Δ degrees of freedom in trinuclei. III. The Argonne Δ model

Abstract

The Argonne \ensuremath{\Delta} model is used to study the effect of one-\ensuremath{\Delta} and \ensuremath{\Delta}\ensuremath{\Delta} degrees of freedom on the triton binding energy (${\mathit{E}}_{\mathit{T}}$). Exploratory calculations decompose the J\ensuremath{\le}4 system of interest into restricted (JL2) calculations, with J\ensuremath{\le}2 and L(N\ensuremath{\Delta}), L(\ensuremath{\Delta}\ensuremath{\Delta})\ensuremath{\le}2, and a 130 keV attractive correction. A JL2 dispersive calculation yields ${\mathit{E}}_{\mathit{T}}$=6.50 MeV, while a full JL2 calculation gives 7.16 MeV, revealing an attractive \ensuremath{\Delta} three-body-force (3BF) contribution of 660 keV. Comparing to the nucleons-only value, ${\mathit{E}}_{\mathit{T}}$=7.58 MeV, the size of the repulsive \ensuremath{\Delta} dispersive effect is 1080 keV. The one-\ensuremath{\Delta} and \ensuremath{\Delta}\ensuremath{\Delta} 3BF contributions are found to be 440 and 220 keV, respectively, while the corresponding full J\ensuremath{\le}4 values are 450 and 290 keV, respectively. The net J\ensuremath{\le}4 result is ${\mathit{E}}_{\mathit{T}}$=7.29 MeV versus a nucleons-only value of 7.67 MeV: the attractive \ensuremath{\Delta} 3BF contribution is not quite sufficient to cancel the 1120 keV repulsive \ensuremath{\Delta} dispersive effect. The cancellation between dispersive and 3BF effects is similar to that found for the Hannover \ensuremath{\Delta} model, although the residual \ensuremath{\Delta} repulsive effect found for the Argonne model is non-negligible: \ensuremath{\Delta} effects are found not to resolve the triton binding energy defect. It is also evident from these results that \ensuremath{\Delta} dispersive effects are not adequately represented in nucleons-only models simply by force of fitting the NN data. Thus, the present results confirm the qualitative implications of our previous studies using the Hannover \ensuremath{\Delta} model, including the fact that \ensuremath{\Delta}\ensuremath{\Delta} effects are appreciable.