Electron impact excitation of Be-like ions: a comparison of DARC and ICFT results

Emission lines of Be-like ions are frequently observed in astrophysical plasmas, and many are useful for density and temperature diagnostics. However, accurate atomic data for energy levels, radiative rates (A-values) and effective electron excitation collision strengths ($\Upsilon$) are required for reliable plasma modelling. In general it is reasonably straightforward to calculate energy levels and A- values to a high level of accuracy. By contrast, considerable effort is required to calculate $\Upsilon$, and hence it is not always possible to assess the accuracy of available data. Recently, two independent calculations (adopting the $R$-matrix method) but with different approaches (DARC and ICFT) have appeared for a range of Be-like ions. Therefore, in this work we compare the two sets of $\Upsilon$, highlight the large discrepancies for a significant number of transitions and suggest possible reasons for these.

Photoionization cross section calculations for the halogen-like ions Kr + and Xe +

Photoionization cross section calculations on the halogen-like ions; Kr + and Xe + have been performed for a photon energy range from each ion threshold to 15 eV, using large-scale close-coupling calculations within the Dirac--Coulomb R -matrix approximation. The results from our theoretical work are compared with recent measurements made at the ASTRID merged-beam set-up at the University of Aarhus in Denmark and from the Fourier transform ion cyclotron resonance trap method at the SOLEIL synchrotron radiation facility in Saint-Aubin, France Bizau et al (2011 J. Phys. B: At. Mol. Opt. Phys. 44 055205) and the advanced light source M{ü}ller (2012 private communication), Aguliar et al (2012 J. Phys.: Conf. Ser . at press). For each of these complex ions our theoretical cross section results over the photon energy range investigated are seen to be in excellent agreement with experiment. Resonance energy positions and quantum defects of the prominent Rydberg resonances series identified in the spectra are compared with experiment for these complex halogen-like ions.

A radiation-damped R -matrix approach to the electron-impact excitation of helium-like ions for diagnostic application to fusion and astrophysical plasmas

Electron-impact excitation collision strengths for transitions between all singly excited levels up to the n = 4 shell of helium-Eke argon and the n = 4 and 5 shells of helium-like iron have been calculated using a radiation-damped R-matrix approach. The theoretical collision strengths have been examined and associated with their infinite-energy limit values to allow the preparation of Maxwell-averaged effective collision strengths. These are conservatively considered to be accurate to within 20% at all temperatures, 3 x 10(5)-3 x 10(8) K forAr(16+) and 10(6)-10(9) K for Fe24+. They have been compared with the results of previous studies, where possible, and we find a broad accord. The corresponding rate coefficients are required for use in the calculation of derived, collisional-radiative, effective emission coefficients for helium-like lines for diagnostic application to fusion and astrophysical plasmas. The uncertainties in the fundamental collision data have been used to provide a critical assessment of the expected resultant uncertainties in such derived data, including redistributive and cascade collisional-radiative effects. The consequential uncertainties in the parts of the effective emission coefficients driven by excitation from the ground levels for the key w, x, y and z lines vary between 5% and 10%. Our results remove an uncertainty in the reaction rates of a key class of atomic processes governing the spectral emission of helium-like ions in plasmas.

The validity of classical trajectory and perturbative quantal methods for electron-impact ionization from excited states in H-like ions

To test the validity of classical trajectory and perturbative quantal methods for electron-impact ionization of H-like ions from excited states, we have performed advanced close-coupling calculations of ionization from excited states in H, Li 2+ and B 4+ using the R -matrix with pseudo states and the time-dependent close-coupling methods. Comparisons with our classical trajectory Monte Carlo (CTMC) and distorted-wave (DW) calculations show that the CTMC method is more accurate than the DW method for H, but does not improve with n and grows substantially worse with Z , while the DW method improves with Z and grows worse with n .

