Relation between the bound state radius and the scattering length: Relativistic effects

Relativistic effects on the relation between the root-mean-square radius rD of the bound state and the scattering length a are examined for models which simulate the triplet S state of the two-nucleon system. Two models are considered; one is based on the one-body Dirac equation and the other on the two-body Dirac equation. The relation is expressed as (rD/a)2=(c0+c1x1+c2x2+...)/8, where x==αr0; α is related to the binding energy and r0 is the effective range. This expansion is compared with the corresponding expansion of the nonrelativistic Schrödinger case. The first three terms are shape independent. The c0 (=1) and c1 (=0) are the same as those of the nonrelativistic case but a relativistic correction appears in c2.