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The KLM+KLN Auger electron spectrum of rubidium in different matrices
А.Kh. Inoyatova,b^ , A. Kovalíka,c^ , L.L. Perevoshchikov a^ , D.V. Filosofova^ , D. Vénos c^ , B.Q. Leed^ , J. Ekmane, A. Baimukhanovaa,f
a (^) Laboratory of Nuclear Problems, JINR, Dubna, Moscow Region, Russian Federation b (^) Institute of Applied Physics, National University, Tashkent, Republic of Uzbekistan c (^) Nuclear Physics Institute of the ASCR, CZ-25068 Řež near Prague, Czech Republic d (^) Department of Nuclear Physics, RSPE, The Australian National University,
Canberra, ACT 2601, Australia e (^) Group for Materials Science and Applied Mathematics, Malmö University, 20506, Malmö,
Sweden d (^) Institute of Nuclear Physics of the Republic of Kazakhstan, Ibragimov St. 1, 050032, Almaty,
Kazakhstan
Keywords:^85 Rb; 85 Sr; KLM-, KLN- Auger transitions; Atomic environment; Chemical shift; Multiconfiguration Dirac-Fock calculations;
Abstract
The KLM+KLN Auger electron spectrum of rubidium (Z=37) emitted in the electron capture decay of radioactive 83 Sr in a polycrystalline platinum matrix and also 85 Sr in polycrystalline platinum and carbon matrices as well as in an evaporated layer onto a carbon backing was experimentally studied in detail for the first time using a combined electrostatic electron spectrometer. Energies, relative intensities, and natural widths of fifteen basic spectrum components were determined and compared with both theoretical predictions and experimental data for krypton (Z=36). Relative spectrum line energies obtained from the semi-empirical calculations in intermediate coupling scheme were found to agree within 3σ with the measured values while disagreement with experiment exceeding 3σ was often observed for values obtained from our multiconfiguration Dirac-Hartree-Fock calculations. The absolute energy of the dominant spectrum component given by the semi-empirical approach agrees within 1σ with the measured value. Shifts of + (0.2±0.2) and - (1.9±0.2) eV were measured for the dominant KLM spectrum components between the 85 Sr sources prepared by vacuum evaporation on and implanted into the carbon foil, respectively, relative to 85 Sr implanted into the platinum foil. A value of (713±2) eV was determined for the energy difference of the dominant components of the KLM+KLN Auger electron spectra of rubidium and krypton generated in the polycrystalline platinum matrix. From the detailed analysis of the measured data and available theoretical results, the general conclusion can be drawn that the proper description of the KLM+KLN Auger electron spectrum for Z around 37 should still be based on intermediate coupling of angular momenta taking into account relativistic effects.
1. Introduction
The KLL Auger group is the most intense and the simplest (only nine basic spectrum components) among the K Auger groups. Consequently, it has been extensively studied both theoretically and experimentally in the past. With increasing energy, intensity of other K Auger groups drastically decreases while their complexity substantially increases (also due to narrower energy intervals they occupy in comparison with the KLL group). Thus in the atomic number region Z ~ 40, the total intensity of the KLM group amounts to only about 35 % of that of the corresponding KLL Auger group (see, e.g., [1,2]) and its full structure consists of 36 close lying components according to the intermediate coupling calculations [3,4] (including twelve doublets and three quartets) of very different intensities. Moreover, many components cannot be resolved experimentally in principle due to their small energy separations in comparison with natural
component widths. As a result, the KLM Auger spectrum actually consists of several overlapping line groups. Even their experimental separation needs application of very high instrumental resolution power and very thin (several monolayers) radioactive sources (if the KLM Auger spectrum is studied in the radioactive decay) to prevent line broadening due to inelastic electron scattering in the source material. The predicted structure [3,4] of the KLM Auger spectrum was “confirmed” in several measurements only in the sense that some KLM lines were observed to be broader than expected on the basis of the natural widths of the atomic shells participating in the transitions and/or slightly “deformed”. Intensity of the KLN Auger group in the Z~40 region reaches only a few percent of the corresponding KLL group (see, e.g., [2]). Nevertheless, the KLN group complicated experimental investigation of the KLM Auger spectrum due to partial overlapping of these two groups. The energy interval of the overlap depends on atomic number Z and increases with it. The complexity of the KLM+KLN Auger spectra and limitations of available electron spectroscopic technique allowed successful experimental research of these spectra mainly in the high Z region in the past. However, radiationless deexcitation of K-shell vacancies dominates in light elements where, moreover, results of the available KLM transition intensity calculations [2,3,5-7] differ substantially from each other (see also Fig. 1). The differences are partly caused by various treatment of relativistic effects and/or coupling schemes. Thus the calculations [3,5] were performed in intermediate-coupling scheme but only without consideration of relativistic effects while the calculations in jj-coupling were evaluated in both relativistic [2,7] and non- relativistic [6] approximations. In contrast, the Auger-electron energies are satisfactorily described by, e.g., widely used semi-empirical calculations [4] based on intermediate-coupling and experimental electron subshell binding energies. So far the KLM Auger spectra of only twelve different elements in the atomic number region 18 < Z < 45 were measured in detail, namely Z=23 [8,9,10], 24 [9,10], 25 [10,11], 26 [10,12,13], 28 [14], 29 [15], 30 [16], 31 [8], 32 [17], 33 [18], 35 [19,20], and 36 [21]. There is also a lack of experimental data