Double ionization of He and H⁻ by high-energy photons

We present theoretical studies on the double ionization and ionization- excitation of helium and H^- by high energy photon (≥ 1 keV). With an accurate Hylleraas-type initial state wavefunction and final state wavefunc- tions with and without correlation we investigate the dynamic motion of the two-continuum electrons in the field of nucleus. We analyze the solution of the Schrödinger equation for the double-continuum system and demonstrate that the 3C wavefunction describes the final state to leading order in Z/k₁ in the full configuration space and satisfies the Kato cusp conditions exactly at the three two-body collision points. A new technique for the analysis of the distortion factor D^(-) in the 3C wavefunction has been developed which can lead to an accurate evaluation of the transition probabilities. Our calculation shows that the double to single ratio and the satellite-to-1s ratio approaches the same asymptotic limit with and without final state correlation. However, at 1 keV the ratios with the 3C wavefunction are increased significantly while they are almost unchanged with the 2C solution. The double to single ratio of helium with the 3C wavefunction is 2.62% at 1 keV and approaches an asymptotic value of R_ph(∞) = 1.65%, which is in excellent agreement with the measurements. For H^- we have made the first reliable calculation at the high energies. The double to single ratio is 1.87% at 1 keV with the 3C wavefunction and approaches an asymptotic value of R_ph(∞) = 1.50%. We also point out that the interaction between the high energy photon and atom is localized in a region with a distance of E-1/2 around the nucleus instead of a point at the center. We introduce a shape function into the formulas suggested by Kabir and Salpeter and by Dalgarno and Stewart which can dramatically improve the evaluation of the absolute cross sections of the double and single ionization at non-relativistic high energies. Moreover, we extend the validity of the formulas down to about 2 keV by including final-state correlation.

The thesis is based in part on the following publications:

• Y. Qiu, J. Tang, J. Burgörfer, and J. Wang, one- and two-electron emission from H^- by high-energy photons, J. Phys. B 30, L689 (1997).

• Y. Qiu, J. Tang, J. Burgdörfer, and J. Wang, Double photoionization of helium from threshold to high energies, to be published.

• Y. Qiu, J. Müller, and J. Burgdörfer, Periodic orbit spectra of hydrogen and helium, Phys. Rev. 54, 1922 (1996).

• J. Burgdörfer, Y. Qiu, and J. Müller, Periodic Orbit Spectra of Simple Atoms, edited by H. Friedrich and B. Eckhardt, in Classical, semiclassical and quantum dynamics in atoms, (Springer-Verlag Berlin Heidelberg, 1997).

• J. Wang, J. H. McGuire, J. Burgdörfer, and Y. Qiu, Consistency test of double ionization of helium by photons and charged particles,, Phys. Rev. A 54, 613 (1996).

• J. Wang, J. H. McGuire, J. Burgdörfer, and Y. Qiu, Differential double ionization of He by Compton photons and charged particles at large energy transfers, Phys. Rev. Lett. 26, 1723 (1996).