The effect of three-body nucleon-nucleon interaction on the ground state binding energy of the light nuclei

TL;DR

This study evaluates how three-body nucleon interactions influence the ground state energies and properties of light nuclei, using variational methods and different nuclear potentials, and compares results with experimental data.

Contribution

It introduces a detailed calculation of three-body effects on light nuclei using LOCV and UIX potentials, providing new insights into their small but significant contributions.

Findings

Three-body interactions slightly increase binding energies.

Results align reasonably with experimental data.

Three-body cluster energy contributions are small.

Abstract

We calculate the ground state binding energies of the light nuclei such as 4He, 6Li, 12C and 14N by considering the effect of three-body nucleon-nucleon interaction. We use the effective twobody potential obtained from the lowest order constrained variational (LOCV) calculations of the nuclear matter for the Reid68, AV14, UV14, and AV18 nuclear potentials in different channels. To calculate the ground state binding energy, we implement the local density approximation by using the harmonic oscillator wave functions while the effect of three-body interaction is considered by employing the UIX potential. We compare the obtained two-body ground state binding energy with the energy related to the three-body effect. We also compare the obtained values with the experimental data and also work of others, and show that the results are relatively acceptable. We compute the root mean-square radius Rrms of the above nuclei for the Reid68, AV14, UV14, and AV18 potentials and compare the results with the experiment. We also obtain the contribution of different channels by matching to the experimental values of the quadrupole moments and magnetic dipole moments. Furthermore, we calculate the three-body cluster energy of the above nuclei and compare the results with that of nuclear matter. According to the obtained results, we see that the three-body cluster energy contribution is small. For example, for 4He nuclide, this value is 0.079 MeV with the Reid68 potential.