Double Photoionization Cross Sections Research Articles

Double photoionization of atomic oxygen: Feshbach resonances in the two-electron continuum

We describe a joint experimental and theoretical investigation on oxygen double photoionization—the emission of two electrons from atomic oxygen following single photon absorption. High-resolution experimental measurements were performed at the Advanced Light Source, revealing sharp resonance structure superimposed on the more familiar Wannier-like, nearly-linear background. These resonance features are attributed to ionization-plus-excitation Feshbach resonances embedded in the double ionization continuum, doubly-excited states that lie above the double-ionization threshold. Such features are absent in the double photoionization cross section of He, or other quasi-two-electron systems, for which the doubly-ionized atomic core remains inert. For a corresponding theoretical analysis, the R-matrix with pseudostates (RMPS) method was invoked by calculating final-state, two-electron resonances-plus-continua wavefunctions and corresponding single-photon absorption cross sections. Overall agreement is found in the direct, background double photoionization cross section. However, the RMPS method, using a small basis due to practical computational limitations, was unable to reproduce quantitatively the smooth background or the sharper resonance features observed in the measurements, showing instead large-scale oscillations about the experimental background, and characteristic pseudoresonance jitter, associated with an insufficient convergence of the pseudostate representation to the true two-electron infinite series of Feshbach resonances embedded in the two-electron continuum. The prominent resonance structure observed highlights the need to consider multiple excitation processes in atoms more complex than He or quasi-two-electron systems.

K-shell Photoionization of the N+, NH+ and ions

SynopsisSingle and double photoionization cross-sections in the photon region straddling the nitrogen K-edge and up to photon energies of ∼450 eV, for the atomic N+ and molecular NH+ and species were measured at the SOLEIL radiation facility in Orsay, France. The measurements are compared with theoretical estimates.

Double photoionization of the Be isoelectronic sequence

We investigate the double photoionization (DPI) process along the Be isoelectronic sequence (Be−Ne6+) by solving the time-dependent Schrödinger equation with a spectral method of configuration interaction type. The results that we obtain of the DPI cross sections are in a good agreement with other reported data. We also present the first results of double-to-single photoionization cross sections ratios for Be-like ions in support of possible photofragmentation experiments with x-ray free electron lasers. Finally, we probe the mutual interaction of the valence electrons at different photon energies and examine the subsequent redistribution of the excess photon energy among them.

Single and double K-shell resonant photoionization and Auger decay of 1s → 2p excited states of O+–O4+

In this work, single and double photoionization cross sections in the vicinity of 1s → 2p resonances are investigated theoretically for quantum states belonging to the ground and first excited configurations of O+ –O4+ . R-matrix method has been employed to obtain the single ionization cross section, whereas the double ionization cross sections are obtained by the branching ratios of the direct double Auger decay to the total Auger decay. By analyzing possible double ionization pathways, we conclude that the double photoionization originates predominately from the direct double Auger decay of the K-shell resonant states. Our theoretical work diagnosed the population fraction of the quantum state prepared in a recent experiment and successfully interpreted the experimental observations on both single and double photoionization cross sections.

Valence-electron correlation in the double K -shell photoionization of atomic beryllium

We extended the multiconfiguration Hartree-Fock (MCHF) + effective charge (EFC) method for double photoionization of atoms and investigated the effect of valence-electron correlation in the double $K$-shell photoionization of atomic beryllium. We used the MCHF method, which accounts for electron correlations, to calculate the initial-state wave function. The wave functions for the two continuum electrons in the final state are calculated in the angle-dependent EFC approximation. The actual interaction potential between the two final-state continuum electrons is approximated by the EFC, which is determined variationally. We studied the effect of valence shell electron correlation on the $K$-shell double photoionization of beryllium for both equal and unequal sharing of excess photon energies at four fixed scattered electron directions in order to study the effects near the double $K$-shell ionization threshold. We found considerable effect of valence shell correlation in the triple-differential cross section for double photoionization of the beryllium atom at each of the excess photon energies.

