Further investigations of off-shell effects in the triton

Abstract

We investigate the off-shell variation of the binding energy of the model triton E T for exactly phase-equivalent separable potentials of rank two. A physical explanation for the large off-shell effects previously found in E T is given which also explains the behaviour of these potentials in nuclear matter as reported by Srivastava et al. The arbitrary attractive form factor g( k) is with one exception chosen to be equal to a Yamaguchi form factor with strength and range parameters γ and β, and binding energy E B. With improved accuracy we can now show that E T( γ, β) reaches a lower limit of about 8.2 MeV if γ β 2 ⪢ 1 or E B ⪢ E D , the deuteron binding energy. This lower limit is shown to be independent of γ and only weakly dependent on β. The dependence on β is shown to be due to the far-off-shell behaviour of the T-matrix. In general we make it plausible that E T is mainly determined by the near-on-shell T-matrix for short-range potentials. It is also shown that for all potentials with E B significantly different from E D the UPA is a good approximation and the deuteron wave function Ψ D does not differ greatly. We also provide evidence that if Ψ D is given in addition to δ( k) and E d then the T-matrix is nearly completely determined even if E B≈ E D. For those limiting potentials ( E B = E D) which produce large values of E T up to 16.2 MeV, the UPA is shown to fail completely, due to a mismatch between δ( k) and Ψ D. This explains the large values of E T in those cases. All the limiting potentials are shown to be long-range potentials. It is also found that an approximately linear relation exists between E T (if E B≠ E D) and the zero-energy wound integral I 0 in analogy with the nuclear-matter results of Haftel and Tabakin.