on the influence of atomic environments on the KLM Auger spectra especially for medium and heavy elements (i.e. involving atomic core levels). Such data are of considerable importance as for basic research in this field as for interpretation of weak effects in extremely complex experimental Auger electron spectra. Moreover, it was found, e.g., in the experimental investigations [22,23] that energies of the KLL Auger electrons are a quite sensitive probe of changes in local atomic environment. In Ref. [22], the krypton KLL Auger spectrum generated by nuclear decay of 83 Rb in two different solid hosts (a bulk of a high purity polycrystalline Pt foil and a vacuum evaporated layer on the same type of Pt foil) was studied, while the KLL Auger spectrum of rubidium following the 83 Sr and 85 Sr decays in three different solid hosts (bulks of a high purity polycrystalline platinum and carbon foils and a vacuum evaporated layer on the same type of carbon foil) was investigated in Ref. [23]. This type of information is desirable also in some present neutrino physics experiments. In the neutrino project KATRIN [24], for example, a long-term stability of the energy scale of an electrostatic retardation β-ray spectrometer on the ±3 ppm level (i. e., ±60 meV at 18.6 keV) for at least two months of continuous measurements is required in order to achieve the intended sensitivity of 0.2 eV in searching for the electron antineutrino mass in tritium beta spectrum. In this regard, applicability of the K conversion electron line (kinetic energy of 17.8 keV) of the 32.2 keV E3 nuclear transition in 83mKr generated in the electron capture (EC) decay of 83 Rb for monitoring of the KATRIN energy scale was extensively investigated in the works [25,26]. The electron sources prepared by ion implantation of 83 Rb into metallic substrates were found to be most suitable. Optimization with respect to the substrate material and implantation conditions requires additional extensive experimental investigations of the influence of local physicochemical environment of 83 Rb atoms. Information on low energy electron spectra emitted in radioactive decay under real condition can also be helpful for another neutrino project, namely “Electron Capture 163 Ho experiment” (ECHo) [27,28] based on high precision and high statistics microcalorimetric measurements of the 163 Ho electron capture spectrum. An improvement of the theoretical description of this spectrum, in
Corresponding amounts of ions were experimentally proved in the contamination layers in the implantation of 83 Rb into the similar Pt foil [25,26]. After the preparation, the sources were exposed to air during transfer to the electron spectrometer and the 83 Sr and 85 Sr ions in the contamination layers were thus bound with oxygen in all possible forms (oxides, hydroxides, carbonates, hydrocarbonates, etc.) and had the oxidation number +2 (as in the case of the 85 Sr source prepared by vacuum evaporation on the carbon substrate, see below the Section 2.1.2.). These contamination layers, however, were not removed from the surface of the Pt substrates (by ion sputtering or any other means) before the electron spectrum measurements.
2.1.2. Thermal vacuum evaporation deposition
Several drops of the strontium fraction were transferred to a Ta evaporation boat (annealed at about 1300 °C) and dried up. To remove possible volatile organic compounds from the chemical separation procedure of strontium (see Section 2.1.1.), the Ta evaporation boat with the deposited activity was first preheated at 800 °C for about 30 s. The source backing (a mechanically cleansed 150 μm thick polycrystalline carbon foil, 12 mm in diameter) was shielded all along the procedure. The source evaporation through an 8 mm diameter circular opening in a mask (fitting tightly to the foil surface) took place at 1400 °C for several seconds. In order to improve homogeneity of the evaporated layer, the source backing with the mask rotated around their common axis at a speed of 3000 turns/min at a distance of about 8 mm from the Ta evaporation boat. No visible effects were observed on the surface of the source backing after the evaporation. Two different (^85) Sr sources were prepared with activities of 2.3 and 1.1 MBq just after their preparation.
The amount of the 85 Sr atoms in each of the prepared sources was several nanograms (i.e. too small to be easily examined by, e.g., the standard XPS method). It is therefore questionable to apply general chemistry terms in such cases. Moreover, the daughter 85 Rb isotope is generated in the electron capture decay of the parent 85 Sr atoms. Thus even if the “chemical state” of the 85 Sr atoms in the sources can be somehow described, it may not be the same for the 85 Rb atoms. Generally, the “chemical state” of the 85 Rb atoms can be characterized as “impurity state” in the parent 85 Sr matrices. The exact chemical state of 85 Sr in the deposited layers in vacuum after the preparation was unknown. Because the prepared 85 Sr sources were exposed to air during their transfer to the electron spectrometer, the 85 Sr ions were bound with oxygen in all possible forms (oxides, hydroxides, carbonates, hydrocarbonates, etc. of different proportions) due to the extreme strontium reactivity and had the oxidation numbers +2. The overwhelming majority of the parent (^85) Sr atoms were most likely in the SrCO 3 chemical form. This statement is based on: (i) specific
chemical properties of strontium, (ii) its known macro-chemistry, (iii) the inner self-consistency of the physicochemical methods used for the preparation of the sources, and (iv) the conditions of their treatment. After the 85 Sr EC decay, the daughter 85 Rb atoms were stabilized in the above 85 Sr matrices. The 85 Rb ions thus were most likely bound with oxygen atoms in anions of all possible relevant forms (О2-, OH-, CO 3 2-, HCO 3 - , etc.). Contrary to 85 Sr, they had the oxidation number +1. It is also supported by similar experiments from the past performed, e.g., with 99mTc (see, e.g., [36- 38]).