Double photoionization of helium from the 1s2p excited state

Time-dependent close-coupling (TDCC) calculations are carried out for the double photoionization of Helium in the excited state. TDCC results are presented for the total and energy differential cross sections for the term. TDCC results are presented for the total and energy differential cross sections for the levels. Differences found between the level resolved double photoionization cross sections are due to varying degrees of continuum correlation found in the outgoing two electrons.

R-matrix with pseudostates study of single photon double ionization of endohedral Be and Mg atoms

We perform R-matrix with pseudostates calculations to investigate single photon double ionization of Be@C60 and Mg@C60. We contrast the present results to our previous studies of He@C60. We find the presence of the confinement resonances in the double photoionization cross sections of endohedral Be and Mg. Keeping the same C60 spherical shell potential in each case for these systems, we explore the change in magnitude and the energy dependence of the resonance features relative to the background cross sections.

Single and double photoionization of Li2

Time-dependent close-coupling methods are used to study the single and double photoionization of Li2. Formulations for both one-active and two-active electron methods make use of Hartree with local exchange potentials for the core electrons. Both the single and double photoionization cross sections for Li2 are found to be larger for linear polarization than for circular polarization, in sharp contrast to that found before for H2. In particular the double photoionization cross sections for Li2 are found to be approximately five times larger than for H2 and thus more easily observed by future experiments.

Auger decay and the direct double ionization probability of a 2p inner-shell hole in a singly charged Ar+ ion

Single and double Auger decay processes of Ar+ 2p −1 hole levels belonging to the configurations of 2p 53s 23p 5 and 2p 53s3p 6 are investigated in the framework of perturbation theory implemented by the distorted wave approximation. The single Auger decay channels and rates are determined and the predicted total rates can differ by more than an order of magnitude for the levels of 2p 53s 23p 5, yet they are very close for levels belonging to 2p 53s3p 6. By combining the double photoionization cross sections of the neutral species, our theoretical Auger spectra of the single Auger decay process nicely interpreted a recent experiment [S.M. Huttula et al., Phys. Rev. Lett. 110, 113002 (2013)]. A configuration averaged branching ratio of 6.5% and 7.3% are predicted for the direct double Auger decay to the total probability for 2p 53s 23p 5 and 2p 53s3p 6, respectively, which is smaller than that of Ar 2p −1 hole states.

Photoionization-Excitation and Double Photoionization of He@C60

The R-matrix with pseudostates (RMPS) and time-dependent close-coupling (TDCC) methods are used to calculate photoionization-excitation and double photoionization cross sections of He and He@C60.

Single and double photoionization of Ne8+

A direct solution of the time-dependent Dirac equation is used to calculate the single and double photoionization cross sections for Ne8 +. Expansion of a two-electron wavefunction in coupled spin–orbit eigenfunctions yields time-dependent close-coupled equations for quad-spinor radial wavefunctions. The repulsive interaction between electrons includes both Coulomb and Gaunt interactions. The fully-correlated ground state radial wavefunction is obtained by solving a time-independent inhomogeneous set of close-coupled equations instead of a relaxation of the time-dependent close-coupled equations in imaginary time. A Bessel function expansion is used to include both dipole and quadrupole effects in the radiation field interaction for both the ‘velocity’ and ‘length’ gauges. Propagation of the time-dependent close-coupled equations in real time yields single and double photoionization cross sections for Ne8 + at energies easily accessible at advanced free electron laser facilities.

Extension of the multiconfiguration Hartree-Fock method to allow double photoionization of atoms

Very recently we were successful in extending the multiconfiguration Hartree-Fock (MCHF) method for electron-impact ionization of atoms to allow double photoionization of atoms. We report, as a test case, the results of our calculation of the triple differential cross section (TDCS) for double photoionization of helium. We have calculated the initial state in the Hartree-Fock and the MCHF approximations and the final state in the Coulomb approximation and the screening potential approximation in order to compare with previously published works. We compare the present results calculated at 30-eV excess photon energy shared equally by two final-state continuum electrons, with other similar theoretical calculations. Finally, we also calculate the TDCS at 20-eV excess photon energy to compare with experimental observation.

