Magnetic Sublevel Cross Sections Research Articles

Relaxation effects on the magnetic cross section and fluorescence radiation polarization after 4d inner-shell photoionization of Ba-like ions

On the basis of the multi-configuration Dirac–Fock method and the density matrix theory treatment of photoionization (PI) dynamics, a systematic investigation for 4d inner-shell PI of exemplary Ba atom and Ba-like Nd4+, Gd8+ and Yb14+ ions is performed. Starting from the general framework of the relativistic, the relaxation effects are considered by using a set of relaxed one-electron orbitals in solving the coupled Dirac equations. Our results uncover for the first time that the relaxation effects, arising from the overlap integrals between orbitals of the initial state and the relaxed final state, may play a paramount role in determining the magnetic sublevel cross sections, the photoelectron angular-distribution asymmetry parameters, and the fluorescence polarizations of the subsequent x-ray radiation, particularly for neutral atoms close to the threshold regime. Yet the importance of inclusion of the orbital relaxation weakens as the incoming photon energy and/or the degree of atom ionization increases. The nature of these influences is explored, which allows us to get more insight on the physical process and mechanism involved. Our results are consistent with those obtained by the experiments and other theoretical predictions.

Detailed electron impact fine-structure excitation cross-sections of Kr+ and linear polarization of its subsequently emitted photons

An extensive calculation for electron impact excitation cross-sections of Kr+ ion is performed using relativistic distorted wave theory. The transitions considered are from the ground state i.e. 4s24p5 (J=3/2) to the 4s24p5 (J = 1/2), 4s4p6 (J=1/2) levels and fine structure levels of 4s24p45s, 4s24p45p, 4s24p46s, 4s24p46p, 4s24p44d and 4s24p45d excited states. The transition matrix is evaluated using the relativistic multi-configuration Dirac-Fock bound state wave functions of the initial and final states of Kr+ ion obtained from the GRASP2K program. The 4s24p5, 4s4p6, 4s24p45s, 4s24p45p, 4s24p46s, 4s24p46p, 4s24p44d and 4s24p45d configuration state functions are used to calculate the required wave functions. The incident and scattered projectile electron continuum wave functions are calculated numerically by solving the Dirac equations using static potential of the target ion. Oscillator strengths and transition probabilities are calculated and reported for the dipole allowed transitions, making these available to check the accuracy of the bound state wave functions for future comparison purposes. The detailed excitation cross-sections and their corresponding excitation rate coefficients are reported for considered 116 fine-structure excitation transitions from the ground state 4s24p5 (J=3/2). Further, analytic fittings of the obtained cross-sections with respect to incident electron energy are also performed for all the transitions considered in the present work so that these can be directly used in any plasma model for diagnostics purposes. In addition, using the obtained magnetic sub-level cross-sections, the degree of linear polarization of the photon emissions from the decay of electron impact excited anisotropic states of Kr+ ion through the dipole allowed transitions is calculated and reported.

Electron-impact excitation of ions within a quantum plasma

We develop a new relativistic model which can describe the dynamics on electron-impact excitation (EIE) of ions within a quantum plasma environment. An exemplary excitation 1s1/2 → 2p3/2 of Fe XXVI by electron impact with the exponential cosine-screened Coulomb potential (ECSCP) is presented, i.e., 25 times ionized atoms of Fe, exist in laser-produced plasmas, astrophysical objects, and electron beam ion trap experiments. For the atomic structure of target ion, using the same potential, a Ritz variational method with a trial wave function that contains unknown variational parameters is also proposed for comparison purposes. In this method, an analytical formula of bound energy is derived from the energy equation, and the variational parameters are determined by the minimization of the energy. The energies obtained from our two methods are compared with each other and other theoretical predictions based on the non-relativistic model and found to be in good agreement. For the collision dynamics, the continuum wave function is determined by solving the modified Dirac equations, in which the ECSCP is included for the solution of the continuum orbital. The total cross sections, magnetic sublevel cross sections, and the degrees of linear polarization of emitted x-rays are calculated as a function of the incident energy and screening parameter by using the distorted-wave method in the relativistic frame. Since there are no experiments or other calculations for EIE cross sections on this ion, the obtained results have been compared with those for an isolated ion. The effect of quantum plasma leads to a reduction in the total and magnetic sublevel cross-sections and thus reduces the degrees of linear polarization of emitted x-rays. Comparative analysis allows to estimate the quality of the proposed approximations. Our dynamic model is practicable and easy to apply, which may provide an alternative route towards information with fluorescence polarization in a quantum plasma environment.