2.2. Measurements and energy calibration
An electrostatic electron spectrometer [39] was used for the electron spectra measurements. As can be seen from Fig. 5, the spectrometer combines an integral spectrometer (a retarding sphere) with differential one (double-pass cylindrical mirror energy analyzer). Several operating modes are available. In the basic mode, the scanning retarding positive voltage being applied to the electron source (1), while the retarding sphere (2) is grounded. Passing the annular conic slit (3), the slowed-down electrons enter the double pass cylindrical energy analyzer. Their energies are analyzed by the constant negative voltage (determining the absolute instrumental resolution of the spectrometer) applied to the outer coaxial cylinder (5) of the cylindrical analyzer while the inner
cylinder (4) is grounded. Four circular slits (3,6) on the inner cylinder delimit the electron beam which strikes the detector (a windowless channel electron multiplier) in the second focus (F2). The detector is protected against the direct radiation from the electron source by two lead absorbers placed in the inner cylinder. The spectra were measured in sweeps. The absolute instrumental resolution and the scanning step applied depended on the intensity of the radioactive source being measured. Examples of the measured spectra are shown in Figs. 6-8. For calibration of the spectrometer energy scale, seventeen low energy conversion electron lines (listed in parentheses) were applied. Twelve of them are emitted in nuclear transitions in (^169) Tm (generated in the EC decay of 169 Yb (T1/2=32.02 d)) with energies Eγ = 8.41017(15) [41]
(M (^) 1,2 , N1,3 ), 20.74370(16) [41] (L1-3 , M1-3 , N 1 ), and 63.12044(3) keV [41] (K), while another five (K, L1-3 , M 1 ) in the 14.41300(15) keV [42] nuclear transition in 57 Fe (originated from the EC decay of 57 Co (T1/2 =271.7 d)). Energies EF (i) ( i is the atomic subshell index) of these calibration lines related to the Fermi level were evaluated by means of the following equation making use of the experimental Fe and Tm electron binding energies Eb,F (i) [43] (related to the Fermi level):
EF (i) = Eγ – Eb,F (i) – Erec (i) (1)
The recoil kinetic energy Erec (i) of an atom after the emission of the conversion electron was calculated to be less than 0.1 eV in all our cases. Sources of the parent 169 Yb and 57 Co isotopes for calibration were prepared by vacuum evaporation deposition (see above Section 2.1.2.) on polycrystalline carbon substrates. Such type of sources should guarantee [44] very similar environments for the daughter 169 Tm and 57 Fe atoms as those for which the Tm and Fe electron binding energies [43] were determined. Nevertheless, we verified the influence of possible differences between real and tabulated [43] electron binding energies on the energy calibration. Maximum measured chemical shifts of the valence electron binding energies of about 2 and 4 eV [45] for Tm and Fe, respectively, were taken into account. The influence of these shifts on the energy calibration was found to be well below the standard deviations of the measured absolute energies of the studied electron lines quoted in Table 1 and in the text.
2.3. Spectra evaluation
To decompose the measured spectra into individual components, the method described in Ref. [46] was employed. The individual Auger-electron line shape was expressed as the convolution of a Gaussian (representing the spectrometer response function for monoenergetic electrons) and an artificially created function based on a Lorentzian. The Lorentzian characterizes the natural energy distribution of the investigated electrons leaving atoms. It is, however, deformed on its low energy slope due to inelastic scattering of the electrons in the source material (surface and bulk plasmon excitations, shake-up/-off effects, lattice vibrations (phonon excitations), etc.). The inelastically scattered electrons exhibit rather complicated energy structure. It consists of a wide discrete energy-loss peak (DEL, see, e.g., Fig. 6) generated mainly by electrons that suffered from surface and bulk plasmon excitations and a very long low-energy tail (going down to the “zero” energy) created by electrons which undergo multiple inelastic scattering. (In contrast, the electrons which left the electron source without any energy loss create the so-called zero-loss (or no-loss) peak which can be described by a convolution of a Gaussian and a Lorentzian resulting in the Voigt function.) Both, the position and width of the discrete energy loss peak are given by properties of the source material. However, its intensity depends on a ratio of the energy dependent mean free path for inelastic electron scattering and the effective source thickness. A description of the energy loss spectra with sufficient accuracy is a very complicated task also due to insufficient information on the measured sources including their thickness, composition, homogeneity, structure, etc. (It should be, however, noted that some progress is being made in this field, see, e.g., Refs. [35, 47- 50].) Therefore, we applied the Monte Carlo approach in the spectra evaluation. It consists in manifold fitting of the measured electron spectra with random variations of the Auger-electron line shape (the same for all fitted lines in the evaluated energy interval) in its energy loss region
was included, corresponding to the 5s 2 valence-shell configuration of a neutral Sr atom. The results obtained are presented in Tables 1 and 2 and in the text.
4. Results and discussion
As can be seen from Fig. 6, we were able to reasonably fit only fifteen components to the measured KLM+KLN Auger spectrum. Their identification was performed on the basis of the widely used semi-empirical Auger-electron energies [4]. In some cases, however, reliability of the results obtained was greatly reduced due to a strong correlation of the fitted parameters. This concerns, in particular, complex multicomponent groups like KL 1 M (^) 2,3 and KL 3 M 1 +KL 2 M (^) 2,. It is seen from Fig. 7 that the measured dominant KL2,3 M (^) 2,3 line groups exhibit very similar structure for the 85 Sr sources prepared by ion implantation in Pt and C substrates despite significantly different substrate atomic numbers Z and ion implantation profiles (see Fig. 4). On the other hand, the discrete energy loss peaks of the spectrum components are much higher for the (^85) Sr source prepared by vacuum evaporation deposition on the carbon foil than for the above
implanted sources. This difference can only be explained by a greater effective thickness for the inelastic electron scattering in the case of the evaporated 85 Sr source.
