Separable expansion fit to the Reid soft-core fully off-shelltmatrices:S01andS13−D13states

The generalized separable expansion method is used to calculate the fully off-energy-shell $t$ matrices from the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ Reid soft-core potentials. It is proved that the bound state is reproduced rigorously by the rank-one approximation. For positive energies, on-shell and half on- (off-) shell scattering amplitudes are reproduced exactly by the generalized separable expansion rank-one and/or, at least, rank-two approximations. The off-shell parts of the $t$ matrices are determined by $N$ fitting parameters which are chosen to minimize the Hilbert-Schmidt norm of the nonseparable term in the rank-$N$ approximation. We obtained a very good off-shell fit for rank-two and rank-three approximations.