Δ degrees of freedom in trinuclei: I. The Hannover one-Δ model

Abstract

The shift in binding energy that results from allowing one explicit \ensuremath{\Delta} in the triton is studied using the Hannover one-\ensuremath{\Delta} force model. The one-\ensuremath{\Delta} analysis extends through J\ensuremath{\le}4, subject only to L(N\ensuremath{\Delta})\ensuremath{\le}4. Our main result is a 103-channel triton binding energy of 7.83 MeV, which corresponds to a net attractive one-\ensuremath{\Delta} effect of 370 keV. The corresponding (repulsive) dispersive effect is found to be 600 keV, so that the full one-\ensuremath{\Delta} three-body-force effect is 970 keV. Appropriately restricted J\ensuremath{\le}2 calculations substantiate the basic results of the original Hannover triton calculations, although differences are found. The original J\ensuremath{\le}2 figures are in good agreement with our full results and dissecting our results shows this to be largely due to cancellations among the various truncations employed in the original calculations. A numerical correction is obtained for each truncation and these are found to be relatively independent of each other. This forms a reliable basis for subsequent \ensuremath{\Delta}\ensuremath{\Delta} studies. The Hannover one-\ensuremath{\Delta} model is also critically examined for physical consistency and the $^{1}$${\mathit{S}}_{0}$ effective range is found to be about 0.1 fm too low, a defect which could be responsible for about half of the net 370-keV increase in triton binding. The approach, methods, and numerical checks that underlie our investigations are also detailed.