Analytic properties of pseudo-potentials

A new examination of the theory of pseudo-potentials, necessitated by the discovery that smoothness of the pseudo-wave function is not a relevant criterion for their effectiveness, provides an understanding of the analytic properties of pseudo-potentials in terms of their pseudo-core energies E_cprime. In particular, it is found for Hermitian pseudo-potentials that, if E_cprime greater, similar <c|H₀|c>, the Born series cannot have good convergence properties, but, for E_cprime = 0, the series has good asymptotic convergence. The new pseudo-potential, with E_cprime = 0, is the correct form to use at all energies, but differs substantially from other forms only at higher energies. Its effectiveness is demonstrated by a model calculation.