The neutron-deuteron $\mathrm{}\left(\mathrm{nd}\right)\mathrm{}$ doublet ${(}^2{a}_{\mathrm{nd}})$ and quartet ${(}^4{a}_{\mathrm{nd}})$ scattering lengths were calculated based on the nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ interactions CD Bonn 2000, AV18, Nijm I, II, and 93 alone and in selected combinations with the Tucson-Melbourne (TM), a modified version thereof, TM99, and the Urbana IX three-nucleon $\mathrm{}\left(3N\right)\mathrm{}$ forces. For each $\mathrm{NN}$ and $3N$ force combination the ${}^3\mathrm{H}$ binding energy was also calculated. In case of TM99 and Urbana IX the 3NF parameters were adjusted to the ${}^3\mathrm{H}$ binding energy. In no case (using $\mathrm{np}-\mathrm{nn}$ forces) the experimental value of ${}^2{a}_{\mathrm{nd}}$ was reached. We also studied the effect of the electromagnetic interactions in the form introduced in AV18. Switching them off for the various nuclear force models leads to shifts of up to $+0.04\mathrm{}\mathrm{fm}$ for ${}^2{a}_{\mathrm{nd}},$ which is significant for present day standards. The electromagnetic effects also have a noticeable effect on ${}^4{a}_{\mathrm{nd}},$ which is extremely stable under the exchange of the nuclear forces otherwise. Only if the electromagnetic interactions are included, the current nuclear forces describe the experimental value. As a consequence of the failure to reproduce ${}^2{a}_{\mathrm{nd}}$ also the newly measured coherent $\mathrm{nd}$ scattering length ${(b}_{\mathrm{nd}})$ cannot be reproduced. The current nuclear force models predict ${}^3\mathrm{H}$ binding energies and the ${}^2{a}_{\mathrm{nd}}$ values around an averaged straight line (Phillips line), but this correlation is broken visibly. This allows us to use ${}^2{a}_{\mathrm{nd}}$ and the ${}^3\mathrm{H}$ binding energy as independent low-energy observables.

• Received 12 May 2003

DOI:https://doi.org/10.1103/PhysRevC.68.034002