Analytic Continuation of Scattering Data to the Region of Negative Energies for Systems That Have One and Two Bound States

An exactly solvable potential model is used to study the possibility of deducing information about the features of bound states for the system under consideration (binding energies and asymptotic normalization coefficients) on the basis of data on continuum states. The present analysis is based on an analytic approximation and on the subsequent continuation of a partial-wave scattering function from the region of positive energies to the region of negative energies. Cases where the system has one or two bound states are studied. The alpha + d and alpha + C-12 systems are taken as physical examples. In the case of one bound state, the scattering function is a smooth function of energy, and the procedure of its analytic continuation for different polynomial approximations leads to close results, which are nearly coincident with exact values. In the case of two bound states, the scattering function has two poles-one in the region of positive energies and the other in the region of negative energies between the energies corresponding to the two bound states in question. Pade approximants are used to reproduce these poles. The inclusion of these poles proves to be necessary for correctly describing the properties of the bound states.