Interchannel interactions and relaxation in the 2p auger spectra of Mg-like ions

Relativistic Auger rates for the 2p spectra of Mg-like ions have been calculated in the atomic range 13 < Z < 36. We used the multiconfiguration Dirac-Fock method but beyond a simple frozen-orbital approach we include also relaxation for the bound electrons and the interchannel interaction between the continuum states. Both effects may alter the individual transition rates remarkably. This is analysed for a few selected states within the isoelectronic sequence. Weak transitions within the 2p spectra can be changed by an order of magnitude because of the continuum coupling. The influence of both effects for higher-Z ions is reduced but still remain visible.

Auger transitions in Li-like and Be-like ions

Measurements of the Auger decay of beam-foil excited Be II and Be I levels are reported along with a proposed assignment of the experimental spectra. The Li I, Be II and Be III (1s 2s^2) ^2 S \rightarrow (1s^2 2s)^2 S Auger transitions as presented in this letter represents the first observation of such states in positive ions with Z \le 5.

Mode coupling for precise measurements of the electronic g-factor of hydrogen-like ions in Penning traps

The g-factor is a constant which connects the magnetic moment $vec{mu}$ of a charged particle, of charge q and mass m, with its angular momentum $vec{J}$. Thus, the magnetic moment can be writen $ vec{mu}_J=g_Jfrac{q}{2m}vec{J}$. The g-factor for a free particle of spin s=1/2 should take the value g=2. But due to quantum electro-dynamical effects it deviates from this value by a small amount, the so called g-factor anomaly $a_e$, which is of the order of $10^{-3}$ for the free electron. This deviation is even bigger if the electron is exposed to high electric fields. Therefore highly charged ions, where electric field strength gets values on the order of $10^{13}-10^{16}$V/cm at the position of the bound electron, are an interesting field of investigations to test QED-calculations. In previous experiments [H"aff00,Ver04] using a single hydrogen-like ion confined in a Penning trap an accuracy of few parts in $10^{-9}$ was obtained. In the present work a new method for precise measurement of magnetic the electronic g-factor of hydrogen-like ions is discussed. Due to the unavoidable magnetic field inhomogeneity in a Penning trap, a very important contribution to the systematic uncertainty in the previous measurements arose from the elevated energy of the ion required for the measurement of its motional frequencies. Then it was necessary to extrapolate the result to vanishing energies. In the new method the energy in the cyclotron degree of freedom is reduced to the minimum attainable energy. This method consist in measuring the reduced cyclotron frequency $nu_{+}$ indirectly by coupling the axial to the reduced cyclotron motion by irradiation of the radio frequency $nu_{coup}=nu_{+}-nu_{ax}+delta$ where $delta$ is, in principle, an unknown detuning that can be obtained from the knowledge of the coupling process. Then the only unknown parameter is the desired value of $nu_+$. As a test, a measurement with, for simplicity, artificially increased axial energy was performed yielding the result $g_{exp}=2.000~047~020~8(24)(44)$. This is in perfect agreement with both the theoretical result $g_{theo}=2.000~047~020~2(6)$ and the previous experimental result $g_{exp1}=2.000~047~025~4(15)(44).$ In the experimental results the second error-bar is due to the uncertainty in the accepted value for the electron's mass. Thus, with the new method a higher accuracy in the g-factor could lead by comparison to the theoretical value to an improved value of the electron's mass. [H"af00] H. H"affner et al., Phys. Rev. Lett. 85 (2000) 5308 [Ver04] J. Verd'u et al., Phys. Rev. Lett. 92 (2004) 093002-1

