Calculation Of Photoionization Cross Sections Research Articles

Photoionization of ammonia

We report the results of separated-channel, frozen core calculations of partial and total photoionization cross sections and asymmetry parameters for NH 3. The calculations were performed using the complex Kohn variational method. The results for the total and partial cross sections agree well with experiment as well as previous theoretical calculations. The asymmetry parameters are found to be a more sensitive test of the accuracy of the wave function.

Partial channel photoionization cross sections of polyenes

We present calculations of partial channel photoionization cross sections and photoelectron spectra of polyenes in the ultraviolet wavelength region. The dependences on molecular size, up to ${\mathrm{C}}_{16}$${\mathrm{H}}_{18}$, on photon energy, including He I and He II spectra, and on the particular ionization channel have been investigated using the independent-channel static exchange method. The channel dependence of the He I cross sections, which is quite strong for ethylene, diminishes, as the molecular length is increased, and becomes weak in the He II region. The energy dependence, which is strong in the He I region for all molecules and/or channels, is also insignificant for He II excitation, with the cross sections of all channels being close to each other. The cross sections are remarkably constant for the different \ensuremath{\pi} levels at any given photon energy. Spectral analyses for the first three smallest molecules---ethylene, butadiene, and hexatriene---show that the independent-channel approach is able to reproduce experimental data quite well.

Electron‐Ion Recombination of Fe v

Ionization balance in the low-ionization stages of iron is important in a variety of astrophysical plasmas. Accurate recombination rates are needed but are difficult to compute in a detailed quantum mechanical treatment. The main difficulty lies in the complexity of strong electron-electron correlation arising due to the open 3d shell. We present the total electron-ion recombination rate coefficients for the process, e+Fe VI → Fe V, obtained in an ab initio manner. Large-scale computations are carried out in the close coupling (CC) approximation using the R-matrix method employing a unified treatment that considers the infinite number of states of the recombined ion and incorporates both the radiative recombiantion (RR) and the dielectronic recombination (DR) processes in a self-consistent manner. It involves calculations of detailed photoionization cross sections, σPI, with autoionizing resonances of a large number of bound states with n≤nmax, such as 1054 bound states for the present case of Fe V. The number also equals the total number of state-specific recombination rates obtained for the ion. The high-n states are treated through the DR theory by Bell & Seaton. The same wavefunction expansion is employed in all photoionization/recombination calculations, thereby ensuring self-consistency. Rates are presented at a wide range of temperature for all practical applications. Present rates for total recombination differ considerably from currently used values obtained using simpler approximations. Application of the new recombination rate coefficients and photoionization cross sections for the ionization structure of iron in planetary nebulae show that under typical conditions the relative fractions of Fe V and Fe VI change by nearly a factor of 2.

Algebraic variational approach to atomic and molecular photoionization cross sections: Removing the energy dependence from the basis

We describe a variational method for calculating photoionization cross sections from a matrix element of the resolvent operator. Scattering boundary conditions are enforced by expanding the resolvent in a basis of square-integrable (${\mathrm{L}}^{2}$ ) and outgoing wave continuum basis functions. By employing several continuum basis functions, with overlaps defined by a suitable analytic continuation, we can, in a single calculation, express the cross section over a continuous range of energies without explicitly resolving the variational equations at each desired energy. The method is illustrated by calculation of the photoionization cross section of atomic Be in the autoionizing region between the ${1\mathrm{s}}^{2}$ 2s and ${1\mathrm{s}}^{2}$ 2p states of ${\mathrm{Be}}^{+}$ .

Differential photoionization cross section calculations for HI using the random-phase approximation with L2 basis functions

Differential photoionization cross section calculations for HI using the random-phase approximation with L2 basis functions

Calculations of photodissociation and photoionization cross sections by using a recursive expansion of Green's operator with absorbing boundary conditions

An iterative method for calculating total cross sections for molecular photodissociation and atomic photoionization is presented. It is based on the recursive expansion of Green's operator with absorbing boundary conditions, recently developed by Mandelshtam and Taylor. The method is tested by calculating cross sections for photodissociation of the molecule and another model problem, as well as for the photoionization of a hydrogen atom in the absence and presence of a strong magnetic field. In all applications the discrete variable representation is employed.

Differential photoionization cross section calculation of in the random phase approximation

A recently proposed K-matrix technique to solve the random phase approximation equations projected on basis sets of functions has been applied to a theoretical study of the outer-shell ionization processes in . Cross sections, photoelectron angular distribution parameters and branching ratios for the ionization of the valence , 1 e and inner-valence shells of ammonia have been calculated as a function of the photon energy in a range of more than 100 eV above threshold.

