Intermanifold similarities in partial photoionization cross sections of helium

Abstract

Using the eigenchannel R-matrix method we calculate partial photoionization cross sections from the ground state of the helium atom for incident photon energies up to the N = 9 manifold. The wide energy range covered by our calculations permits a thorough investigation of general patterns in the cross sections which were first discussed by Menzel and co-workers [Phys. Rev. A 54, 2080]. The existence of these patterns can easily be understood in terms of propensity rules for autoionization. As the photon energy is increased the regular patterns are locally interrupted by perturber states until they fade out indicating the progressive break-down of the propensity rules and the underlying approximate quantum numbers. We demonstrate that the destructive influence of isolated perturbers can be compensated with an energy-dependent quantum defect.

Partial cross sections of doubly excited helium below the ionization thresholdI7

“…Menzel et al reported on measurements of partial cross sections up to the ionization threshold I 5 employing two spherical-sector-plate electrostatic analyzers [9,10] and discussed the observed general patterns in n . Here, n describes the PCS for the channel leading to He + , with the single electron in a state with principal quantum number n. Very recently, Schneider et al [11] and van der Hart et al [12] confirmed in their calculations these regularities in n up to the ionization threshold I 9 . The similarities in the PCSs for the energy region with a small number of pertubers, also called "general patterns," can be well understood with the so-called propensity rules based on the molecular adiabatic approximation [11].…”

“…Here, n describes the PCS for the channel leading to He + , with the single electron in a state with principal quantum number n. Very recently, Schneider et al [11] and van der Hart et al [12] confirmed in their calculations these regularities in n up to the ionization threshold I 9 . The similarities in the PCSs for the energy region with a small number of pertubers, also called "general patterns," can be well understood with the so-called propensity rules based on the molecular adiabatic approximation [11]. As the photon energy increases, the structures in the PCS get more and more complicated due to interferences caused by an increasing number of pertubers, and the general patterns begin to dissolve.…”

“…In addition to this it is also necessary that the amplitudes of resonances in the PCS are considerably larger than those in the TCS. However, as observed in the theoretical cross sections up to ionization threshold I 9 [11], the amplitudes in the PCS decrease by the same amount with increasing N as the amplitudes in the TCS. As a consequence, we do not expect a general mirroring behavior in helium below higher-N ionization thresholds I N with 2 even much smaller than 0.01.…”

“…3 in Ref. [11]), no general mirroring behavior will be expected in the double-excitation region of helium. Mirroring behavior occurs only accidentally, e.g., if the PCS P mirrors T .…”

Nonresonant Cross-Section, Fano-Shape Parameter and Correlation Coefficient for the Photoionization of 2s2p (1P∘) in Heliumlike

“…Domke et al [9] resolved for the first time the third Rydberg series, 2pnd, below the n = 2 ionization threshold. Theoretically, various methods were developed to deal with doubly excited states of helium, including configurationinteraction (CI) methods [13][14][15], hyperspherical coordinate methods [16][17][18][19][20][21][22][23], close-coupling approximations [24][25][26], R-matrix methods [27][28][29][30][31][32], complex coordinate method [33][34][35][36], Feshbach projection formalism [37][38][39][40], and the diagonalization method [41][42][43][44][45][46][47]. A detailed review was recently performed by Tanner et al [48].…”