Variation in Trinucleon Bound-State Properties with Phase-Equivalent Nucleon-Nucleon Interactions

Abstract

We use the Faddeev formalism to investigate the variation of the trinucleon binding energy and electromagnetic form factors with phase-equivalent transformations of the Reid softcore potential. The transformed nucleon-nucleon interactions used in our calculations are the same as, or slight variations of, those considered by Haftel and Tabakin in studies of nuclear matter. The corresponding transformed two-nucleon wave functions are essentially unchanged for nucleon separations greater than 1 fm. The variation of the trinucleon binding energy follows the same trend as (but is generally much smaller than) the corresponding variation of $\frac{{E}_{B}}{A}$ for nuclear matter. The largest increase in ${E}_{B}$ (trinucleon) is 0.19 MeV, which gives ${E}_{B}(\mathrm{total})\ensuremath{\approx}6.9$ MeV. The position of the minimum of the calculated $|{F}_{\mathrm{ch}}^{^{3}\mathrm{He}}({Q}^{2})|$ (experimental value: ${Q}^{2}\ensuremath{\approx}{11.8}^{\ensuremath{-}2}$) varies between ${Q}^{2}=14.4 \mathrm{and} 18$ ${\mathrm{fm}}^{\ensuremath{-}2}$.