Phaseshift in the case of scattering from a spherically symmetric potential: connection with valence state parameters

It is shown that the behaviour of the phaseshift describing the scattering of the electron with a certain value of the orbital quantum number l from a structureless potential of a finite action radius at small energies is determined, to high precision, by the energy εb and the mean radius rb of the highest bound state with the same l value in this potential. The exactness of this relation increases as the εb value decreases. In the case of long-range potentials, a part of the total phaseshift caused by the scattering from an inner part of the potential, localized within a sphere, is also determined by values of εb and rb characterizing the inner potential. A scheme for determining the parameters εb and rb by using experimental information on the phaseshift is proposed. (author)