Simple local potentials for elastic scattering of electrons by noble-gas atoms

Quantum defects at the critical charge

The quantum defect is an empirically introduced notion that has allowed convenient interpolations of spectral data along atomic isoelectronic sequences and their extrapolation with respect to the principal quantum number. Both yield valuable spectral information, the latter providing estimates of low-energy-electron elastic scattering phase shifts as well. We examine a recently proposed conjecture concerning the extrapolated value of the quantum defect along an isoelectronic sequence: If the binding energy of the outermost electron vanishes in the singly negative ion, then its asymptotic quantum defect is an integer whose value is equal to the number of occupied shells with the same orbital angular momentum. This behavior is associated with the fact, established by means of appropriate electronic structure calculations, that-asymptotically-the outermost orbital becomes an infinitely diffuse hydrogen-like orbital. In most cases explored the asymptotic behavior can be ascertained by analysis of spectral data along the appropriate isoelectronic sequence, but in some cases the approach to the asymptotic value takes place over a very narrow range of nuclear charge in the vicinity of that of the negative ion.

Deep l-independent potentials from supersymmetric inversion

Central potentials, independent of both the energy and the angular momentum l, are constructed from elastic phase shifts. The ambiguities of a fixed- l inversion are exploited to fit the phase shifts of other partial waves. The fitted quantities are the energy and normalization constant of forbidden bound states, and the small-distance behavior of the potential. The method is based on supersymmetric transformations of the radial Schrodinger equation. It is applied to the alpha+alpha collision in nuclear physics, and to the e(-)+Ne collision in atomic physics.