4.1. Transition energies
In the evaluation, the absolute energy (related to the Fermi level) of the dominant and well separated KL 3 M 2 (^3 P 2 ,^3 S 1 )+KL 3 M 3 (^3 P 0 ) spectral component (line No. 9) as well as energies of other spectral components relative to this one were determined. They are given in Table 1 together with results of both the semi-empirical energy calculations [4] for rubidium (4 th^ -6 th^ columns) and the ab initio calculations performed in the present work for our specific case, i.e., for the KLM+KLN Auger transitions in 85 Rb following the electron capture decay of 85 Sr (7th^ and 8 th^ columns). In the case of the semi-empirical calculations [4], the relative energies are given as for the dominant components of the fitted line groups (4th^ column) as for the fitted line group energies determined as weighted mean of the semi-empirical transition energies [4] of the corresponding line group components using the theoretical transition intensities [3] (6th^ column). It is seen from Table 1 that the relative semi-empirical energies [4] agree with the measured values within 3σ (see 5th^ column) while disagreement with experiment exceeding 3σ is often observed for values obtained from our ab initio calculations (see the last column). Moreover, the energy interval occupied by the KLM spectrum (i.e. from the first to the last spectrum lines) calculated in the present work is wider by (8.2±1.1) eV than the experimental one (485.1 eV contrary to (476.9±1.1) eV). Most of the discrepancy between the calculated energies in this work and the semi-empirical or observed energies can most likely be attributed to electron correlation effects, which are not considered in the present case (as mentioned in Section 3). It should be, however, noted that the value of 9.5 eV obtained from our calculations for the separation of the KL 1 M 2 and KL 1 M 3 spectrum lines (i.e. the spectrum components Nos. 2 and 3) closely matches the experimental one (9.6±0.6) eV. Values of 8.4 eV (determined from the dominant transition energies) and 8.8 eV (determined from the weighted mean energies of these two components) were obtained from the semi-empirical calculations [4]. In the case of the separation of the KL 3 M 2 (^3 P 2 ,^3 S 1 )+KL 3 M 3 (^3 P 0 ) and KL 3 M 3 (^3 D 2 ,^3 D 3 ,^1 P 1 ) components (fitted lines Nos. 9 and 10), the both semi-empirical values [4] 5.9 eV (dominant transition energies) and 6.2 eV (weighted mean energies) as well as our theoretical value of 6.7 eV matched well with the experimental value of (6.1±0.5) eV. As can be seen from Table 1, the same situation is observed for the separation of the most intense spectrum components KL 2 M 3 (^1 D 2 ,^3 D 1 )+KL 2 M 2 (^3 P 1 ) and KL 3 M 2 (^3 P 2 ,^3 S 1 )+KL 3 M 3 (^3 P 0 ) (fitted lines Nos. 7 and 9). As can be seen from Table 1, the absolute energy (related to the Fermi level) of the dominant fitted component (No. 9) determined as the weighted mean of the semi-empirical energies [4] and the theoretical intensities [3] of the KL 3 M 2 (^3 P 2 ,^3 S 1 )+KL 3 M 3 (^3 P 0 ) Auger transitions (the 6th^ column) is identical with the absolute energy of the KL 3 M 2 (^3 P 2 ) Auger transition
as the rates [3] for the KL 3 M 3 (^3 P 0 ) and KL 3 M 2 (^3 S 1 ) transitions reach only 15 and < 1 per cents, respectively, of the KL 3 M 2 (^3 P 2 ) term. This value agrees very well (within 1σ) with the measured absolute energy (also related to The Fermi level) of the fitted component No. 9. Contrary, our calculated value for the KL 3 M 2 (^3 P 2 ) transition is lower by (14.8±1.3) eV though it is related to the vacuum level. If the work function of 2.6 eV [56] for the polycrystalline strontium (the probable matrix of the daughter rubidium atoms) is taken into account, then the discrepancy found is enlarged up to (17.4±1.3) eV. (There are, however, sound reasons to suppose that the work function of our spectrometer should be taken into account, i.e. that one of aluminum oxide which amounts to about 4 eV). But application of the correction [4] of the Auger transition energies for the solid-state effect using the value of 6.0 eV [4] for the solid-state correction term of strontium increases our calculated energy of the KL 3 M 2 (^3 P 2 ) transition to 13110.8 eV, i.e. the above discrepancy is reduced to (11.4±1.3) eV. Further increase of our calculated KLM+KLN Auger transition energies in rubidium (resulting in improvement of the agreement between our energy calculations and experimental values) is expected when experimental electron binding energies rather than the ab initio binding energies (which was adopted in our calculations) are used. Quite different situation was discovered [23] in the case of the KLL Auger spectrum of rubidium measured with the same evaporated source on the polycrystalline carbon foil. The measured absolute energy (related to the Fermi level) of the dominant KL 2 L 3 (^1 D 2 ) transition was found to be higher by (6.1±1.6) eV than the semi-empirical prediction [4]. A conclusion based on various facts was made that the main cause of the higher experimental transition energy stems from the so-called “atomic structure effect” (see, e.g., [57]) which was revealed in KX-rays of holmium for the first time. In this context, higher energies of the K Auger transitions following the EC decay can be explained as a result of additional screening of the daughter nucleus by a “spectator” electron because the 10 -16^ -10-17^ s lifetime of the 1 s atomic hole produced in the EC decay is so short that the intermediate state has an outer-electron configuration close to that of the parent atom. In X-rays, the effect is the most pronounced for rare earth elements and especially for those from the 4 f and 5 f groups. In the case of rubidium which belongs to the “5 s elements”, the influence of the “atomic structure effect” is expected to be less pronounced for the K Auger transition energies. According to our calculations, the absolute energies of the KLM+KLN Auger transitions following the creation of initial vacancies by the internal conversion processes in the 85mRb daughter decays are lower by (6.9±0.1) eV than those following the electron capture decay
