Coster-Kronig Yields Research Articles

Measurements of L subshell and L shell x‐ray fluorescence cross‐sections for U and Th

AbstractThe Ll, Lα1, 2, Lη, Lβ6, Lβ2, 4, 15, 17, Lβ1, 3, 5, Lβ9, 10, Lγ1, Lγ2, 3, 6, 8, Lγ4,4′ and Lγ5 x‐ray fluorescence cross‐sections for U and Th were measured at 59.5 keV incident photon energy by using theoretical Li subshell photoelectric cross‐sections, fluorescence and Coster–Kronig yields and fractional emission rates, and calculated theoretically by using atomic parameters. The measured values were compared with the theoretical values and experimental results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.

Closing of Coster–Kronig transitions in multiply ionised gold atoms

The paper discusses the effect of closing of L- and M-shell Coster–Kronig (CK) transitions in multiply ionised Au atoms, for which the selected CK transitions become energetically forbidden. This effect plays an important role when the Coster–Kronig energy for single-hole configuration is relatively low, being comparable with a change of the electronic binding energies in multiply ionised atom. We show, by using a simplified model, that for gold the effect of closing of CK transitions occurs for strong L1–L3M4,5 transition for the L1-subshell as well as the M3–M5N6,7 and M4–M5O3,4 CK transitions for the M3- and M4-subshell, respectively. We demonstrate that the discussed effect of closing CK transitions substantially changes the X-ray fluorescence and Coster–Kronig yields and thus has to be considered in interpretation of X-rays excited by heavy ion impact.

The role of multiple ionization and subshell coupling effects inL-shell ionization of Au by oxygen ions

The ionization of L-subshell electrons in gold by the impact of0.4-2.2 MeV amu-1 O ions was studied by observing excitedLγ(L-N, O) x-rays. We demonstrate that both the multipleionization in outer M- and N-shells as well as the couplingeffects in the L-shell play an important role in understandingthe measured L-subshell ionization cross sections. The multipleionization was found to be important in two aspects: first, theanalysis of x-ray energy shifts and line broadening was crucialfor proper interpretation of measured x-ray spectra; second,the additional vacancies in the M- and N-shells substantially influenced the L1-subshell fluorescence and Coster-Kronig (CK)yields, mainly by closing strong L1-L3M4,5 CKtransitions. The data are compared with the simplifiedcoupled-channels calculations using the `coupled-subshell model'(CSM) based on the semiclassical approximation (SCA), whichdescribes both direct Coulomb ionization as well as theL-subshell couplings within the same theoretical approach. Agood agreement of the present data with the theoreticalpredictions based on the discussed SCA-CSM approach is observed.Present findings partly explain the long-standing problem ofinadequate theoretical description of L-shell ionization byheavy ion impact.

L 1–L 3 Coster–Kronig yield for Ir, Pt and Bi

The L 1–L 3 Coster–Kronig yield, f 13, for 77Ir, 78Pt and 83Bi was determined using measured intensities of the Lα X-rays following photoionisation in the L i ( i=1,2,3) subshells in different proportions by the 59.5 keV γ-rays and the characteristic K X-rays of the Br/Sr/Y elements. The measurements involved an Si(Li) detector and photon sources consisting of an 241Am source used in (i) the direct excitation mode and (ii) the secondary excitation mode together with the KBr, SrCO 3 and Y secondary exciters. The measured values of the f 13 yield are 0.467±0.025, 0.527±0.027 and 0.620±0.025 for 77Ir, 78Pt and 83Bi, respectively. These values are found to be substantially smaller than those based on the relativistic Dirac–Hartree–Slater calculations.

L‐shell Coster–Kronig yields for Pb

AbstractThe f13 Coster–Kronig yield for Pb was determined as 0.60±0.03 using measured intensities of the Lα x‐rays emitted following selective ionization in the L3 sub‐shell by the Rb K x‐rays (B < Einc. < B) and of those emitted following ionization in the Li (i = 1, 2, 3) sub‐shells by 59.54 keV γ‐rays (B < Einc. < BK), BK and B being the K shell and Li sub‐shell ionization thresholds of Pb, respectively. The measurements were performed using a 241Am annular source in direct excitation mode and in secondary excitation mode along with an RbNO3 secondary exciter as photon sources and an Si(Li) detector. Measurements of the f12 and f23 Coster–Kronig yields using similar experimental set‐ups are also discussed. It is concluded that the f12 and f23 Coster–Kronig yields for 12 elements with 59 ≤ Z ≤ 90 measured by Oz et al. using a similar experimental set‐up are not reliable. Copyright © 2002 John Wiley & Sons, Ltd.

