The Lambda n Scattering Length and the Lambda nn Resonance

The possibility of determining the Lambda n scattering length from the measurement of a resonance in the Lambda nn system is explored. A rank-one separable formalism of the Hamiltonian is utilized. The eigenvalues of the kernel of the relevant Faddeev equations are tracked in the complex energy plane in order to analytically continue the kernel onto the second Riemann energy sheet. Specifically, the largest eigenvalue is followed as the Lambda n s-wave spin-singlet and spin-triplet potentials are scaled. As the scale factor is increased, the pole in the Lambda nn continuum evolves from a subtheshold resonance to a physically observable resonance and, finally, to a bound state.