Electron impact N-shell excitation of Se-like to Ga-like tungsten ions and polarization of their subsequent emissions

Study of electron impact excitation of W40+ (Se-like), W41+ (As-like), W42+ (Ge-like), and W43+ (Ga-like) ions using fully relativistic distorted wave theory has been presented. The excitation cross-sections of E1 and E2 allowed transitions of these ions are reported across the wide range of incident electron energies from excitation threshold to 20 keV. The obtained cross-sections of all the transitions of the four ions are fitted with an analytical expression for the applications in the plasma modelling. Further, using the magnetic sublevel cross-sections, the degree of linear polarization of the photon emissions from the electron impact excited anisotropic states of tungsten ions through the dipole allowed transitions are also calculated.

Angular Distribution and Linear Polarization of X-ray Radiation Resulting from Electron Impact Excitation of Highly Charged Ions in Debye Plasmas

Plasma-screening effects on the $$1s _{1/2} \rightarrow 2l \; (l = s , p )$$ and $$1s _{1/2} \rightarrow 3d _{3/2}$$ electron-impact excitation of highly charged ions are investigated, together with their subsequent radiative decay. The analysis is performed based on the multi-configuration Dirac–Fock method and the fully relativistic distorted-wave method incorporating the Debye–Huckel potential. To explore the nature of the effects, calculations are carried out based on detailed analyses of the integrated total and magnetic sublevel cross sections, the alignment parameters, the linear polarizations, and the angular distribution of the X-ray photoemission, as well as on corresponding data calculated in various Debye lengths/environments, taking the $$2p _{3/2}\rightarrow 1s _{1/2}$$ and $$3d _{3/2}\rightarrow 1s _{1/2}$$ characteristic lines of H-like $$\hbox {Fe}^{25+}$$ ion as an example. The present results are compared with experimental data and other theoretical predictions where available.

Relativistic effects on the linear polarization and angular distribution of x-ray radiation emitted by inner-shell photoionization of atoms

We present a theoretical study of relativistic effects on the linear polarization and angular distribution of x-ray radiation for the L () characteristic line following inner-shell single photoionization of Cd, Ba, Yb and Ra atoms. The analysis is performed based on the multi-configuration Dirac–Fock method and the density matrix theory. To explore the nature of these effects, calculations are carried out based on detailed analyses of the total and magnetic sublevel cross sections, the linear polarization, and the angular distribution of the x-ray photoemission, as well as on corresponding data calculated in the nonrelativistic limit. Our results show a significant difference in the above parameters compared to the nonrelativistic treatment, which is mainly due to the relativistic treatment of the target. Higher multipole contributions are also estimated, and found to be generally weaker. The importance of inclusion of the relativistic effects grows with increasing atomic number and the incoming photon energy.

The influence of Breit interaction and E1-M2 quantum interference on polarization following inner-shell electron-impact excitation of Li-like ions

SynopsisThe total and magnetic sublevel cross sections of electron-impact excitation from the ground state 1s22s 2S1/2 to the inner-shell excited states 1s2s2p (J=3/2) are calculated based on a relativistic distorted-wave method for highly charged Li-like ions. The important influence of the Breit interactions and quantum interferences between electronic dipole (E1) and magnetic quadrupole (M2) transition on polarization of emitted X-ray are systematically studied.

Electron-impact excitation rate-coefficients and polarization of subsequent emission for Ar+ ion

Electron impact excitation in Ar+ ions has been studied by using fully relativistic distorted wave theory. Calculations are performed to obtain the excitation cross-sections and rate-coefficients for the transitions from the ground state 3p5 (J=3/2) to fine-structure levels of excited states 3p44s, 3p44p, 3p45s, 3p45p, 3p43d and 3p44d. Polarization of the radiation following the excitation has been calculated using the obtained magnetic sub-level cross-sections. Comparison of the present rate-coefficients is also done with the previously reported theoretical results for some unresolved fine structure transitions.

Dominance of the radiative cascades in the cross section and circular polarization of x-ray radiation

The radiative cascade typically appears as a somewhat small correction to the direct impact process. We demonstrate here, however, that for the longitudinally-polarized electron impact excitation of highly charged ions, radiative cascades may play a significant role that can change the cross section and circular polarization of the emitted x-ray radiation qualitatively. This conclusion is verified by taking the 1s2 (J = 0) 1s2s1/2 (J = 1) excitation of He-like Fe Ge Mo Ag and ions as examples. For these ions, the dominant cascade channels from high-lying levels 1 snp (n = 2, 3, 4, 5, 6) will strongly dominate the direct excitation process and greatly modify the Mf = −1 magnetic sublevel cross sections, as well as leading to a considerable change in the expected circular polarizations of the x-ray emission pattern.

