Binding energy of3H andn−d doublet scattering length with charge-dependent forces

Abstract

The relation between the triton binding energy (Ez) and the doublet n--d scattering length Za is discussed. It is shown that the interpretation of the experimental data is ah open question even if one assumes charge dependent forces. The existing calculations of the triton ground state energy ET, and of the neutron-deuteron doublet scattering length 2a, show a remarkable feature: The calculated values of E T and 2a stay close to a straight line (the PmLLIPS line [1]) on a E T --2a plot [2]. Ifwe put on this plot the new (E T = --8.48 MeV, 2a = 0.15• fin [3]) and the old (E T = --8.48 MeV, 2a --~ 0.7• fm [4]) experimental points, it turns out that the PHILLIPS line goes through the old experimental point. If we accept the new experimental point, we are faced with the task of finding such features of the interaction between nucleons which, in a theoretical calculation, would lead us to the new experimental point, i.e. which would enable us to get off the PnILLIPS line.The linear relation between E T and 2a is best established in calculations based on separable two-body forces in which some parameters (e.g. the singlet effective range, the strength of the tensor force, the hard shell radius) have been varied (see, e.g.[5], [6]). Most of the existing calculations with local twobody forces also stay close to the PHILLIPS line.* This suggests that by playing with locality versus nonlocality of the two-body forces we should not expect to get off the PHILLIrS line. Furthermore, this enables us to apply nonlocal separable interactions in investigating the cffect of some special features of nuclear forces on EŸ and 2a.In this talk we shall discuss whether the charge-dependence of nuclear forces may help us in reproducing the new experimental point. Best established is the charge-dependence in the 1S 0 state in which the n --p potential is about 2 ~ more attractive than the n-n potential (see, e.g., [10]). This conclusion is based on a comparison between the values of the n--p singlet scattering length and effective range [11], * An exception ate some of the results obtained in [7] and [8]. However, some of the two-body potentials applied in [8] have also been applied in [9] with the resuhing values for E T and 2a which differ from those of [8]. This shows that the accuracy of the numerical results of some of the local potential calculations is not satisfactory.