In this paper we develop a practical ‘‘hybrid’’ numerical representation of the nucleon-nucleon T matrix. Part of the expression contains nonseparable terms which are easily calculated, and the rest consists of a separable representation of small rank in terms of Weinberg states. The method rests on the observation that when a set of positive-energy Weinberg states is used to obtain a separable representation of the potential V then the residue ΔV, due to the basis-set truncation, has very special properties: (1) The contribution ΔT to the T matrix due to ΔV is identical to the undistorted T matrix for ΔV alone, ${\mathit{T}}_{\mathrm{\Delta }}$, i.e., the usual Moeller distortion factors in the two-potential formula are unity in this case. (2) A perturbative-iterative treatment of ${\mathit{T}}_{\mathrm{\Delta }}$ in powers of ΔV is found to be equivalent to the finite-rank representation of operators of the type T, T-V, T-V-${\mathit{VG}}_0$V, and so on. This equivalence has both practical and theoretical implications. On the one hand, it provides a reliable method for calculating the T matrix and for analyzing the corresponding accuracy properties. On the other hand, a connection is established between each order of the quasiparticle method and the different variational principles which underlie the finite-rank representation of operators such as T, T-V, T-V-${\mathit{VG}}_0$V, etc. Numerical examples are provided for two different nucleon-nucleon singlet potentials (Reid soft core and Malfliet-Tjon). In the Malfliet-Tjon case, for instance, two Weinberg states are found to be sufficient in order to give an accuracy of 0.1% for the calculation of T-V-${\mathit{VG}}_0$V, while for T-V and T the same two states give an accuracy of 1% and 10%, respectively, in an interval of 6 ${\mathrm{fm}}^{\mathrm{-}1}$ around the on-shell point.

• Received 6 September 1990

DOI:https://doi.org/10.1103/PhysRevC.44.60