of 85 Sr. The uncertainty in the shift is the standard deviation of the differences in peak positions in folded line spectra. The folding procedure ensure that the number of dominant components is the same in the two spectra, although the number of unfolded lines differ substantially. However, the different reference level used in our calculations and the different phase of matter considered did not enable us to investigate the influence of the “atomic structure effect” on the KLM+KLN Auger spectrum emitted in the 83 Sr decay. As mentioned above (see Section 2.1), three different 85 Sr sources (namely C (^) evap, Pt (^) impl, and C (^) impl) were prepared in order to investigate the influence of the physicochemical environment of the daughter 85 Rb atoms on the KLM spectrum of Auger electrons emitted in their deexcitation. The dominant line groups of the spectra measured with these sources are compared in Fig. 7. It is seen from the figure that the positions of the two most intense components KL 2 M 3 (^1 D 2 ,^3 D 1 )+KL 2 M 2 (^3 P 1 ) (No. 7) and KL 3 M 2 (^3 P 2 ,^3 S 1 )+KL 3 M 3 (^3 P 0 ) (No. 9) are almost the same for the C (^) evap and Pt (^) impl while those for the C (^) impl are slightly lower. From the energies of these two lines as well as the KL 3 M 3 (^3 D 2 ,^3 D 3 ,^1 P 1 ) one (No. 10) we determined the energy shifts between the three spectra to be (Pt impl - C evap ) = - (0.2±0.2) eV and (Pt impl – C impl) = + (1.9±0.2) eV. These values agree within 3σ with those of - (0.7±0.1) and + (2.2±0.1) eV [23], respectively, obtained for the rubidium KLL Auger spectra following the EC decay of 85 Sr in the same sources. Because of the significantly lower atomic number (and hence also much lower probability for inelastic electron backscattering resulting in reduction of the low-energy tails of electron lines), the carbon substrate would be more suitable for the super stable calibration 83 Rb/83mKr sources in the KATRIN project than the platinum one. But the experimental data on the KLL [23] and
intensities. So it can be concluded that transition intensities of the rubidium and krypton KLM+KLN Auger electron spectra fit well with each other. A comparison between the theoretical results and the experimental data indicates that the relativistic calculations ([2] and the present work) reproduce better the measured intensities for the KL 1 M 1 and KL 1 M (^) 2,3 lines than the non-relativistic ones. This can be attributed [58] to contributions from the relativistic effects which play an important role for the K Auger transitions resulting in two or one s -vacancies in any shell. On the other hand, the relativistic calculations [2] in jj-coupling fail in the intensity description of the dominant fitted components (Nos. 7 and 9). While the predictions of both the non-relativistic calculations [5] and the present calculations in intermediate coupling scheme for these two components agree with the measured data within 2σ, the relativistic values [2] jj-coupling are lower by 4σ. It is known (see, e.g., [59]) that intensities of the KL 1 M (^) 2,3 , KL 2 M (^) 2,3 , and KL 3 M (^) 2,3 Auger transitions are very sensitive to the coupling of angular momenta used in the calculations. Because the calculations [2,5, this work] differ in treating of the relativistic effects, we followed a recommendation [58] and compared theoretical and experimental values for the KL 3 M (^) 2,3 /KL 2 M (^) 2, transition intensity ratio in order to investigate this effect on the rubidium KLM Auger electron spectrum. It was shown in Ref. [58] that the KL2,3 M (^) 2,3 transitions are negligibly influenced by the relativistic effects but the KL 3 M (^) 2,3 /KL 2 M (^) 2,3 transition intensity ratio is very sensitive to the coupling type. As can be seen from Table 2 (the last row) and Fig. 1 (the open circle) that the KL 3 M (^) 2,3 /KL 2 M (^) 2,3 intensity ratio derived from the intermediate coupling calculations [5, this work] agrees with the experimental value within 1σ while the jj-coupling prediction [2] differ from it by 17 σ. It is, moreover, seen from Fig. 1 that new and precise experimental data on the KL 3 M (^) 2,3 /KL 2 M (^) 2,3 intensity ratio in the atomic number region 37<Z are especially needed to find the upper Z limit where the intermediate coupling scheme should be applied in the calculations of the KLM transition rates. The above performed comparison of the theoretical and experimental KLM transition intensities leads to the general conclusion that the MCDHF calculations accomplished in the present work are the most successful in the prediction of the KLM Auger transition rates for rubidium.
4.4. Natural widths of the spectrum components
Natural widths of some fitted spectrum components of the KLM+KLN Auger electron
spectrum of 85 Rb (measured with the 85 Sr source prepared by vacuum evaporation deposition on the polycrystalline carbon foil) are compared in Table 3 with the estimated values obtained as a
sum of the corresponding experimental rubidium atomic level widths based on the data [60-62].
