Linear relation between the scattering length and the size of a loosely bound two-body system: One-dimensional model analysis

Relativistic and nonrelativistic models in one dimension which simulate the deuteron and the /sup 3/S/sub 1/ nucleon-nucleon (NN) scattering are constructed and the relation between the scattering length a/sub t/ and the root-mean-square radius r/sub m/ of the simulated deuteron is examined for a variety of interactions. The linear relation between a/sub t/ and r/sub m/, which was found by Klarsfeld et al. for realistic NN potentials, holds for a wide class of potentials, relativistic as well as nonrelativistic. Within the limitation of our one-dimensional models, this suggests that the discrepancy between theory and experiment which was pointed out by Klarsfeld et al. regarding a/sub t/ and r/sub m/ cannot be resolved by relativistic effects.