Separable representation of the two-body Reid soft core T operator in terms of positive energy Weinberg states.

Abstract

A separable approximation ${T}^{(S)}$ to the two-body T matrix of the form 〈${\mathit{kT}}^{(\mathrm{S})}$(E)k'〉=〈kVk'〉+${\mathrm{\ensuremath{\Sigma}}}_{\mathit{s}=1}^{\mathrm{S}}$ 〈kV${\mathrm{\ensuremath{\Gamma}}}_{\mathit{s}}$(E)〉(1-${\ensuremath{\gamma}}_{\mathit{s}}$${)}^{\mathrm{\ensuremath{-}}1}$ 〈${\mathrm{\ensuremath{\Gamma}}}_{\mathit{s}}$(E)Vk'〉 is examined, where V is the Reid soft core potential, ${\ensuremath{\Gamma}}_{s}$ are the Weinberg eigenstates of the operator ${G}_{0}$(E)V for positive energy E, and ${\ensuremath{\gamma}}_{s}$(E) are the corresponding discrete complex eigenvalues. General projection techniques which improve the convergence of the sum above are considered. For the triplet state a nonlocal potential U is defined which in the l=0 channel represents the effect of the tensor coupling to the l=2 channel. It is found that the presence of U in the triplet state is responsible for the increased number of terms needed in the separable representation of T, as compared to the representation in the singlet state, where U is absent. The effect of U is largest for momenta less than 1 or 2 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. .AE