Generally, reasonable agreement is seen between the measured and estimated values mainly due
to the large uncertainties of the former ones. This finding is somewhat surprising because all fitted
spectrum components are multiplets and, moreover, some of them (e.g., Nos. 4, 7, 9, 10) are
expected to exhibit [3,4] very complicated structure. Thus, e.g., the dominant KL 3 M (^) 2,3 spectrum
line group consists of six components [4]: the KL 3 M 2 line is a doublet (terms 3 P 2 ,^3 S 1 ) while the
KL 3 M 3 one is a quartet (terms 3 P 0 , 3 D 2 , 3 D 3 , and 1 P 1 ). These six terms occupy an energy interval of 13.9 eV [4] in such a way that the 3 P 0 , 3 P 2 , and 3 S 1 terms are grouped in the 0.8 eV interval and
the others in 7.9 eV with a gap of 5.2 eV between these two groups. According to the non-
relativistic intermediate coupling transition intensity calculations [3], intensities of the
KL 3 M 3 (^3 D 3 , 1 P 1 ) terms are negligible (about 2% of the total KL 3 M 3 line intensity) and those of the
KL 3 M 3 (^3 P 0 ) and KL 3 M 3 (^3 P 2 ) terms amount to 39 and 59 % of the total KL 3 M 3 transition intensity,
respectively. Since the intensity of the KL 3 M 2 (^3 S 1 ) term is also insignificant (less than 1% [3] of
the total KL 3 M 2 transition intensity), the six KL 3 M (^) 2,3 components are reduced to three ones. As
the energies of the KL 3 M 3 (^3 P 0 ) and KL 3 M 2 (^3 P 2 ) terms differ only by 0.1 eV [4] (and thus cannot
be resolved experimentally in principle due to their natural widths, see Table 3), the KL 3 M (^) 2,3 line
group should be seen in an experimental spectrum taken with high instrumental resolution as two lines with the following predicted “KL 3 M 3 ”/”KL 3 M 2 ” intensity ratios (see also Table 2, the next-
to-last row): 1.09 [2] (jj-coupling), 0.20 [3] (intermediate coupling), 0.38 [this work] (intermediate
coupling), 0.49 [5] (intermediate coupling) (or 0.25 after a “redistribution” of the KL 3 M (^) 2,3 terms
between the fitted components Nos. 9 and 10). This conclusion is confirmed by the results of the
decomposition of our spectrum (see Fig. 6) including the natural widths of the two fitted
components (Nos. 9 and 10) into the KL 3 M (^) 2,3 line group which agree well with the expected values
(see Table 3) for the single lines without any broadening. Taking into account this finding and
reasonable (within 2σ) agreements of the “KL 3 M 3 ”/”KL 3 M 2 ” intensity ratios obtained from the calculations based on the intermediate-coupling scheme with the experimental value of 0.28(5) for
Rb (see Table 2), one should state again that the KLM Auger electron spectrum must be described
within the frame of the intermediate-coupling scheme. The same conclusion can be drawn from a
detailed analysis of the KL 2 M (^) 2,3 line group.
5. Conclusion
An experimental investigation of the KLM+KLN Auger electron spectrum is very
complicated due to its low intensity and high complexity. However, the low energy nuclear electron spectroscopy method for solid radioactive samples developed in our laboratory enabled
us to perform a detailed analysis of the KLM+KLN Auger spectrum of rubidium (Z=37) following
the electron capture decay of radioactive 83 Sr and 85 Sr incorporated in different matrices. A general
conclusion was drawn from the detailed analysis of the measured data and available theoretical
results that the proper description of the KLM+KLN Auger electron spectrum for Z around 37
should still be based on intermediate coupling of angular momenta taking into account relativistic
effects. To find the upper Z limit for application of this approach, new precise experimental data particularly on the KL 3 M (^) 2,3 /KL 2 M (^) 2,3 transition intensity ratio (which was found to be very
sensitive to the coupling type) are needed in the atomic number region 37< Z <60. The results
obtained on energy shifts of the dominant spectrum components between different matrices clearly
indicate that, among others, the choice of the host matrix for super stable calibration 83 Rb/83mKr
electron sources for the KATRIN neutrino mass experiment plays an important role and should,
therefore, be thoroughly investigated.
Acknowledgement
The work was partly supported by grants GACR P 203/12/1896 and RFFI 13-02-00756.
Table 1 : ( continued )
e (^) -340.8(7) means – (340.8 ± 0.7). f (^) The absolute energy related to the Fermi level. g (^) The absolute energy of the KL 3 M 2 ( (^3) P 2 , (^3) S 1 )+KL 3 M 3 ( (^3) P 0 ) line group determined as the weighted mean of the semi-
empirical transition energies [4] and the theoretical transition intensities [3] of the corresponding line group components. h (^) The absolute energy related to the vacuum level.
DL - Differences between the values obtained from the semi-empirical calculations [4] for the dominant components and the experimental data. DTW – Differences between the values obtained from the present calculations for the dominant components and the experimental data.
Table 2 The measured relative intensities (in %) of the KLM+KLN Auger transitions in 85 Rb following the electron capture decay of (^85) Sr evaporated on a polycrystalline carbon foil (C (^) evap ) compared with results of the calculations [2,5] and those performed in
the present work.
Line №
Transition(s)a^ Experiment Theoryc This workb^ This work c^ Ref. [21] c^ (Kr) Ref. [2]d^ Ref. [5] This work 1 KL 1 M 1 (^1 S 0 ,^3 S 1 )e^ 8.3(5)f^ 10.0(6) 9.8(3) 9.9 8.2 10. 2 KL 1 M 2 (^1 P 1 ,^3 P 0 ) 7.9(8) 9.5(9) 17.0(13) 7.8(4) 17.1(6) 5.6 6.4 7. 3 KL 1 M 3 (^3 P 1 ,^3 P 2 ) 6.2(8) 7.5(9) 9.3(4) 9.2 7.6 8. 4 KL 2 M 1 (^1 P 1 ,^3 P 0 )+ KL 1 M (^) 4,
5 KL 3 M 1 (^3 P 1 ,^3 P 2 ) 4.4(8) 5.3(9) 9.5(13) 5.9(2) 8.4(3) 8.5 7.7 7.
6 KL 2 M 2 (^1 S 0 ) 3.5(8) 4.2(9) 2.5(2) 1.7 2.4 2.
7 KL 2 M 3 (^1 D 2 ,^3 D 1 )+
KL 2 M 2 (^3 P 1 )
8 KL 1 N 2.4(4) 2.9(5)
25.8(46)g
14.6(25)g^ 21.3g
28.7g 9 KL 3 M 2 (^3 P 2 ,^3 S 1 )+ KL 3 M 3 (^3 P 0 )
10 KL 3 M 3 (^3 D 2 ,^3 D 3 ,^1 P 1 ) 6.7(12) 8.1(14) 6.7(6) 22.1 12.3 9.
11 KL 2 M 4,5 2.6(3) 3.1(4) 3.3(2) 2.6 3.
12 KL 3 M 4,5 3.6(3) 4.3(4) 4.7(3) 6.0 4.
13 KL 2 N2,3 2.5(3) 3.0(4)
26.9(37)g
24.7(12)g^ 15.3g
25.3g 14 KL 3 N 1 0.7(2) 0.8(2) 7.5(22)g
6.9(6)g^ 10.6g
9.2g 15 KL 3 N2,3 3.7(3) 4.5(4) 39.8(41)g
49.4(19)g^ 48.2g
36.8g
10/9 “KL 3 M 3 ”/”KL 3 M 2 ” h^ 0.28(5) 0.23(2) 1.09 0.49 0. KL 3 M (^) 2,3 /KL 2 M (^) 2,3 1.30(5)i^ 1.30(3) 2.13 1.32 1.
