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

Abstract

We calculate the ground state binding energies of the light nuclei such as ${}^{4}He$, ${}^{6}Li$, ${}^{12}C$ and ${}^{14}N$ by considering the effect of three-body nucleon-nucleon interaction. We use the effective two-body potential obtained from the lowest order constrained variational (LOCV) calculations of the nuclear matter for the $Reid68$, $A{V}_{14}$, $U{V}_{14}$, and $A{V}_{18}$ 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 $R_{rms}$ of the above nuclei for the $Reid68$, $A{V}_{14}$, $U{V}_{14}$, and $A{V}_{18}$ 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 ${}^{4}He$ nuclide, this value is 0.079 MeV with the $Reid68$ potential.