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Extra nodes and the phase shift of the scattering wave function for a nonlocal potential
, T.O. Krause, B. Mulligan
Published in
Volume: 15
Issue: 5
Pages: 1623 - 1625
This paper examines the presence of extra nodes in the scattering wave function for a nonlocal potential. Extra nodes are known to result from the nonlocality of an effective potential which incorporates the Pauli principle. It is shown that an extra node is directly linked to the existence of a continuum bound state or a spurious state in the scattering spectrum. Thus the presence of extra nodes occurs in conjunction with zeros of the Fredholm determinants D±(k) and D(k) associated with the integral equations for the physical and regular scattering solutions, respectively. The behavior of the nodes due to spurious states and continuum bound states is differentiated. Two possible definitions of the phase shift for a nonlocal potential are discussed in connection with this behavior. Both are consistent with the local limit. The definition of the phase shift as the negative of the phase of the Jost function L+(k) is suggested as preferable. This definition is shown to be in accord with the nodal behavior of the wave function and its interpretation in terms of an absolute value of the phase shift. Examples of potentials with a spurious state and of potentials with a continuum bound state are given. The nodal behavior of the wave function and the associated phase shift behavior are examined for each. NUCLEAR REACTIONS Scattering by a nonlocal potential, extra nodes, Fredholm determinants and their zeros, continuum bound states, spurious states, phase shifts. © 1977 The American Physical Society.
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