Sensitivity of cross sections to the diffuseness of the confining potential in time-dependent close-coupling calculations of the double photoionization of He@C60

Calculations of the photoionization of endofullerenes often use a square-well potential to represent the confining fullerene. The sensitivity of the photoionization cross sections to the form of this model potential is explored here by the use of a diffuse potential. The cross sections for single photoionization with excitation and double photoionization of He@C${}_{60}$ are found to show damping of the confinement resonance structure as the degree of diffuseness is increased using a commonly adopted well depth of 8.22 eV. For a deeper well depth of 11.00 eV, the double-photoionization cross section is found to be insensitive to the diffuseness of the confining potential, as has also been reported recently for the single photoionization of H@C${}_{60}$ and Xe@C${}_{60}$ [Dolmatov, King, and Oglesby, J. Phys. B 45, 105102 (2012)].

Photoinduced K-shell hollow atoms

The mechanisms leading to the production of hollow K shell atoms via single photon impact were investigated for a variety of light elements with 12≤Z≤23. The double 1s vacancy states were produced by irradiating the samples with intense monoenergetic synchrotron radiation beams. The double-to-single K-shell photoionization probabilities PKK and the absolute double K-shell photoionization cross sections σ2+ were determined by measuring with a high-resolution bent von Hamos crystal spectrometer the Kαh hypersatellite X-ray emission of the samples. The measurements were performed over a wide range of incoming photon energies from threshold up to energies beyond the broad maximum of the double-to-single photoionization cross section ratios. The PKK and σ2+ were determined from the relative yields of the resolved Kαh hypersatellite lines. For Mg, Al and Si, the two-electron one-photon (TEOP) Kααh transitions which represent an alternative but much weaker decay channel for double 1s vacancy states could be also observed, using a highly efficient flat crystal wavelength dispersive spectrometer. This observation of single photon-induced TEOP transitions has shown that the I(Kαh)/I(Kααh) branching ratios are very poorly reproduced by most of existing theoretical models. Besides the relative yields of the hypersatellite and TEOP transitions, the energies and natural linewidths of the Kαh and Kααh X-ray lines were also determined. The energies are found to be in good agreement with different theoretical predictions, whereas the linewidths are significantly underestimated by the calculations, except if non-lifetime broadening effects such as the outer-shell ionization and the open valence configuration are taken into consideration.

Single photoionization with excitation and double photoionization of He@C36, He@C60 and He@C82

In anticipation of future experimental investigations of two-electron processes in endohedral atoms, the double photoionization and single photoionization with excitation of helium confined in the fullerenes C36, C60 and C82 have been studied using the time-dependent close-coupling method. It is found that both He@C60 and He@C82 display strong confinement resonances in the double photoionization cross section, whereas for He@C36, the confinement resonances are suppressed. For single photoionization leaving the He+ ion in its ground state, we found not only that the magnitudes of the cross sections for He@C36, He@C60 and He@C82 are similar to the case of helium but that confinement resonances are also apparent. For single photoionization with excitation to the n = 2 shell, the endofullerene cross sections showed a reduction as compared to bare He atoms, while for photoionization with excitation to the n = 3 shell, the cross sections for the endofullerenes are enhanced, with a particularly strong enhancement evident for He@C36.

