Triton binding energy and the deuteron wave function

Abstract

Recent investigations (l-a) with phase-equivalent spin-independent S-wave interactions indieatc that the t r i ton binding energy is mainly sensitive to changes in the deuteron wave function. The results of ]~IEDELDEY (1) show that even modifications of the two-body phase shifts above 20 MeV hardly influence the tri ton binding energy, once the deuteron wave function has been fixed. AFNAN and SERDUKE (4) have found a similar dependence with central forces in the tr iplet S state, having fixed the singlet S interaction. All these calculations neglect the tensor force which couples the 3S1 and 3D 1 part ial waves. In this le t ter we want to consider this dependence in the more realistic case when a tcnsor force is present and the deuteron properties are well reproduced. For this purpose we have constructed separable tensor potentials, having the same deuteron wave function as tha t of realistic tensor potentials, taken from the phaseequivalent set given by HAFTEL and TABAKIN (5). We shall compare the t r i ton bindingenergy results for these separable potentials with those already obtained for some potentials of the phase-equivalent set. HAFTEL and TABAKIN generate a set of phase-equivalent potentials by applying short-range unitary transformations to the Reid soft-core potential. The transformations are prcpresented by simple analytical forms. Therefore the construction of the separable potential which has the same bound-state wave function as a given member of the set is rather easy. This procedure in fact yields the unitary pole approximation (6) of each transformed potential. The resulting potentials are of the following form in the notation of TABAKIN (~):