Covariant Dynamical Calculation of the Nucleon-NucleonSWaves

Abstract

We compute the binding energy of the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ $\mathrm{NN}$ states (known to be bound by 2.22 and - 0.07 MeV) using a covariant, singular-core, three-body model of the $\mathrm{NN}\pi$ system with ${{\mathcal{r}}_c}^{\mathrm{NN}}=0.7\mathrm{}$ fm, ${}_{}{}^3{}_{}{}^{}f_{\infty }^{}{}_{}{}^{}=1.8\mathrm{}$, and ${}_{}{}^1{}_{}{}^{}f_{\infty }^{}{}_{}{}^{}=0.3\mathrm{}$ as observed at high energy. For the $\pi N$ $P_{11}$ input we use ${{\mathcal{r}}_c}^{\pi N}=0.18\mathrm{}$ fm fitted (or $\frac{\hslash }{\mathrm{Mc}}=0.22\mathrm{}$ fm postulated) and find 3.26 (2.59) for ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and 1.41 (0.73) for ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$.