Simple model for the ionization of helium atoms by fully and partially stripped ions in the strong interaction region

Theoretical calculations employing the modified over-barrier model to investigate single and double ionization cross sections of helium in collisions with highly charged ions are presented in the strong perturbation region. It shows the velocity and charge state dependences of cross sections, which coincides with the available experimental data. In order to determine the reliability of this model for partially stripped projectiles, the cross-section ratios have been measured for CZp+, OZp+-He (Zp=1-4) by the coincidence technique in the velocity range of 1-4.5 a.u. The calculated results are approximately in agreement with the experimental data.     

Photoionization cross sections of Fe XXI

Total and partial photoionization cross sections for (Fe XXI+hν→Fe XXII+e) are presented for the ground and excited bound states with n?10 and l?9. Fe XXI is prevalent in high-temperature astrophysical plasmas as well as in photoionized plasmas excited by hard X-rays. Results are reported for the first time for the high-energy photoionization with core excitations to n=2,3 states. Details of photoionization, especially the high-energy features that often dominate considerably over the low energy ones, are illustrated. These prominent features will affect the photoionization and the recombination rates in high-temperature plasmas. Calculations are carried out in the close coupling (CC) approximation using the R-matrix method. A large CC wavefunction expansion for Fe XXII which includes the ground and 28 excited core states from n=2 and 3 complexes and spans over a wide energy range is used. A total of 835 discrete bound states of Fe XXI in the singlet, triplet, and quintet symmetries are obtained. Total photoionization cross sections, σ_PI(nLS), for ionization into all 29 states are presented for all 835 final bound states and partial photoionization cross sections, σ_PI(g,nLS), for ionization into the ground ²P⁰ state of the core are presented for 685 states. While the n=2 core excitations are at relatively lower energy range (within 15 Ry from the ionization threshold), the n=3 excitations lie at considerably higher energy, 73 Ry and above, yet introduce resonant features and enhancements more prominent than those of n=2 states. Larger numbers of resonances are formed due to Rydberg series of autoionizing states converging on to the 29 core states. However, most noticeable structures are formed in the excited state cross sections by the photoexcitation-of-core (PEC) resonances in the photon energy range of 73-82 Ry. All these high-energy features are absent in the currently available results. The present results should enable more accurate modeling of the emission spectrum of highly excited plasma from the optical to far-ultraviolet region.     

Photoionization of highly stripped atomic ions: Relativistic calculations

Relativistic central-field (Dirac-Slater) calculations of photoionization of atoms and ions have been performed. The results show that the photoionization cross sections for inner-shell njl electrons are largely unaffected by removal of outer shell electrons (with principal quantum number greater than n) except for a shift in threshold, just as in the non-relativistic case. The most dramatic results are obtained for Th(Z=90) compared with Th⁸⁰⁺ where σ(hv) remains almost constant through 80 stages of ionization. The results are explained in terms of the fact that 〈r〉 is primarily a function of principal quantum number.     

K-vacancy production by 3.6-, 4.75-, and 5.9-MeV/amu238U Ions

Projectile (Z ₁) and target (Z ₂)K-vacancy production cross sections induced by 3.6-, 4.75-, and 5.9-MeV/amu²³⁸U ions in selected targets between C and U are reported. The cross sections are discussed within the context of the molecular model of inner-shell vacancy production in heavy-ion-atom collisions. The measured 1sσ and 2pσ excitation cross sections are compared with semiempirical formulas, and with the perturbed-stationary-states calculations of Betz et al. The dependence of these cross sections onZ _u =Z₁+Z ₂ agrees well with the Betz calculations. However, the measured cross sections are factors of 2 to 4 (1sσ) and 4 to 5 (2pσ) larger than the theoretical values.     

Giant resonance in the total photoabsorption cross section of Z ≈ 90 nuclei

Total photoabsorption cross sections of ²³²Th, ²³⁵U, ²³⁸U and ²³⁹Pu have been measured in the giant resonance region by the absorption method. Measured cross sections were approximated by two Lorentz lines. Lorentz line parameters, integrated cross sections, deformation parameters and quadrupole moments are given. The analysis of the nuclear optical anisotropy evolution with the increase of Z shows that Z ≈ 90 nuclei seem to be transitional, similar to N ≈ 90 nuclei. A comparison of experimental cross sections with dynamic collective model calculations has been performed. The evidence that quadrupole photoabsorption occurs in the 20–25 MeV energy region is also presented.     

