Abstract
The generalized separable expansion method is used to calculate the fully off-energy-shell $t$ matrices from the $^{1}S_{0}$ and $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ 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.NUCLEAR REACTIONS Nucleon-nucleon interactions, new separable expansion method for the $^{1}S_{0}$, $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ states via the Reid soft-core potentials.
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