Description of the low-energy doublet neutron-deuteron scattering in terms of parameters characterizing bound and virtual triton states

Low-energy doublet neutron-deuteron scattering is described in terms of the energies of the bound and virtual triton states and the nuclear vertex constants for these states. For the first time, the van Oers-Sea-grave formula is derived from the Bargmann representation of the S matrix for a system having two states. The presence of a pole in this formula is shown to be a direct corollary of the existence of a low-energy virtual triton state. Simple explicit expressions for the nd scattering length and for the pole of the function kcot delta are obtained in terms of the parameters of the bound and virtual triton states. The low-energy parameters of nd scattering are calculated numerically, whereby it is shown that these parameters are highly sensitive to variations in the asymptotic normalization constant: C-v(2) for the virtual state. The C-v(2) value fitted in our model to the experimental result for the nd scattering length is 0.0592. (C) 2000 MAIK "Nauka/Interperiodica".