Abstract
Perturbation theory combined with the variational principle in the form of the perturbational-variational Rayleigh-Ritz (PV RR) matrix formalism is a powerful method for applying large-order perturbation theory to the Stark effect for hydrogenic ions. A paradigm is derived and implemented which permits the precise construction of a variational ansatz from which the Stark Rayleigh-Schrodinger (RS) eigenvalue (polarizability) and eigenfunction perturbation series for the ground state are generated via PV RR to any prespecified order. We have also computed high-order RS series of the kinetic- and potential-energy components of the Stark eigenvalue series, and determined the Bender-Wu-type asymptotic formulae which govern the limiting behaviour of their large-order coefficients. PV RR is not restricted to one-electron systems.
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