Grazing incidence pumped Zr x-ray laser for spectroscopy on Li-like ions

X-ray laser fluorescence spectroscopy of the 2s-2p transition in Li-like ions is promising to become a widely applicable tool to provide information on the nuclear charge radii of stable and radioactive isotopes. For performing such experiments at the Experimental Storage Ring ESR, and the future NESR within the FAIR Project, a grazing incidence pumped (GRIP) x-ray laser (XRL) was set up at GSI Darmstadt using PHELIX (Petawatt High Energy Laser for heavy Ions eXperiments). The experiments demonstrated that lasing using the GRIP geometry could be achieved with relatively low pump energy, a prerequisite for higher repetition rate. In the first chapter the need of a plasma XRL is motivated and a short history of the plasma XRL is presented. The distinctive characteristic of the GRIP method is the controlled deposition of the pump laser energy into the desired plasma density region. While up to now the analysis performed were mostly concerned with the plasma density at the turning point of the main pump pulse, in this thesis it is demonstrated that also the energy deposition is significantly modified for the GRIP method, being sensitive in different ways to a large number of parameters. In the second chapter, the theoretical description of the plasma evolution, active medium and XRL emission properties are reviewed. In addition an innovative analysis of the laser absorption in plasma which includes an inverse Bremsstrahlung (IB) correction factor is presented. The third chapter gives an overview of the experimental set-up and diagnostics, providing an analytical formula for the average and instantaneous traveling wave speed generated with a tilted, on-axis spherical mirror, the only focusing system used up to now in GRIP XRL. The fourth chapter describes the experimental optimization and results. The emphasis is on the effect of the incidence angle of the main pump pulse on the absorption in plasma and on output and gain in different lasing lines. This is compared to the theoretical results for two different incidence angles. Significant corrections for the temperature evolution during the main pump pulse due to the incidence angle are demonstrated in comparison to a simple analytical model which does not take into account the pumping geometry. A much better agreement is reached by the model developed in this thesis. An interesting result is also the appearance of a central dip in the spatially resolved keV emission which was observed in the XRL experiments for the first time and correlates well with previous near field imaging and plasma density profile measurements. In the conclusion also an outlook to the generation of shorter wavelength XRL’s is given.

Optimum Electron Temperature and Density for Short-Wavelength Plasma-Lasing from Nickel-like ions

Soft X-ray lasing across a Ni-like plasma gain-medium requires optimum electron temperature and density for attaining to the Ni-like ion stage and for population inversion in the View the MathML source3d94d1(J=0)→3d94p1(J=1) laser transition. Various scaling laws, function of operating parameters, were compared with respect to their predictions for optimum temperatures and densities. It is shown that the widely adopted local thermodynamic equilibrium (LTE) model underestimates the optimum plasma-lasing conditions. On the other hand, non-LTE models, especially when complemented with dielectronic recombination, provided accurate prediction of the optimum plasma-lasing conditions. It is further shown that, for targets with Z equal or greater than the rare-earth elements (e.g. Sm), the optimum electron density for plasma-lasing is not accessible for pump-pulses at View the MathML sourceλ=1ω=1μm. This observation explains a fundamental difficulty in saturating the wavelength of plasma-based X-ray lasers below 6.8 nm, unless using 2ω2ω pumping.

Radiative rates for E1, E2, M1, and M2 transitions in Br-like ions with 43≤Z≤50

Energies and lifetimes are reported for the eight Br-like ions with 43≤Z≤50, namely Tc IX, Ru X, Rh XI, Pd XII, Ag XIII, Cd XIV, In XV, and Sn XVI. Results are listed for the lowest 375 levels, which mostly belong to the 4s²4p⁵, 4s²4p⁴4ℓ, 4s4p⁶,4s²4p⁴5ℓ, 4s²4p³4d², 4s4p⁵4ℓ, and 4s4p⁵5ℓ configurations. Extensive configuration interaction among 39 configurations (generating 3990 levels) has been considered and the general-purpose relativistic atomic structure package (grasp) has been adopted for the calculations. Radiative rates are listed for all E1, E2, M1, and M2 transitions involving the lowest 375 levels. Previous experimental and theoretical energies are available for only a few levels of three, namely Ru X, Rh XI and Pd XII. Differences with the measured energies are up to 4% but the present results are an improvement (by up to 0.3 Ryd) in comparison to other recently reported theoretical data. Similarly for radiative rates and lifetimes, prior results are limited to those involving only 31 levels of the 4s²4p⁵, 4s²4p⁴4d, and 4s4p⁶ configurations for the last four ions. Moreover, there are generally no discrepancies with our results, although the larger calculations reported here differ by up to two orders of magnitude for a few transitions.