The near threshold photoionization cross section of atomic scandium

A photoionization cross-section calculation for atomic scandium, which has the LS coupled ground-state configuration ([Mg] 3p 63d4s 2) [ 2D] is performed in the formalism of many-body perturbation theory for photon energies ranging from the first ionization threshold to 70 eV. We considered excitations from 3p, 3d and 4s subshells, which resulted in a total of 32 partial photoionization final states in LS coupling. Our results indicate that the total cross section is dominated by the 3p 63d4s 2 → 3p 63d4s( 3D)kp 2P partial cross section below the 3d threshold at 7.29 eV, and by 3p → 3d resonance excitations in the photon energy range of 27–40 eV. Good qualitative agreement with experiment is found.

Calculation of the differential photoionization cross section of HF

Cross sections, photoelectron angular distribution parameters and branching ratios for the ionization of the valence 1π, 3σ and inner-valence 2σ shells of hydrogen fluoride have been calculated in the Random Phase Approximation (RPA). The computational procedure is based on the K-matrix technique and projection on basis sets of L2 functions to solve the RPA equations for the three coupled ionization channels in a way that recovers the electronic continuum degeneracy.

First experimental determination and theoretical calculation of partial photoionization cross sections of lithium over the energy region of hollow Atomic States.

Photoelectron spectrometry has been used for the first time to study autoionization of photoexcited hollow lithium atoms into the various continua of the ${\mathrm{Li}}^{+}$ ion. Absolute values of the partial photoionization cross sections have been determined. The R-matrix approximation has also been used to calculate the energies of the hollow states as well as all partial photoionization cross sections. Experimental and theoretical results are in very good agreement.

Photoionization Experiments with an Atomic Beam of Tungsten in the Region of the 5p and 4f excitation.

An atomic beam of tungsten and photoexcitation with monochromatized synchrotron radiation were used to measure the first photoion yield spectra of ${\mathrm{W}}^{+}$ and ${\mathrm{W}}^{2+}$ in the region of 30--60 eV. The comparison with calculated photoionization cross sections shows that the resonance structure can be explained by discrete $5p\ensuremath{\rightarrow}5d,6s$ and $4f\ensuremath{\rightarrow}5d$ transitions if one takes into account the thermal population of the initial states ${5d}^{4}{6s}^{2}^{5}D_{0,1,2,3,4}$ and ${5d}^{5}6s^{7}S_{3}$.

Complex coordinate L2 calculation of partial photoionization cross sections: theory and a model computation

It has been known for quite some time that L2 methods can be used to obtain the total photoabsorption cross sections for atomic and molecular photo-detachment or ionization without explicit enforcement of coordinate space boundary conditions. Such methods use matrix manipulations followed by use of moment-imaging techniques or various implementations of analytic continuation to construct the total cross section from discretized input data. The present work extends these methods by giving a prescription for obtaining partial photoabsorption cross sections with no prior enforcement of coordinate space boundary conditions, and still retains the desirable feature that only L2 basis functions are used. The problem of computation of the flux into non-degenerate two-body final states, even at intermediate energy where three- or many-body break-up channels are open, has thus been solved using analytic continuation of appropriate matrix elements of the full resolvent combined with analogous continuations of the Fredholm determinant.

Photoionization cross section with excitations for Na

Many-body perturbation theory is applied to the calculation of photoionization cross sections with excitations (2p, 3s) to (4s, kl) and (3p, kl) of sodium. The double-electron excitations (2p, 3s) to (4s, nl) and (3p, nl) are included and lead to the resonance structure between 38.5 and 46.5 eV. The cross section for the transition (2p to kd+ks) is obtained taking into account the random-phase approximation (RPA) and an important part of the Brueckner-orbital (BO) and structure-radiation (SR) corrections. A comparison of the contributions from RPA, BO and SR for the transition (2p to kl) is presented. The contributions of substantial correlations shake-off, virtual-Auger, knock-out and ground-state correlation (GSC) have been calculated and discussed for the transitions (2p, 3s) to (4s, kd) and (3p, kp), respectively. The ratios of the contributions from the cross section of photoionization with excitations to the cross section of the transition (2p to kl) are in good agreement with experiment.

Photoionization of two-electron atoms via the hyperspherical artificial-channel method: Application to H- and He.