DoubleK-shell photoionization and hypersatellite x-ray transitions of12⩽Z⩽23atoms

Single-photon double $K$-shell ionization of low-$Z$ neutral atoms in the range $12\ensuremath{\leqslant}Z\ensuremath{\leqslant}23$ is investigated. The experimental method was based on measurements of the high-resolution $K\ensuremath{\alpha}{}^{h}$ hypersatellite x-ray spectra following the radiative decay of the $K$-shell double-vacancy states excited by monochromatic synchrotron radiation. The photon energy dependence of the double $K$-shell ionization was measured over a wide range of photon energies from threshold up to and beyond the maximum of the double-to-single photoionization cross section ratios. From the high-resolution x-ray emission spectra the energies and linewidths of the hypersatellite transitions, as well as the $K{\ensuremath{\alpha}}_{1}^{h}$:$K{\ensuremath{\alpha}}_{2}^{h}$ intensity ratios, were determined. The relative importance of the initial-state and final-state electron-electron interactions to the $K$-shell double photoionization is addressed. Physical mechanisms and scaling laws of the $K$-shell double photoionization are examined. A semiempirical universal scaling of the double-photoionization cross sections with the effective nuclear charge for neutral atoms in the range $2\ensuremath{\leqslant}Z\ensuremath{\leqslant}47$ is established.

Double photoionization of atoms and ions confined in charged fullerenes

The double photoionization of a helium atom and a singly charged lithium positive ion enclosed in charged Cq60 fullerenes is studied using the time-dependent close-coupling method. Continuum raising and lowering effects are seen in the shift of the double-ionization threshold of the confined atom or ion. Confinement resonances in the double-photoionization cross section, previously observed for helium confined inside a neutral fullerene, persist for helium confined in both positively and negatively charged fullerenes and are found to be independent of the charge on the fullerene. The double photoionization of a confined singly positively charged lithium ion is found to exhibit similar behaviour to a confined neutral atom, with confinement resonances present in the double-photoionization cross section for confinement in neutral, positively and negatively charged fullerenes. In addition, the confinement resonances are shown to be sensitive to the width of the fullerene with the resonances having a smaller amplitude for larger fullerene widths.

Photoionization of highly charged atomic ions

Photoionization processes in highly charged atomic ions are studied by direct solution of the time-dependent Dirac equation. Expansion of a one-electron wave function in spin-orbit eigenfunctions yields close-coupled equations for bi-spinor radial wave functions. Expansion of a two-electron wave function in coupled spin-orbit eigenfunctions yields close-coupled equations for quad-spinor radial wave functions. Single photoionization cross sections using the close-coupled bi-spinor equations are calculated for Ne${}^{9+}$ and ${\mathrm{U}}^{91+}$. Single- and double-photoionization cross sections using the close-coupled quad-spinor equations are calculated for Ne${}^{8+}$ and ${\mathrm{U}}^{90+}$. All single photoionization cross sections are found to be in good agreement with fully relativistic perturbation theory results.

Time-dependent close-coupling calculations of the double photoionization of He@C60

The double photoionization of a He atom enclosed in a ${\mathrm{C}}_{60}$ molecule, He@C${}_{60}$ was investigated using the time-dependent close-coupling method with the ${\mathrm{C}}_{60}$ molecule represented by a spherical shell potential and the He atom treated nonperturbatively. Comparisons are made with the double photoionization of a bare He atom. The ratio of the total double photoionization cross section of He@C${}_{60}$ to that of a bare He atom is found to exhibit oscillations due to reflection of a slow electron. This is confirmed by calculations of the single energy differential cross section that peaks at unequal energy sharing when one of the ejected electrons has an energy comparable to the ${\mathrm{C}}_{60}$ well depth. Triple differential cross sections are found to be shifted in magnitude, but unchanged in shape from the bare He atom.

Single-photon double K-shell ionization of low-Z atoms

The photon energy dependence of the double K-shell ionization of light atoms is reported. Experimental double-to-single photoionization cross section ratios for Mg, Al, Si and Ca were obtained from measurements of high-resolution x-ray emission spectra. The double photoionization (DPI) cross-sections for K-shell hollow atom production are compared to convergent close-coupling calculations (CCC) for neutral atoms and He-like ions. The relative importance of the initial-state and final-state electron-electron interactions to the K-shell DPI in many-electron atoms and two-electron ions is addressed. Physical mechanisms and scaling laws of the K-shell double photoionization are examined. A semiempirical universal scaling of the DPI cross sections with the effective nuclear charge for neutral atoms 2≤Z≤47 is established.