Nuclear Forces in Momentum Space with One-Boson-Exchange Model

Abstract

A one-boson-exchange potential (OBEP) with six kinds of bosbns (rr, rJ, p, w, 7J and lJ) is treated in momentum space to describe the nucleon-nucleon interaction below 400MeV. Integral equations containing OBEP with full nonstatic effects are solved numerically. All the experimental phase shifts for the states with L;:;;;1 are well reproduced by adjusting only four parameters of w-nucleon coupling constant g~/4rr, lJ-nucleon coupling constant g~/4rr, rJ-nucleon coupling constant gl1 2 /4rr and mass of rJ-meson m 11 • The contribution from 7Jcmeson exchange is shown to be small. S-state phase shifts are also reproduced if the contribution from higher momentum part is cut off. A list of all the matrix elements of the nonstatic OBEP is given. § 1. IntroductionAs experimental data on various polarization parameters have revealed, nonstatic effects of nuclear forces are important even at moderately low energies. These effect's have been investigated largely on the basis of potential models represented in coordinate space. However, any theory in coordinate space is more or less unsatisfactory in that nonstatic effects are taken into account only partially. The theory is particularly inconvenient if we intend to extend it into higher energy region. Theories in momentum space are expected to remove this difficulty. 2 l-5 l It has been made clear that one-boson-exchange model (OBE model) is valid at least qualitatively to explain the nuclear forces in the inner region surrounding the nucleon core. 6 l The success in the explanation of the strong L · S force found in this region may be regarded as a main result of the model. Furthermore, it has also been conjectured that the repulsive core which is characteristic of the nuclear forces in the innermost region could be interpreted by the exchange of a meson, especially an is·oscalar vector meson (J).The one-boson-exchange model in momentum space has been investigated by Gotzmann and Hochberg 7 l and especially by Wada. 6 l However, their work has studied only some parts of all possible states in the t~o-nucleon system. Especially, triplet-coupled states remain untouched in spite of their importance in an-

Nucleon-nucleon interaction: A typical/concise review

“…For many calculations associated with NN interaction, it is suitable to express Schrodinger equation as an integral equation in momentum-space; look, for instance, at [18,19] for some typical studies. The nonrelativistic scattering theory that leads to Lippmann-Schwinger (LS) equation and T-matrix are useful in this approach.…”