Determination of L 2 to L 3 Coster–Kronig yield of Pr

Atomic L shell Coster–Kronig yields ( f 23) for Pr was determined semiemprically. Experimental measurements were carried out using a Si(Li) detector and a Fe-55 radioisotope. The values of f 23 of Pr was found using experimental L α X-ray production cross section, theoretical L 2 and L 3 subshell photoionization cross section, L 3 subshell fluorescence yield and L α X-ray fraction in L 3 subshell X-rays. The present result was compared with theoretically predicted and semiempirical value.

Comment on “Coster-KronigL-shell yieldf23of Dy, W, and Bi”

We have analyzed the experimental method used by \ifmmode \mbox{\c{S}}\else \c{S}\fi{}im\ifmmode \mbox{\c{s}}\else \c{s}\fi{}ek [Phys. Rev. A 62, 052517 (2000)] for determination of the L-shell Coster-Kronig yield ${f}_{23}$ in Dy, W, and Bi. The ${f}_{23}$ yield for the target element was deduced from the measured intensity of the $L\ensuremath{\alpha}$ x rays, produced due to ionization of the ${L}_{2}$ and ${L}_{3}$ subshells of the target element by the Kp $(p=\ensuremath{\alpha},\ensuremath{\beta})$ x rays of an exciter ${(E}_{{L}_{3}}l{E}_{K\ensuremath{\alpha}}l{E}_{{L}_{2}}$ and ${E}_{{L}_{2}}l{E}_{K\ensuremath{\beta}}l{E}_{{L}_{1}},$ ${E}_{{L}_{q}}$ is the ${L}_{q}$-subshell ionization threshold for the target element), by subtracting the contribution of those produced by direct ionization of the ${L}_{3}$ subshell. In view of very small magnitude of this difference and the errors associated with the measurements, we infer that the deduced ${f}_{23}$ value must have been associated with enormously large error as compared to the quoted one, \ensuremath{\sim}7%, thus making the measurements inconsequent.

L1–L3 Coster–Kronig and Li (i = 1,2,3) sub‐shell fluorescence yields for Th and U

AbstractThe L1–L3 Coster–Kronig yield, f13, for Th and U was determined using measured intensities of the Lα x‐rays emitted following selective ionization of the L3 sub‐shell by Mo K x‐rays (B < Einc. < B) and of those emitted following ionization of the Li (i = 1,2,3) sub‐shells by the 59.54 keV γ‐rays (B < Einc. < BK), where B is the K shell/Li sub‐shell ionization threshold of the target element. The measurements were performed using an energy‐dispersive x‐ray fluorescence set up involving an Si(Li) detector and photon sources consisting of an 241Am radioactive annular source used in (i) the direct excitation mode and (ii) the secondary excitation mode together with the Mo secondary exciter. In addition, the Li (i = 1,2,3) sub‐shell fluorescence yields (ωi) for Th and U were deduced using our earlier measured x‐ray fluorescence cross‐sections at incident photon energies in the range 17–60 keV and the theoretical photoionization cross‐sections. The measured f13 and ωi yields were compared with the available semi‐empirical values and the theoretical values based on relativistic Hartree–Dirac–Slater (RDHS) calculations. Copyright © 2002 John Wiley & Sons, Ltd.

Comments on “L 2 subshell Coster–Kronig yield at Z=76 and 81”

We have analyzed the experimental method used by Simsek [Nucl. Instr. and Meth. B 173 (2001) 269] for determination of the L 2 subshell Coster–Kronig (CK) yield f 23 in 76Os and 81Tl. It involved measurements of the intensities of the L α X-rays excited by the K X-rays of two secondary exciters which were primarily excited by the 59.5 keV γ-rays from the 241Am radioisotope. The first of the secondary exciters chosen was having the energy ( E K p ) of the K p (p=α, β) X-rays such that B L 3 < E K α < B L 2 < E K β < B L 1 and the second was having the energy of the K X-rays such that E K α < B L 3 and B L 3 < E K β < B L 2 , where B L j is the L j subshell ionization threshold for the target element. The f 23 value was deduced from small intensity (∼1%) of the L α X-rays resulting following the L 2–L 3 CK transitions, which was determined by subtracting the intensity of the L α X-rays produced following the direct ionization of the L 3 subshell from the total intensity of the L α X-rays produced in the case of target excitation by the first secondary exciter. It is concluded that the deduced f 23 value must be associated with an enormously large error as compared to the quoted one ∼20%; thus making the measurements inconsequent. An experimental setup with different sets of secondary exciters is being proposed, which is expected to result in the f 23 values with much lesser error.