Table 3
Natural widths (in eV) of some fitted spectrum components of the KLM+KLN Auger electron spectrum of 85 Rb emitted in the electron capture decay of 85 Sr evaporated on a polycrystalline carbon foil.
Line № Spectrum component This work Estimateda 1 KL 1 M 1 11.6(18)b^ 10.7(11) 2 KL 1 M 2 8.5(25) 8.6(10) 3 KL 1 M 3 7.5(25) 8.7(10) 4 KL 2 M 1 (^1 P 1 ,^3 P 0 )+KL 1 M (^) 4,5 9(3) 8.3(6)c 7 KL 2 M 3 (^1 D 2 ,^3 D 1 )+KL 2 M 2 (^3 P 1 ) 5.3(7) 6.3(5)d 9 KL 3 M 2 (^3 P 2 ,^3 S 1 )+KL 3 M 3 (^3 P 0 ) 4.9(13) 6.1(5)e 10 KL 3 M 3 (^3 D 2 ,^3 D 3 ,^1 P 1 ) 5.9(13) 6.2(5)f 11 KL 2 M (^) 4,5 5.6(19) 4.4(5) 13 KL 2 N2,3 8.5(25) 15 KL 3 N2,3 3.3(11)
a (^) A sum of natural widths of the atomic levels participating in the
Auger transition. b (^) 11.6(18) means 11.6 ± 1.8. c (^) A value evaluated for the KL 2 M 1 transition. d (^) A value evaluated for the KL 2 M 3 transition. e (^) A value evaluated for the KL 3 M 2 transition. f (^) A value evaluated for the KL 3 M 3 transition.
References
[1] M.I. Babenkov, B.V. Bobykin, V.K. Petukhov, Izv. Akad. Nauk. SSSR, Ser. Fiz., 36 (1972) 2139.
[2] M.H. Chen, B. Crasemann, H. Mark, At. Data Nucl. Data Tables, 24 (1979) 13.
[3] W.N. Asaad, E.H.S. Burhop, Proc. Phys. Soc., 71 (1958) 369.
[4] F.P. Larkins, At. Data Nucl. Data Tables, 20 (1977) 311. (DOI: 10.1016/0092-640X(77)90024-9)
[5] M.I. Babenkov, V.S. Zhdanov, S.A. Starodubov, in Proc. 36th Conf. Nuclear Spectroscopy and Nuclear Structure, 1986, Nauka, Leningrad, p. 268 (in Russian).
[6] P.V. Rao, M.H. Chen, B. Crasemann, Phys. Rev. A, 5 (1972) 997.
[7] C.P. Bhalla, H.R. Rosner, D.J. Ramsdale, J. Phys. B, 3 (1970) 1232.
[8] M.I. Babenkov, V.S. Zhdanov, S.A. Starodubov, JETP Letters, 45 (1987) 148.
[9] A. Kovalík, M. Ryšavý, V. Brabec, O. Dragoun, A. Inoyatov, A. F. Novgorodov, Ts. Vylov I.A.Prostakov: Physica Scripta, 37 (1988) 871.
[10] A. Némethy, L. Kövér, I. Cserny, D. Varga, P.B. Barna, J. Electron Spectrosc. Relat. Phenom., 82 (1996) 31.
[11] A. Kovalík, V. Brabec, J. Novák, O. Dragoun, V.M. Gorozhankin, A.F. Novgorodov, Ts. Vylov, J. Electron Spectrosc. Relat. Phenom., 50 (1990) 89.
[12] A. Kovalík, A. Inoyatov, A.F. Novgorodov, V. Brabec, M. Ryšavý, Ts. Vylov, O. Dragoun, A. Minkova, J. Phys. B: At. Mol. Phys., 20 (1987) 3997.
[13] A. Kovalík, V.M. Gorozhankin, Ts. Vylov, D.V. Filosofov, N. Coursol, E.A. Yakushev, Ch. Briançon, A. Minkova, M. Ryšavý, O. Dragoun, J. Electron Spectrosc. Relat. Phenom., 95 (1998) 1.
[14] S. Egri, L. Kövér, W. Drube, I. Cserny, M. Novák, J. Electron Spectrosc. Relat. Phenom., 162, (2008) 115.
[15] A.Kh. Inoyatov, L.L. Perevoshchikov, V.S. Zhdanov, D.V. Filosofov, A. Kovalík, J. Electron Spectrosc. Relat. Phenom., 189 (2013) 23.
[16] A. Kovalík, A.V. Lubashevsky, A. Inoyatov, D.V. Filosofov, N.A. Korolev, V.M. Gorozhankin, Ts. Vylov, I. Štekl, J. Electron Spectrosc. Relat. Phenom., 134 (2004) 67.
[17] A. Kovalík, E.A. Yakushev, D.V. Filosofov, V.M. Gorozhankin, I. Štekl, P. Petev, M.A. Mahmoud, Proc. 50th Int. Conf. Nuclear Spectroscopy and Nuclear Structure "Clustering phenomena in nuclear physics", Jun 14-17, 2000, St.- Petersburg, Russia, p.173.