Scattering of charged particles by atoms

A closed variant of the Born approximation for calculating differential scattering cross sections in ion-atom collisions is developed. An expression in terms of the matrix elements J _ij with respect to the single-electron states of the atom is found for the matrix element describing the target atom in the formula for the differential cross section. The matrix elements J _ij are averaged over the relative orientation of the momentum transferred in the collision and the symmetry axis of the electronic orbitals of the target atom, using the single-electron Rutaan-Hartree-Fock wave functions. The algebraic representation of the matrix elements J _ij makes it possible to perform calculations for atoms with any value of Z. The model developed is used to calculate the cross sections σ_Σ and characteristic scattering angles θ_c for the process of electron loss by H^? ions with energy E = 0.1–100 MeV in targets consisting of atoms with Z = 2–54. It is shown that σ_Σ ∝ E ^?1 and θ_c ∝ E ^?1/2 for all Z, and for fixed E the behavior of σ_Σ(Z) and θ_c(Z) is determined by the order of filling of the electronic shells of the target atoms (the ionization potential). The computational results are analyzed and compared with the experimental data and the results of other calculations.     

Double <Emphasis Type="Italic">K</Emphasis>-shell ionization of atoms by a single photon

We investigate the double K-shell ionization of heliumlike ions by a single photon. A fast convergence of QED perturbation theory with respect to the parameter 1/Z is demonstrated in the entire nonrelativistic domain for moderate nuclear charge numbers Z≥2. The ratio of double-to-single photoionization cross sections is calculated for light heliumlike ions, taking into account the leading orders of 1/Z and αZ expansions. A comparison of our results with the available experimental data for a number of neutral atoms is presented.     

Double-differential cross sections and kerma coefficients for light-charged particles produced by 96 MeV neutrons on carbon

Double-differential cross sections of inclusive light-ion (p, d, t, ³He and α) production in carbon induced by 96 MeV neutrons have been measured at eight laboratory angles from 20° to 160° in steps of 20°. Experimental techniques, as well as procedures for data taking and data reduction, are presented. Deduced energy-differential and production cross sections are herewith reported. Experimental cross sections are compared with theoretical reaction model calculations and experimental data in the literature. The measured production cross sections for protons, deuterons, tritons, ³He, and α particles support the trends suggested by data at lower energies. Deduced partial kerma coefficients for carbon are also shown.     

Asymptotics of the cross section of the electron loss by fast ions in light media

The dependence of the single electron loss cross section on the nuclear charge Z of a projectile and on the nuclear charge Zt of a target atom for fast collisions is studied theoretically using the plane-wave Born approximation and the sum rule. The results of calculations for fast singly and triply charged ions show that the single electron loss cross section increases monotonically as Z and Zt increase. This can be used to interpolate cross sections of processes if there are no experimental data. The results of calculations compare with the experimental and theoretical data of other authors.     

Photoionization cross sections and oscillator strengths of neutral cesium

The absolute photoionization cross sections from the 6p ²P_1/2 excited state of cesium at threshold and above the threshold region have been measured using the saturation absorption technique. The photoionization cross section at the ionization threshold is determined as 22.6±3.6 Mb, whereas in the region above threshold its value ranges from 22 to 20 Mb for photoelectron energies up to 0.1 eV. A comparison of the photoionization cross sections with earlier reported theoretical and experimental data have been presented and are in good agreement within the uncertainty. In addition, the oscillator strengths of the 6p ²P_1/2→n d ²D_3/2 (21≤n≤60) Rydberg transitions of cesium have been calibrated using the threshold value of the photoionization cross section. A complete picture of the oscillator strengths from the present work and previously reported data from n=5–60 is presented.     