Measurement of atomic L shellCoster-Kronig yields (f12, f23 and f13) for someelements in the atomic number range 59⩽Z⩽90

Non-radiative transitions cause changes in the generation of the intensityof the L lines. In order to investigate the physical quantities relevant tothe L lines affected by the non-radiative transitions, experimentalmeasurements were carried out using a Si(Li) x-ray spectrometer. Atomic Lshell Coster-Kronig yields (f12, f13 andf23) for some elements in the atomic number range 59⩽Z⩽90 were determined. These selected measuredsemi-empirical values were also fitted by least squares to polynomials inZ of the form ∑nanZn (except forf13) and compared with theoretical and with earlier fittedvalues.

L 2 sub-shell Coster–Kronig yield at Z=76 and 81

The total Coster–Kronig (CK) transition probability f 23 for the L 2–L 3 transition in Os and Tl have been determined from measurements on L X-rays emitted following photoionization. The measurements were performed using a double reflection experimental set up and a Si(Li) detector. The values of f 23 are 0.142±0.029 and 0.122±0.026 at Z=76 and 81, respectively. We compared our results with theoretically predicted values and semiempirical values.

Coster-KronigL-shell yieldf23of Dy, W, and Bi

The L-shell Coster-Kronig yield ${f}_{23}$ has been measured for Dy, W, and Bi using an annular source double-reflection geometrical setup. Results for Dy, W, and Bi are $0.168\ifmmode\pm\else\textpm\fi{}0.013, 0.146\ifmmode\pm\else\textpm\fi{}0.008,$ and $0.135\ifmmode\pm\else\textpm\fi{}0.011,$ respectively. These results are compared with available theoretical calculations.

Measurement of Coster-Kronig yields of the L2 subshells of Er, Yband Hf

The Coster-Kronig yields, f23, were measured for Er, Yb and Hf using aSi(Li) detector employing the double reflection geometry set up. Theresults (0.159±0.012,0.149±0.013 and 0.138±0.010,respectively) are in good agreement with the theoretically predictedvalues.

Coster-Kronig, fluorescence, and Auger yields of the47AgLsubshells measured through synchrotron photoionization

The decay of individual L subshell vacancies in ${}_{47}\mathrm{Ag}$ has been investigated through selective photoionization by monochromatized synchrotron radiation. By tuning the radiation energy over the L edges, the ionization of particular subshells can be turned off and on. The corresponding subshell ionization cross sections including the subtle structure caused by electron correlations are known from our previous studies. The x-ray fluorescence emitted in the vacancy decay was recorded by a Si (Li) detector. Advanced fitting techniques were employed to extract the intensities of lines originating from different subshells. The extracted line intensities were plotted versus energy of the primary radiation. The relative jumps of the line intensities occurring at the edges directly correspond to the Coster-Kronig yields, whereas the absolute values of the total subshell fluorescence give the fluorescence yields. The following Coster-Kronig yields were obtained: ${f}_{12}=0.14(3),$ ${f}_{13}=0.58(5),$ and ${f}_{23}=0.18(3).$ Adopting the value ${\ensuremath{\omega}}_{3}=0.056(7)$ from literature, the following fluorescence yields are obtained: ${\ensuremath{\omega}}_{1}=0.013(2)$ and ${\ensuremath{\omega}}_{2}=0.067(9).$ The results agree reasonably with theoretical calculations. In particular, the rather large value of ${f}_{13}$ indicates that the ${L}_{1}{\ensuremath{-}L}_{3}{M}_{4,5}$ Coster-Kronig channel is well allowed.

Fluorescence and Coster-Kronig yields of theL1shell in gadolinium

Using a Si(Li) x-ray spectrometer, we have measured the respective fractions of ${L}_{1},$ ${L}_{2},$ and ${L}_{3}$ x rays in the L x-ray spectrum emitted in the ${}^{157}{\mathrm{T}\mathrm{b}\ensuremath{-}}^{157}\mathrm{Gd}$ electron-capture decay. Using, in addition, our previously measured value for the ratio of L and K x rays, we deduce values for the fluorescence and Coster-Kronig yields of the ${L}_{1}$ subshell. These are ${\ensuremath{\omega}}_{1}=0.101\ifmmode\pm\else\textpm\fi{}0.005,$ ${f}_{12}=0.166\ifmmode\pm\else\textpm\fi{}0.020,$ and ${f}_{13}=0.287\ifmmode\pm\else\textpm\fi{}0.014.$ The ${f}_{12}$ and ${f}_{13}$ values are significantly below the predictions of the independent-particle model (IPM). The deduced ${L}_{1}$ level width of 3.7 eV is also significantly below the IPM width of 4.6 eV.