[18] A. Kovalík, M. Ryšavý, V. Brabec, O. Dragoun, A. Inoyatov, A.F. Novgorodov, Ts. Vylov, A. Minkova, J. Electron Spectrosc. Relat. Phenom., 43 (1987) 225.
[35] A. Špalek, Surface and Interface analysis, 15 (1990) 739. (DOI: 10.1002/sia.740151206)
[36] M. Fišer, V. Brabec, O. Dragoun, A. Kovalík, J. Frana and M. Ryšavý, Int. J. Appl. Radiat. Isot., 36 (1985) 219.
[37] V.N. Gerasimov, A.G. Zelenkov, V.M. Kulakov, V.A. Pchelin, A.A. Soldatov, L.V. Chistyakov, Yader. Fiz., 34 (1981) 3.
[38] V.N. Gerasimov, A.G. Zelenkov, V.M. Kulakov, V.A. Pchelin, M.V. Sokolovskaya, A.A. Soldatov, L.V. Chistyakov, Zh. Eksp. Teor. Fiz., 82 (1982) 362. (English translation: JETP, 55 (1982) 205)
[39] Ch. Briançon, B. Legrand, R.J. Walen, Ts. Vylov, A. Minkova, A. Inoyatov, Nucl. Instrum. Methods, 221(1984)547. (DOI: 10.1016/0167-5087(84)90062-0)
[40] V.M. Gorozhankin, V.G. Kalinnikov, A. Kovalík, A.A. Solnyshkin, A.F. Novgorodov, N.A. Lebedev, N.Yu. Kotovskij, E.A. Yakushev, M.A. Mahmoud and M. Ryšavý, J. Phys. G: Nucl. Part. Phys., 22(1996)377. (DOI: 10.1088/0954-3899/22/3/011 )
[41] Coral M. Baglin, Nucl. Data Sheets for A=169, 109(2008)2033. (DOI: 10.1016/j.nds.2008.08.001)
[42] R.B. Firestone, V.S. Shirley, Tables of Isotopes, 8th ed., Wiley-Interscience, New York, 1996, Appendix C-3.
[43] K.D. Sevier, Atom. Data Nucl. Data Tables, 24 (1979) 323. (DOI: 10.1016/0092-640X(79)90012-3)
[44] А.Kh. Inoyatov, A. Kovalík, D.V. Filosofov, Yu.V. Yushkevich, M. Ryšavý, M. Zbořil, J. Electron Spectrosc. Relat. Phenom., 202 (2015) 46. (DOI:10.1016/j.elspec.2015.02.015)
[45] A. V. Naumkin, A. Kraut-Vass, S.W. Gaarenstroom, and C.J. Powell, NIST Standard Reference Database 20, Version 4.1, (“X-ray Photoelectron Spectroscopy Database”), http://srdata.nist.gov/xps/selEnergyType.aspx
[46] A. Inoyatov, D.V. Filosofov, V.M. Gorozhankin, A. Kovalík, L.L. Perevoshchikov, and Ts. Vylov, J. Electron Spectrosc. Relat. Phenom., 160(2007)54. (DOI: 10.1016/j.elspec.2007.06.005)
[47] A. Špalek, Nucl. Instr. Meth. A, 264 (1988) 410. (DOI:10.1016/0168-9002(88)90932-1)
[48] A. Špalek, Nucl. Instr. Meth., 198 (1982) 399.
[49] A. Špalek and O. Dragoun, J.Phys. G: Nucl. Part. Phys., 19 (1993) 2071. (DOI:10.1088/0954-3899/19/12/012)
[50] O. Dragoun, A. Špalek, A. Kovalík, M.Ryšavý, J. Frána, V. Brabec, E.A. Yakushev, A.F. Novgorodov, D. Liljequist, Nucl. Instrum. Methods in Physics Research B, 194 (2002) 112.
(doi:10.1016/S0168-583X(02)00688-2)
[51] P. Jönsson, G. Gaigalas, J. Bieron, C, Froese Fischer and I.P. Grant, Comput. Phys. Commun. 184 (2013) 2197.
[52] I. P. Grant, Relativistic quantum theory of atoms and molecules: theory and computation, Vol. 40, Springer, 2007.
[53] B. McKenzie, I. Grant and P. Norrington, Comput. Phys. Commun. 21 (1980) 233.
[54] S. Fritzsche, Comput. Phys. Commun. 183 (2012) 1525.
[55] T. Åberg, G. Howat, in: W. Mehlhorn (Ed.), Corpuscles and Radiation in Matter I, in: Encyclopedia of Physics, vol. XXXI, Springer, Berlin, 1982, p. 469.
[56] H.L. Skriver and N.M. Rosengaard, Phys. Rev. B, 46 (1992) 7157. (DOI: 10.1103/PhysRevB.46.7157)
[57] G.L. Borchert, P.G. Hansen, B. Jonson, I. Lindgren, H.L. Ravn, O.W.B. Schult and P. Tidemand-Petersson, Phys. Lett. A, 66(1978)374. (DOI : 10.1016/0375-9601(78)90063-4)
[58] M.I. Babenkov, V.K. Petukhov, J. Phys. B: Atom. Molec. Phys., 10 (1977) L85.
[59] M.I. Babenkov, V.S. Zhdanov, S.A. Starodubov, J. Phys. B, 19 (1986) L563.
[60] А.Kh. Inoyatov, M. Ryšavý, A. Kovalík, D.V. Filosofov, V.S. Zhdanov, Yu.V. Yushkevich, Eur. Phys. J. A, 50(2014)59.
[61] M.O. Krause, J.H. Oliver, J. Phys. Chem. Ref. Data 8 , 329(1979).
[62] J.L. Campbell, T. Papp, Atom. Data Nucl. Data Tables 77 , 1(2001). (DOI: 10.1006/adnd.2000.0848)
