Nucleon-nucleon interaction as derived from the De Rújula, Georgi, Glashow phenomenological quark-quark potential

The nucleon-nucleon interaction, originating from the phenomenological quark-quark interaction: one gluon exchange with an ad hoc confining potential, is rigorously derived. The coupling constants of this potential and the quark masses—which determine the strengths of the $\mathrm{NN}$ potentials in the various channels—had been previously reliably determined from the masses of the $s$-wave baryons. Two distinguishing features of this study are the reliable nature of the coupling constants and quark masses used and the inclusion of the detailed radial dynamics of quarks. The main results are as follows: (i) exchange of colored quarks among other things leads to short-range strongly repulsive central $\mathrm{NN}$ potentials in the odd channels alone, i.e., it yields the saturation property of nuclear forces; (ii) the spin-orbit (tensor) potential between quarks goes over to the spin-orbit (tensor) potential between nucleons; (iii) both these spin-orbit and tensor potentials between nucleons are found to have the correct signatures but they are very weak; (iv) there is insufficient attraction in the $\mathrm{NN}$ potentials in the intermediate range, so that the colored quark-exchange mechanism is not adequate to keep the deuteron bound. The $\mathrm{NN}$ potentials derived from one gluon exchange with an ad hoc confining potential are compared finally with the corresponding phenomenological ones.