π, S (isoscalar-scalar-meson) and ω, which are exchanged between two nucleons via the third nucleon. The off-mass-shell πN amplitude needed for the calculation is constructed on the basis of the chiral invariance and the πN scattering data. Uncertainties caused by the uncertainties inherent in boson-vertices are considerably reduced by requiring that the three-nucleon potentials due to S and ω become the same as the one-S and one-ω exchange two-nucleon potentials, respectively, if the interactions of S and ω with the third nucleon are switched off. We calculate the binding energy per nucleon in nuclear matter using the three-nucleon potentials thus obtained with the two-nucleon OBEP of Ueda and Green (UGI), and find 0.4, 4.3 and −1. 3MeV at k F = 1.4 fm −1 for the net contributions from the three-nucleon potentials due to π, S and ω, respectively. The sum of the two- and three-nucleon potentials gives approximately correct binding energy at the normal density. However, its density dependence is such that it produces overbinding at higher density. A suggestion for removing this difficulty is made.

Three Nucleon Potential and Triton Binding Energy

The two-pion-exchange three-nucleon potential 7CJrF which involves the sand p 7lN-scattering with PCAC constraint is presented. The first order perturbation calculation of the 7r7rF contribution to the triton binding energy is made by use of the Faddeev wave function that is obtained in 18 angular-momentum-state bases with the Reid soft-core potential and the URG II OBEP. The resulting triton binding energy is 8.2 ~8.7 MeV, closely comparable with the experimental value, 8.482 MeV.

Three‐nucleon potential due to π, S and ω and nuclear matter

We derive the three‐nucleon potentials due to π, S (isoscalar‐scalar meson) and ω, which are exchanged between two nucleons via the third nucleon. We calculate the binding energy per nucleon in nuclear matter using the three‐nucleon potentials with the two‐nucleon OBEP of Ueda and Green (UGI), and find 0.4, and −1.3 MeV at kF=1.4 fm−1 for the net contributions from the three‐nucleon potentials due to τ, S and ω, respectively. The sum of the two‐ and three‐nucleon potentials gives approximately correct binding energy at the normal density. However, its density dependence is such that it produces overbinding at higher density. To remove the difficulty, we point out the possible importance of the Pauli principle effect in nuclear matter on the intermediate nucleons of an interacting two‐pion pair, which is a part of the two‐pion exchange potential.

NUCLEAR THREE-BODY FORCES ARISING FROM TRIPLE-BOSON COUPLINGS

Publisher Summary This chapter focuses on three-nucleon potentials (TNPs) because of triple-boson couplings and the 3–3 resonance. It discusses their effects on the properties of the nuclear matter. Three-nucleon (N) forces because of the two-Π exchange have been investigated by many people. They may be important in the long-range part, however, the inner part may be considerably influenced by other mechanisms because of heavy bosons. The one-boson exchange potentials (OBEP), incorporating Π, σ, ρ, and ω, have been very successful in describing the two-N interaction. From a similar point of view, this chapter presents six important diagrams for the three-N interaction. The chapter discusses qualitative features of the TNPs are described. The TNPs have longer ranges than the corresponding two-N potentials.