Abstract
It is demonstrated that 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 (LOPT) to the Stark effect for hydrogenic ions. Unlike other more specialized LOPT methods, which do not invoke the variational principle, application of the PV-RR formalism is not restricted to one-electron systems. A paradigm is derived and implemented which permits the precise construction of a Rayleigh-Ritz variational ansatz from which the real Stark ground-state Rayleigh-Schr\"odinger perturbation series for the eigenfunction, eigenvalue, and arbitrary expectation values can be generated via the PV-RR procedure to any prespecified order in the most economical way possible. A novel method of analysis, based on a combination of the Stark virial, Hellmann-Feynman, and remainder theorems, is developed for studying the physical origins of high-order atomic and molecular polarizabilities; the procedure is illustrated by application to the hydrogenic Stark effect. It is concluded on the basis of this work and of similar high-order PV-RR polarizability calculations for ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ that the prospects for extending the PV-RR formalism to accurate polarizability studies of more complex systems are promising.
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