Radiative rates for E1, E2, M1, and M2 transitions in F-like ions with 37≤Z≤53

Calculations of energy levels, radiative rates and lifetimes are reported for 17 F-like ions with 37≤Z≤53. For brevity, results are only presented among the lowest 113 levels of the 2s²2p⁵, 2s2p⁶, 2s²2p⁴3ℓ, 2s2p⁵3ℓ, and 2p⁶3ℓ configurations, although the calculations have been performed for up to 501 levels in each ion. The general-purpose relativistic atomic structure package (grasp) has been adopted for the calculations, and radiative rates (along with oscillator strengths and line strengths) are listed for all E1, E2, M1, and M2 transitions of the ions. Comparisons are made with earlier available experimental and theoretical energies, although these are limited to only a few levels for most ions. Therefore for additional accuracy assessments, particularly for energy levels, analogous calculations have been performed with the Flexible Atomic Code (fac), for up to 72 259 levels. Limited previous results are available for radiative rates for comparison purposes, and no large discrepancy is observed for any transition and/or ion.

Dielectronic recombination in He-like titanium ions

Dielectronic recombination (DR) has been studied in highly charged He-like Ti ions using an electron beam ion trap. X-rays emitted from radiative recombination (RR) and DR were observed as the electron beam energy was scanned through the resonances. Differential DR resonant strengths were determined by normalizing the DR x-ray intensity to the RR intensity using theoretical RR cross sections. KLn (2 less than or equal to n less than or equal to 5) resonant strengths were determined for He-like Ti ions. The differential resonant strengths were calibrated without reference to any theoretical DR calculations while the electron energy scale was derived with reference to the well-known energy for ionization of the He-like and H-like ions from the ground state. Calibration in this way facilitates a more exacting comparison between theory and experiment than has been reported previously. To facilitate this comparison, total and differential theoretical resonance strengths were calculated. These calculations were found to be in good agreement with the measured results.

Systematic study of visible transitions in Ti-like high Z ions

The magnetic dipole transitions between fine structure levels in the ground term of Ti-like ions, (3d(4)) D-5(2)-D-5(3), were investigated by observation of visible and near-UV light for several elements with atomic numbers from 51 to 78. The wavelengths are compared with theoretical values we recently calculated. The differences between the present calculations and measurements are less than 0.6%. The anomalous wavelength stability predicted by Feldman, Indelicato and Sugar [J. Opt. Soc. Am. B 8, 3 (1991)] was observed. We attribute this anomalous wavelength stability to the transition from LS to JJ coupling and the asymptotic behavior of the transition energies in the intermediate coupling regime.

Dielectronic recombination in He-like, Li-like, and Be-like highly charged ions in the KLL and KLM manifolds

This paper reports a systematic study of the dependence on atomic number of the dielectronic recombination resonance strengths for He-like, Li-like and Be-like ions. Recent measurements of dielectronic recombination resonance strengths for the KLL and KLM manifolds for iron, yttrium, iodine, holmium, and bismuth are also described. The resonance strengths were normalized to calculated electron impact ionization cross sections. The measured resonance strengths generally agree well with theoretical calculations using the distorted wave approximation. However, KLM resonance strength measurements on high atomic number open-shell ions gave higher values than those suggested by calculations. Using recently measured data, along with existing results, scaling laws have been generated as a function of atomic number for He-like, Li-like, and Be-like ions in the KLL and KLM manifolds.

Ground state energy of He isoelectronic sequence treated variationally via Hylleraas-like wavefunction

In this study, the energy for the ground state of helium and a few helium-like ions (Z=1-6) is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.