An application of the artificial-channel method with hyperspherical coordinates to the calculation of photoionization cross sections of two-electron systems is presented. The method yields ``bound-free'' transition amplitudes and bound-state energies of any two-electron system. It obviates the separate generation of bound- and continuum-state wave functions by calculating directly the desired amplitudes. As applications, the photodetachment cross section of the ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ ion and the photoionization cross section of the He atom have been calculated. The computations are compared with other theoretical calculations and with experiments. The results obtained are in excellent agreement with experimental results for all the energies considered. Of equal significance is the close agreement, attesting to the high accuracy of the method, between results obtained by using the length form for the field-matter interaction and those obtained with the acceleration form.

Molecular photoionization cross sections by the Lobatto technique. II. core level photionization

The logarithmic derivative Kohn-Lobatto (LDKL) method for determining molecular electronic continuum wave functions is applied to the calculation of core level photoionization cross sections. The description of the photoionization process is based on a local effective potential obtained from density functional theory. However, the LDKL method avoids a shape approximation to the potential like the muffin-tin form underlying the continuum multiple scattering (CMS) method. Different from the procedure for the investigation of valence photoionization the influence of the attractive hole has to be taken into account explicitly. Slater's transition state potential in the local density approximation (LDA) leads to very satisfactory predictions of photoionization cross sections and asymmetry parameters. This is demonstrated for the well known cases of N 2 and CO. Applications to the inner shell photoionization of SF 6 illustrate that the LDKL method in the present LDA implementation affords an efficient and accurate treatment of larger molecules for which it offers an alternative superior to the widely used CMSXα method.

Many-body calculation of total and partial photoionization cross sections in atomic nitrogen

Polarizabilities and photoionization cross sections are computed for the 4So ground state of atomic nitrogen. The present method is based on the use of basis sets and on an integral equation (dispersion relation) that relates the real polarizability on the imaginary frequency axis to the photoionization cross section. Many-body perturbation theory is used to compute the polarization and the perturbation expansion is complete to second order in the Coulomb interaction. Hence, there is a comprehensive inclusion of correlation effects in our calculations. Comparison with other theory and experiment is made.

Photoionization of the 2s, 2p and 3s subshells of Mg+

We present calculations of total and partial photoionisation cross sections for the 2s, 2p and 3s subshells of Mg+ from their ionisation thresholds up to a photon energy of 220 eV. Photoelectron angular distribution parameters are also calculated for the 2p subshell. Oscillator strengths are given for discrete structure, and calculated energy levels compared with experimental values. The significance of electron correlations and two electron excitation for this atomic ion is discussed.

Differential photoionization cross section calculations for H 2S using the random phase approximation with L 2 basis functions

The photoionization cross sections and asymmetry parameters of the four main valence ionization processes in H 2S, corresponding to the formation of respectively 2b 1, 5a 1, 2b 2 and 4a 1 holes, have been calculated in the random phase approximation (RPA). By resorting to a recently proposed computational procedure, based on the K-matrix technique, the RPA equations for the four coupled ionization channels have been projected on a basis set of L 2 functions and solved, at any excitation energy above the ionization threshold, in a way that allows to recover the electronic continuum degeneracy.

On the use of the semiclassical approximation for the calculation of oscillator strengths and photoionization cross sections

The semiclassical formula for the radial integrals of bound-bound dipole transitions derived in a previous paper is modified for obtaining more accurate estimates and extending to bound-free transitions. The possibility of these is due to the special definition of the mean value of energy generalizing that of the previous paper. It is shown that the definition is optimal in the sense of the best agreement between semiclassical and exact quantum mechanical results in a limiting case. Matching with the corresponding expression for free-free transitions is also obtained. Good agreement with experiment and more accurate calculations is found.

Many-body calculation of photoionization cross sections in CO.

Total and partial photoionization cross sections are computed for CO at the fixed equilibrium internuclear separation. Finite basis sets were used, with no explicit recourse to continuum orbitals, and there is no need for input of empirical data such as the ionization threshold. By the present method the first step is to compute the (real) polarizability \ensuremath{\alpha}(i\ensuremath{\eta}) on the imaginary frequency axis. Many-body perturbation theory is used for that purpose, and the expansion is complete to second order in the Coulomb interaction. In the next step the cross sections are obtained from \ensuremath{\alpha}(i\ensuremath{\eta}) by inverting a simple integral equation of the Fredholm first kind (dispersion relation). For the partial cross sections, extra approximations may be necessary, as some diagrams to first and second order make contributions to more than one specific partial cross section. The computed total cross section is in very good agreement with experiment, and good agreement is also obtained for the 1\ensuremath{\pi} partial cross section. For the strongly interacting \ensuremath{\sigma} shells, the comparison with experiment is less certain. The present results, which include comprehensive correlation corrections, are also compared with existing theoretical results that are on the independent-particle level of accuracy.