Creation, destruction, and transfer of atomic multipole moments by electron scattering: relativistic treatment1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

We have obtained expressions for the creation, destruction, and transfer of atomic multipole moments by electron scattering under relativistic conditions. More specifically, we have obtained separate expressions for different-level processes (inelastic scattering) and for same-level processes (elastic and inelastic scattering). The cross sections for different-level processes are expressed in terms of inelastic magnetic sublevel cross sections, except for the coherence transfer cross section, which is expressed in terms of an angular integral of a product of inelastic magnetic sublevel amplitudes. The same-level cross sections are expressed in terms of the imaginary part of the elastic forward scattering amplitude and in terms of elastic scattering magnetic sublevel cross sections, except for the coherence transfer cross section, which is expressed in terms of the (complex) forward elastic scattering amplitudes and an angular integral of a product of elastic scattering magnetic sublevel amplitudes. If the collisional model supports the optical theorem, then the same-level cross sections can be rewritten in such a form that they are broken up into two parts: an elastic scattering part and an inelastic scattering part. In carrying out this work, we have used the density matrix formalism of Fano and Blum in combination with the electron scattering formalism of Gell-Mann and Goldberger.

Electron-impact excitation of Ti21+ in Debye plasmas

The plasma screening effect on electron-impact excitation is studied by using the relativistic distorted-wave description and exemplified by the excitation of Ti21+ ion. The total and differential cross sections for the 1s–2s and 1s–2p excitations are calculated in the energy range from threshold to 5 times threshold energy, and the magnetic sublevel cross sections are also given. Comparison of present calculations with other results, when available, is made.

Ionization–excitation of helium to He+(2p)magnetic sublevels following electron, proton, and molecular hydrogen (H2+ andH3+)impact

Experimental magnetic sublevel scattering-angle-integrated cross sections followingionization–excitation of He(1s2)1S to He+(2p)2Po ine− + Heand Hm+ + He (m = 1–3)collision systems have been determined using a combination of totalcross sections and polarization fraction measurements in the extremeultraviolet range. The derived magnetic sublevel cross sections, σ0 and σ1, for ML = 0 +/- 1have been studied over a wide range of velocities (2–8.5 au) for electron impact onhelium. These results are compared with previous experimental proton crosssections (2–6 au) as well as new measured data for hydrogen molecularimpact (1.4–4.0 au) for equi-velocity. In addition, our electron and protonmeasurements are compared with earlier theoretical predictions, our recentsecond-Born calculations fully including off-shell energy terms, and presentpredictions from a hybrid first-order and second-order distorted-wave plusR-matrix (close-coupling) model(DWB1 + RMPS andDWB2 + RMPS).Finally, we have extended our polarization measurements for H+ + Hecollisions and found excellent agreement between theory and experiment at nearlyall impact energies. However, the present second-Born and DWB1 + RMPSresults deviate slightly from the experimental electron data while the DWB2 + RMPScalculations tend toward the experimental data of Forand et al (1985 J. Phys. B:At. Mol. Phys. 18 1409).

Scattering angle-integrated (total) and magnetic sublevel cross-sections and degree of linear polarization for electron and proton induced excitation [HeI [formula omitted] ( n=2–5)] of helium

Experimental scattering-angle-integrated (total) cross-sections σ ̄ , (scattering) angle-integrated magnetic sublevel cross-sections σ ̄ M L , and degree of linear polarization data have been measured in the extreme ultraviolet (EUV) wavelength region following decay of HeI (1 snp) 1P 0 ( n=2–5) states induced by electron and proton impact on a neutral helium target. These measurements are compared with a first Born approach as well as more sophisticated theoretical calculations. Specifically, theoretical values for electron impact include convergent close-coupling (CCC) and R-matrix with pseudo states (RMPS) methods in addition to first Born (Born 1) approximation while proton induced excitation cross-sections are compared with atomic-orbital close-coupling (AOCC) and first Born predictions.

Ionization–excitation magnetic sublevel cross sections for He+ (2p)2P0 states following fast electron and proton impact

The first experimental magnetic substate scattering-angle-integrated cross sections following ionization–excitation of He(1s2)1S to He+(2p)2P0 in the e−+He collision system have been determined using a combination of total cross sections and polarization fraction measurements in the extreme ultraviolet range. The derived magnetic sublevel cross sections, σ0 and σ1, for ML=0, ±1 have been studied over a wide range of electron velocities (2–8.5 a.u.). These results are compared with previous cross sections for equi-velocity proton impact. In addition, our experimental data are compared with earlier theoretical predictions, our recent second-Born calculations fully including off-energy shell terms, and new R-matrix results. We have extended our polarization measurements for H++He collisions and found excellent agreement between theory and experiment at nearly all impact energies. However, the present second-Born and R-matrix results deviate slightly from the experimental electron data.

