Isolated-core excitations in strong electric fields. I. Theory F. Robicheaux Department of Physics, Auburn University, Auburn, Alabama 36849 Received 14 January 2000; published 17 August 2000 A basic theory is presented for the photoexcitation of a core state of a Rydberg atom in any type of static field; in this situation, the core state is excited by the photon while the Rydberg electron is essentially a spectator. This simple picture is made interesting through the interaction of the Rydberg electron with the core which can cause a change in the Rydberg electron’s state and can cause the Rydberg electron to autoionize. The method is computationally efficient and has been used for alkaline-earth atoms in a static electric field. An approximation to the formalism is presented that illustrates a mechanism controlling the isolated core excita- tion in a static electric field; this approximation may serve as a paradigm for extending the interpretation of isolated core spectra to other types of fields. PACS numbers: 32.60.+i, 32.80.Dz, 32.80.Rm I. INTRODUCTION There are many tools that have been used to probe corre- lation in many electron atoms. The study of photoabsorption spectra is especially useful since the high resolution of the laser allows precise determination of the energies and widths of the states while the strength of transitions contains infor- mation about the composition of the state. Most photoab- sorption studies use compact initial states which thus probe final-state correlation as manifested near the nucleus. By contrast, the technique known as isolated core excitation uti- lizes a highly excited initial state 1–8. With this technique, the atom is initially prepared such that one electron is excited to a Rydberg state with the remaining electrons left in the ground state of the positive ion. A second laser is then scanned over optically allowed transitions of the positive ion. A large ionization signal is observed at the frequencies of optically allowed transitions in the core; ionization is also observed at other frequencies because both the core and the Rydberg electron can simultaneously make transitions due to the electron-core interaction. The isolated core excitation directly probes the interaction of the Rydberg electron with the core electrons. In the exci- tation process, the core changes character which thus changes the potential for the Rydberg electron. The strength of the excitation to the final state depends almost solely on the projection of the initial Rydberg wave function onto the final Rydberg wave function. If the potential for the Rydberg electron is unchanged, then only one final state is excited. As the change in the potential increases, then the character of the final states change and increasingly many final states can be excited. The electron-core interaction is also manifested through the autoionization widths of the final states. Often, the resonance widths can be measured quite simply using isolated core excitations because there is very little direct excitation to the open channels. Thus, there is little interfer- ence between the direct ionization path and the indirect ion- ization path through the resonance states; the photoabsorp- tion cross section near a resonance is often a simple Lorentzian. In the past, most isolated core experiments and all isolated core calculations were for atoms unperturbed by static fields. Two previous studies presented experimental results for iso- lated core excitations by a cw laser for Mg in a static electric field 6 and by a pulsed laser for Mg in a static electric field 7. It is important to extend the study of isolated core exci- tations to atoms in strong, static fields. Photoionization by isolated core excitations is the time reverse of dielectronic recombination DR. In DR, an electron scatters from an ion, excites the ion so that it is captured into a doubly excited resonance state, and is stabilized when the core electrons emit a photon. It is known that static electric fields for ex- ample, the microfields that exist in plasmas can affect the recombination rate due to the l mixing of the autoionizing Rydberg states 9,10. Early measurements 11 and calcula- tions 12 showed the effect of electric fields on a Rydberg series. However, it has not yet been possible to perform de- tailed comparisons between experimental and calculated re- combination cross sections for individual resonances in a static electric field; this is because the resolution in electron scattering experiments is not high enough to resolve the Ry- dberg states that are most strongly affected. The isolated core excitations can be studied with high resolution since the limi- tation is from the resolution of a laser. Thus, detailed com- parison can be performed at the individual resonance level. Finally, it is also worth studying isolated core excitations in static electric fields as an interesting example of channel interactions and correlations between different degrees of freedom. The Hamiltonian for the nonrelativistic treatment of a hydrogen atom in a static electric field separates in para- bolic coordinates. However, the Hamiltonian does not sepa- rate for any other atom in a static electric field. For a Ryd- berg state with an excited ion core, the electron-electron interactions can cause the Rydberg electron to scatter be- tween different channels in parabolic coordinates while keeping its total energy fixed; also, this interaction can cause an exchange of energy between the Rydberg electron and the ion which may lead to the ejection of an electron from the atom. The competition and interplay between these two types of correlation can give interesting features in the spectra. In the isolated core excitation, the initial state is already a Ry- dberg state and can be chosen to be a state that is essentially an uncoupled state in parabolic coordinates or a state that is essentially an angular momentum eigenstate; this leads to a PHYSICAL REVIEW A, VOLUME 62, 033406 1050-2947/2000/623/0334067/$15.00 ©2000 The American Physical Society 62 033406-1