L-subshell Coster-Kronig yields measured with synchrotron radiation

The synchrotron photoionization method was applied to measure L-subshell Coster-Kronig yields. This method is based on the capability of tuning the energy of the synchrotron photons producing a selective subshell ionization. Two foil samples of Yb and Ta were irradiated and their characteristic spectra were recorded. Data were analyzed using a new formalism (based on a matrix representation) for expressing X-ray fluorescence intensities involving Coster-Kronig transitions. The results obtained in this work are f 12 = 0.249 ± 0.021, f 13 = 0.408 ± 0.055 and f 23 = 0.186 ± 0.040 for Yb, and f 12 = 0.168 ± 0.039, f 13 = 0.322 ± 0.072 and f 23 = 0161 ± 0.053 for Ta. These data are very reliable and represent a valuable information for spectroscopists, considering the lack of data for L-shell parameters.

Coster-Kronig yields of the 54Xe L subshells measured through synchrotron photoionization.

The method of selective photoionization of individual subshells by monochromatized synchrotron radiation has been employed to measure all Coster-Kronig yields of the $_{54}\mathrm{Xe}$ L subshells. The energy of the primary radiation was set at about 50 energy points in the range of the L edges. At each setting, the induced Xe L fluorescence and the induced Ar K fluorescence (used for normalization purposes) were recorded simultaneously by a Si(Li) detector. Both Xe and Ar were in the gaseous state. The recorded fluorescence spectra were carefully analyzed with proper modeling of the line tailing due to the intrinsic line profile and the detector line shape. The Coster-Kronig yields were derived by fitting the measured fluorescence intensities versus primary energy with the photoelectric cross sections. The derived yields are sensitive to the precise dependence of the cross sections on primary energy. Evaluations have been performed assuming a smooth power-law dependence and employing corrections for electron-correlation effects, which were estimated from comparative calculations in the independent-particle approximation and linear-response approximation models. Still, the uncertainties of the correlation effects constitute the main contribution to the uncertainties of the derived Coster-Kronig yields. The finally adopted values are ${\mathit{f}}_{12}$=0.12\ifmmode\pm\else\textpm\fi{}0.03, ${\mathit{f}}_{13}$=0.23\ifmmode\pm\else\textpm\fi{}0.04, and ${\mathit{f}}_{23}$=0.14\ifmmode\pm\else\textpm\fi{}0.02.

M -subshell ionization of Th and U by alpha particle bombardment

The M x-rays of Th and U have been produced by alpha particle bombardment in the energy range of 2.5-4.5 MeV. N6,7 → M5(Mα), N6 → M4(Mβ), N5 → M3(Mγ), N4 → M2 and N2 → M1 lines were selected to deduce M-subshell x-ray production cross sections. The radiative transition rates and the Coster-Kronig yields and M-subshell fluorescence yields were used to convert the x-ray production cross sections into M-subshell ionization cross sections. The deduced M-subshell ionization cross sections were compared with the ECPSSR predictions. The discrepancies of our experimental results from the theoretical calculations are discussed.

Thermal ionization effects on inner-shell line emission for Au target heated by intense light ion beams

In order to deduce the experimental beam conditions from the observed x-ray line emission spectrum of high Z elements, atomic radiative data for transition energies and oscillator strengths, ion-atom impact ionization cross sections, Coster–Kronig yields, and fluorescence yield are needed. In this paper, we report on calculations to study the dependence of these atomic data on ionization stage. It has been found that proton impact ionization cross sections decrease slowly with increasing ionization stage, and the fluoresence yields have discrete jumps when the dominant Auger, Coster–Kronig transitions become energetically forbidden. Our study indicates that thermal ionization effects are not important for the dominant K-, L-, and M-line emissions for plasmas with Te ∼ 102 eV.

Reduced L1 level width and Coster-Kronig yields by relaxation and continuum interactions in atomic zinc.

Calculations of the level width \ensuremath{\Gamma}(${\mathit{L}}_{1}$) and the ${\mathit{f}}_{12}$ and ${\mathit{f}}_{13}$ Coster-Kronig yields for atomic zinc have been performed with Dirac-Fock wave functions. For \ensuremath{\Gamma}(${\mathit{L}}_{1}$), a large deviation between theory and evaluated data exists. We include the incomplete orthogonality of the electron orbitals as well as the interchannel interaction of the decaying states. Orbital relaxation reduces the total rates in all groups of the electron-emission spectrum by about 10--20 %. Different, however, is the effect of the continuum interaction. The ${\mathit{L}}_{1\mathrm{\ensuremath{-}}}$${\mathit{L}}_{23}$X Coster-Kronig part of the spectrum is definitely reduced in its intensity, whereas the MM and MN spectra are slightly enhanced. This results in a reduction of Coster-Kronig yields, where for medium and heavy elements considerable discrepancies have been found in comparison to relativistic theory. Briefly, we discuss the consequences of our calculations for heavier elements.