On the correlation between the triton binding energy and the neutron-deuteron doublet scattering length

Abstract

A detailed explanation of the well-known Phillips line is presented. This line, which represents the correlation between calculated values of the triton binding energy and then-d doublet scattering length, is shown to be due to the fact that the binding energies of both the triton and the deuteron, as well as the energy eigenvalue of the two-nucleon singlet virtual state, are all small on the energy scale of nuclear forces. The equivalent statement is that the Phillips line is due to the loose spatial structure of these few-nucleon systems. These conclusions are obtained on the basis of (i) qualitative analysis of the problem. (ii) calculation of the above correlation in both zero and linear approximations in the range of nuclear forces, and (iii) comparison of the results of the calculation with the Phillips line.