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

The shift in binding energy that results from allowing one explicit Δ in the triton is studied using the Hannover one-Δ force model. The one-Δ analysis extends through J≤4, subject only to L(NΔ)≤4. Our main result is a 103-channel triton binding energy of 7.83 MeV, which corresponds to a net attractive one-Δ effect of 370 keV. The corresponding (repulsive) dispersive effect is found to be 600 keV, so that the full one-Δ three-body-force effect is 970 keV. Appropriately restricted J≤2 calculations substantiate the basic results of the original Hannover triton calculations, although differences are found. The original J≤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 ΔΔ studies. The Hannover one-Δ 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.