Further investigations of off-shell effects in the triton

Details Further investigations of off-shell effects in the triton Further investigations of off-shell effects in the triton

Jul 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972nupha.189...83f&link_type=abstract

Nuclear Physics A, Volume 189, Issue 1, p. 83-112.

Physics

Nuclear Physics

8

Scientific paper

We investigate the off-shell variation of the binding energy of the model triton ET for exactly phase-equivalent separable potentials of rank two. A physical explanation for the large off-shell effects previously found in ET 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 EB. With improved accuracy we can now show that ET(γ, β) reaches a lower limit of about 8.2 MeV if γ/β2 >> 1 or EB >> ED, 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 ET is mainly determined by the near-on-shell T-matrix for short-range potentials. It is also shown that for all potentials with EB significantly different from ED the UPA is a good approximation and the deuteron wave function ΨD does not differ greatly. We also provide evidence that if ΨD is given in addition to δ(k) and Ed then the T-matrix is nearly completely determined even if EB~ ED. For those limiting potentials (EB = ED) which produce large values of ET up to 16.2 MeV, the UPA is shown to fail completely, due to a mismatch between δ(k) and ΨD. This explains the large values of ET 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 ET (if EB≠ED) and the zero-energy wound integral I0 in analogy with the nuclear-matter results of Haftel and Tabakin.

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