Near-threshold electron-impact excitation of the vacuum-ultraviolet resonance transitions in Ne, Ar, Kr, and Xe

Results of semirelativistic $R$-matrix calculations for electron-impact excitation of the ${(np}^{6}{)}^{1}{S}_{0}\ensuremath{\rightarrow}{\mathrm{np}}^{5}[n+1]s$ $(J=1)$ transitions in the noble gases Ne $(n=2),$ $\mathrm{Ar}(n=3),$ Kr $(n=4),$ and Xe $(n=5)$ are compared with experimental values for light polarizations and angle-integrated magnetic sublevel cross sections. The calculations focus on the near-threshold regime, where negative-ion resonances have a significant effect on the results. In light of the complexity of the structures, the agreement between theory and experiment is very encouraging. Nevertheless, further improvements in the theoretical treatment of both the target structure and the collision dynamics seem necessary.

Oscillatory alignment phenomena in Rydberg-atom–rare-gas collisions

Retention of orbital alignment during near-resonant energy transfer collisions of rare-gas projectiles with excited alkaline-earth-metal atoms is explored theoretically for scattering of Xe from Rydberg states of Ca. For such collisions, conventional interpretations of alignment phenomena, which are based on potential curves for a transient molecule thought to form during the collision, are not relevant. Theoretical partial magnetic sublevel cross sections for Ca**(4s17d D2→4s18p P1) transitions confirm the existence of alignment effects, as demonstrated experimentally by Spain et al. @J. Chem. Phys. 102, 9532 ~1995!#, at a mean relative velocity of 914 m/s. Theory further predicts heretofore unobserved oscillatory structures in these cross sections as a function of relative velocity and that these oscillations depend strongly on the initial magnetic quantum number of the Rydberg electron. @S1050-2947~98!50301-0#

Electron scattering from Kr. II. Differential cross sections for the 5s(11/2)1 and 5s'(01/2)1 excitations

Differential cross sections have been determined for the 5s(11/2)1 and 5s'(01/2)1 excitations of Kr using a crossed-beam method. The measurements were carried out in the angular range 10-125' at impact energies of 20, 30, 40, 50, 60 and 80 eV. The inelastic scattering cross sections were normalised to the absolute differential cross sections for elastic scattering. Differential magnetic sublevel cross sections have also been determined for the first time at impact energies of 40, 50, 60 and 80 eV and scattering angles of 10', 15', 20', 25' and 30' with the help of previously measured lambda parameters.

Electron-impact excitation of electronic states in argon at incident energies between 16 and 100 eV

Normalized, absolute differential cross sections have been measured for electron-impact excitation of 23 individual or composite electronic states of argon lying within 14.30 eV of the ground state. Incident electron energies are 16, 20, 30, 50, and 100 eV, and the range of scattering angles 5\ifmmode^\circ\else\textdegree\fi{}-138\ifmmode^\circ\else\textdegree\fi{}. The absolute differential cross sections are extrapolated to 0\ifmmode^\circ\else\textdegree\fi{} and 180\ifmmode^\circ\else\textdegree\fi{} and integrated to yield integral and inelastic-scattering momentum-transfer cross sections for the excitation processes. Errors in the differential cross section are grouped into the classes $A(26%)$, $B(31%)$, and $C(45%)$, with slightly larger errors given to the integrated quantities owing to extrapolation uncertainties. Comparisons of the present data are made with previous measurements where available, and with results of several distorted-wave and Born calculations. Differential magnetic sublevel cross sections for the $^{3}P_{1}$ and $^{1}P_{1}$ levels are also obtained at 50-eV incident energy and 5\ifmmode^\circ\else\textdegree\fi{} scattering angle using previously measured $\ensuremath{\lambda}$ parameters.

Experimental-theoretical comparisons of 11S to 21P differential magnetic sublevel cross sections for electron-helium scattering at 60 eV and 80 eV

Experimental absolute differential cross sections (DCS) for the excitations 11S to 21P and 23P in helium are reported at incident electron energies of 60 eV and 80 eV, and at scattering angles between 5 degrees and 136 degrees . By combining the present DCS measurements for the 21P excitation with results of recent electron-photon coincidence measurements, absolute DCS for the excitation of the individual magnetic sublevels 21P0 and 21P+or-1 are obtained from purely experimental data. These magnetic sublevel cross sections, as well as their sum, are compared with results of calculations in the multichannel eikonal, distorted-wave and first-order many-body theories.