Asymptotics of the cross section for the electron loss by atoms and ions in light media

The dependence of the cross section of electron loss on the nuclear charge Z of a bombarding ion and on the nuclear charge Z _t of a target atom for fast collisions is studied theoretically using the plane-wave Born approximation and the sum rule. The results of calculations show that the cross section of electron loss for fast collisions increases monotonically as Z and Z _t increase, which can be used to interpolate cross sections for the processes for which there are no experimental data.     

Influence of nondipolar effects on the photoelectron angular distribution upon photoionization of 2p and 3d atomic shells

Relativistic calculations of the angular distribution of photoelectrons upon photoionization of 2p and 3d shells in the range of photoelectron energies from 1 to 10 keV are carried out for unpolarized and linearly polarized radiation. An exact expression for the angular distribution of photoelectrons that takes into account nondipolar terms of the order of O[(kr)²] (k is the photon energy and r is the radius of the ionized shell) is obtained in the case of unpolarized radiation. It is shown that the contribution of the O[(kr)²] terms to the differential cross section can be considerable, reaching 24% at the maximum energy considered. Accounting for such terms in the calculation of the ratio of differential cross sections, which is experimentally measured at a certain geometry of angles in the case of linearly polarized radiation, can change this ratio twofold. The parameters of the angular distribution, which are necessary for the conduction of a quantitative x-ray photoelectron analysis, are given for the 2p _1/2 and 2p _3/2 shells of elements with 11≤Z≤29 and for the 3d _3/2 and 3d _5/2 shells of elements with 30≤Z≤54.     

Measurements ofK-shell ionization with132Xe and208Pb projectiles in the energy range of 1.4–5.9 MeV/u

Projectile and targetK-shell ionization cross sections induced by 3.6-, 4.7-, and 5.9 MeV/u¹³²Xe ions and 1.4-, 3.6-, 4.7-, and 5.9 MeV/u²⁰⁸Pb ions from the UNILAC in thin solid targets between C and U are measured. The cross sections are discussed in terms of the molecular model of innershell vacancy production in heavy ion-atom collisions. The sharing of 2p _1/2σ vacancies between theK shells of the two collision partners in these very heavy ion-atom collisions is found to deviate from the Meyerhof-Demkov formula forR≦10^?2. The measured ionization cross sections are compared with theoretical calculations for 1sσ and 2p _1/2σ excitation cross sections. AZ _UA=Z₁+Z ₂ dependence is found independent ofZ ₁/Z ₂. Outer-shell vacancy configurations measured in these close encounters are reported.     

Photoionization of the excited He atom in Debye plasmas

We present theoretical photoionization cross sections for He 1s2s ¹S and He 1s2p ¹P states in a Debye plasma environment by the complex coordinate rotation method, using a finite L² basis set constructed from one electron Laguerre orbitals. The plasma environment is found to appreciably influence the photoionization cross sections near the ionization threshold. In this regard, the photoionization cross sections of isolated He are compared with other theoretical and experimental results. Our results are in good agreement with the previous results. A new minimum appears in the photoionization cross section curve for the metastable 1s2s ¹S state. Results are given for the S- and D-wave partial photoionization for the excited 1s2p ¹P state.     

Search for the density effect in inner-shell lonization by ultra relativistic electron impact

We have extended the measurements ofK-andL-shell ionization cross sections by electron impact into the ultra relativistic energy region, 0.9≦E≦2.0 GeV, in order to search for a saturation of the cross section. This phenomenon, which is due to the polarization of the target medium, is called density effect. It is predicted to occur at several hundred MeV impact energy and preferentially for lowZ target elements. Theoretical calculations are presented, based on the one-photon-exchange approximation. The absolute measurements of theK-andL-shell cross sections for Ni(K), Cu(K), Ag(K, L) and Au(L) performed at the 2.5 GeV electron synchrotron of the Bonn University, however, exhibit that the cross sections show no saturation but are still increasing. Furthermore, from theK X-ray yields, obtained at 0.9 and 2.0 GeV by bombarding the lowZ elements S, Ca, Mn, Ni and Ge, we obtain for the corresponding cross section ratio σ _K (2GeV)/σ _K (0.9GeV)=1.08±0.01 on the average. TheK X-ray yield of a composite Ca — Mn target amounts to $$[\sigma _K (Ca;2.0GeV)/\sigma _K (Mn;2.0GeV)]/[\sigma _K (Ca;0.9GeV/\sigma _K (Mn;0.9GeV)] = 0.99 \pm 0.02.$$ . All three results are in disagreement with theory. This severe discrepancy is discussed but the origin for it is not yet understood.     

Measurement ofL-shell photoelectric cross sections in highZ elements at 60 keV

L-shell photoelectric cross sections have been measured at 60 keV for six elements in the range 74≤Z≤92. The measurements are found to agree with theoretical calculations.     

Ionization of <Emphasis Type="Italic">nS</Emphasis>, <Emphasis Type="Italic">nP</Emphasis>, and <Emphasis Type="Italic">nD</Emphasis> lithium,potassium, and cesium Rydberg atoms by blackbody radiation

The results of theoretical calculations of the blackbody ionization rates of lithium, potassium, and cesium atoms residing in Rydberg states are presented. The calculations are performed for nS, nP, and nD states in a wide range of principal quantum numbers, n = 8?65, for blackbody radiation temperatures T = 77, 300, and 600 K. The calculations are performed using the known quasi-classical formulas for the photoionization cross sections and for the radial matrix elements of transitions in the discrete spectrum. The effect of the blackbody-radiation-induced population redistribution between Rydberg states on the blackbody ionization rates measured under laboratory conditions is quantitatively analyzed. Simple analytical formulas that approximate the numerical results and that can be used to estimate the blackbody ionization rates of Rydberg atoms are presented. For the S series of lithium, the rate of population of high-lying Rydberg levels by blackbody radiation is found to anomalously behave as a function of n. This anomaly is similar to the occurrence of the Cooper minimum in the discrete spectrum.     

X-ray photoionization cross sections for quantitative analysis

The relative photoemission intensities from subshells of 51 elements and simple compounds have been measured using X-ray photoelectron spectroscopy. The chemical composition of each specimen surface was monitored by Auger electron spectroscopy and contamination was minimized by Ar⁺ ion bombardment. Experimental photoelectron cross sections derived for MgKα (1254 eV) radiation were compared with theoretical Hartree-Slater subshell photoionization cross sections calculated by Scofield. Good correlation (r = 0.96) between theory and experiment was observed over two orders of magnitude for most of the elements studied. Relative cross sections for subshells of a given element are also consistent with theoretical values, with several notable exceptions. The results indicate that quantitative analysis of ESCA spectra is possible using the Scofield cross sections.     

Fragmentation cross sections of16O at 60 and 200 GeV/nucleon

We used CR39 plastic nuclear track detectors (C₁₂H₁₈O₇) in combination with automatic track measurement to determine total charge changing and partial cross sections for the production of fragments of chargeZ=6 andZ=7 in collisions of¹⁶O beam nuclei at energies of 60 GeV/nucleon and 200 GeV/nucleon in targets H, C, CR39, CH₂, Al, Cu, Ag and Pb. Total charge changing cross sections due to the process of electromagnetic dissociation are calculated based on a theoretical model and found to be consistent with total and partial electromagnetic dissociation cross sections derived from this experiment. The energy dependence of pure nuclear fragmentation is investigated.     

Triton-emission cross sections with 30 MeV d(Be) break-up neutrons

Triton-emission cross sections were measured for Al, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo, Ag, Ta, Tl, Pb and Bi with a 30 MeV d(Be) break-up neutron spectrum characterized by a multiple-foil activation technique. The accumulated tritium was separated by vacuum extraction and measured by low-level gas-phase β^? counting. The systematic trend in the cross sections is somewhat similar to that in the 53 MeV d(Be) break-up neutron spectrum; apart from some initial decrease as a function of Z, the cross section is almost constant over the entire range of Z = 22 to 83. The magnitudes of the cross sections lie between those with 14 MeV neutrons and 53 MeV d(Be) break-up neutrons. Hauser-Feshbach calculations show that the statistical model describes the triton-emission cross sections for nuclei in the (2s, ld) shell within a factor of 2; for the heavier nuclei, however, the calculated cross sections are much smaller than the experimental values.