- Email: [email protected]
Energy systematics of the KαLi satellite transitions
Nuclear Instruments and Methods in Physics Research B 150 (1999) 8±13
Energy systematics of the KaLi satellite transitions I. T or ok a
a,*
, T. Papp a, S. Raman
b
Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), Pf. 51, H-4001 Debrecen, Hungary b Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Abstract The presence of X-ray satellites is common in X-ray spectra. The last compilation of satellite lines, frequently cited in the open literature, is the X-ray energy collection of Cauchois and Senemaud, Wavelengths of X-ray Emission Lines and Absorption Edges, Pergamon, Oxford, 1978 [1], which is restricted to electron and photon excitations. In the last decades, many ion-induced satellite measurements have been performed, the range covered in Ref. [1] have been extended for 40 < Z < 92, spectator vacancy number from 2 to 7, and energy-shifts from 200 to 1200 eV. In analytical work and in basic atomic physics research one needs the best data available on the satellite lines. We are working on a new and comprehensive compilation of experimental values for the K-satellite, and K-hypersatellite energy shifts. Some problems encountered during this work are discussed. A new semi-empirical formula for the description of the KaLi satellite energy shifts is given. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 0785; 2930; 3220R; 3320R; 7870 Keywords: X-ray emission spectra; Multiple ionization satellites
1. Introduction A broad range of information, stretching from analytical work to neutrino mass studies and from star evolution to plasma temperatures, can be derived from X-ray spectra. To achieve maximum accuracy, all details of the X-ray spectra need to be understood. The intensive, so-called diagram lines often are accompanied at their high energy sides with weak (in the case of photon or electron excitation) or
* Corresponding author. Tel.: +36-52-417-266/1403; fax: +36-52-416-181; e-mail: [email protected]
stronger (in the case of ion excitation) satellite peaks, originating from multiple ionization. It means, that e.g. producing a K hole can be accompanied by producing further L, M, N, O, etc. hole(s) in the same collision process. The K hole will be ®lled sooner than the outer vacancies. The so-called spectator holes on the outer shell(s) shift the energy of the K line, due to reduced screening of the nucleus. The L holes give a shift in the order of 10 eV, the M holes do it in the range of 1 eV. So, if the hole resides in a higher main quantum number shell, then the energy shift will be lower. In the case of K lines the L satellites have the strongest shifts (several 10 eV up to a few 100 eV). Approximately an additional L hole produces an
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 1 0 4 5 - 3
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
additional satellite peak, in ®rst approximation, this results in a spectrum with equally spaced satellite peaks. The maximum number of spectator vacancies for KL satellites is 7. Such satellite spectra (obtained by heavy ion bombardment) look like a gloves shape, each ®nger meaning a given number of L spectator holes. These satellites can be resolved by crystal spectrometers. Additional M shell spectator holes shift the K diagram line and the KL satellite lines with additional few eV, generally unresolved even by crystal spectrometers, but shifting and widening the peaks. In the following we speak about KL satellites not regarding the possible M, N, etc. components. The last compilation of satellite lines, frequently cited in the open literature, is Ref. [1], which is restricted to electron and photon excitations. We are working on a new and comprehensive compilation of experimental values for the K-satellite, and K-hypersatellite energy shifts, including the results obtained by ion impact ionization. Some methodical problems encountered during this work are discussed. Diculties arising from the chemical eects, additional outer-shell ionization, large number of possible transitions, solid-liquid-gas effects, assignments, notations, projectile Z and energy dependence, energy calibration of the measurements, etc., are presented using a representative portion of our KaLi satellite database. The large number of new data made it possible to test a simple description of the KL satellite energy shifts [2], and we found that a new semiempirical formula improves the agreement between calculated and experimental energy shifts of KL satellites. 2. Methods used for compilation Unfortunately, a wide variety of notations are used by dierent authors. The Siegbahn notation to name the peaks of decreasing intensity within the group like Ka1 , Ka2 , Ka3 , Ka4 , Ka5 ; . . . ; Ka0 , Ka00 ; . . . ; Ka14 , were used in Ref. [1]. The Arabic numerals were combined with primes, Roman numerals, etc. This notation mixes the diagram lines and their satellites. For many cases the authors attempted to give the electron or hole con-
9
®gurations of the initial and ®nal states. The large number of possible real transitions makes these notations ambiguous. In most cases it is even not sure whether e.g. the L hole is on the 2s or 2p subshell. There is IUPAC Notation, published in 1991 [3], which requires the naming of transitions by level assignments, which in many cases still is ambiguous. Their proposed system of notation for the satellites of unknown origin repeats the disadvantages of the Siegbahn notation. In several papers the authors were not assigning real transitions, they rather gave special notations of the resolved peaks, e.g. A, B, C, D, E. The most frequently used notation is to name the gloves ®nger-like resolved KL satellites KL0 , KL1 , KL2 , KL3 , KL4 ; . . . ; KL7 , upwards from the diagram line; with the superscript giving the number of L spectator vacancies. The KLi notation proved to be the most usable in compilation. In the case of KL satellites, the most signi®cant eect of additional M, N, etc shell spectator holes is the additional M ionization. As we are interested in the eect of the L spectator holes, we regarded the energy shift relative to the average energy of the diagram lines shifted by the M ionization in the given spectrum, instead of the tabulated value of them. The eect of the additional M ionization on the sequence of the KLi satellites in a ®rst approximation can be regarded to be the same for the dierent i values. So spectra obtained from bombardment by projectiles of dierent energy and Z can provide similar energy shifts. The same eect is seen in MN satellites, etc. [4]. The large number of unresolved additional higher order satellites (e.g. M for L) wash these transitions into a common peak, and the experiment can determine only the average energy of the KLi group. Theoreticians try to calculate all, or at least many distinct transitions, but at higher Z region the number of these transition makes it complicated to get reliable energy and intensity values. Polasik [5] reports that the KaL1 M2 satellite band of a medium Z element has about 15 000 distinct possible transitions. In such cases the non well-resolved peaks are averaged by the spectrometer, producing the gloves-like structure. Assignment: Generally we accepted the line and transition assignments given by the original au-
10
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
Fig. 1. Some notations of KaL satellites. The example spectrum is from metallic Mg bombarded by 3.2 MeV He ions. Ei is the energy of the satellite, E0 the energy of its diagram line. The bar structures are the calculated satellite transition energies from Ref. [6].
thors, if the assignment of a transition in the source had been found to be contradictory, we made a new more probable assignment. Several times the original authors themselves or others corrected later the erroneous assignments. These satellites themselves are structured. There is a tradition, that the gloves-like spectra are regarded as if the distinct ``®ngers'' were representing a given KLi group. The reality is more complicated, the KLi groups are overlapping, see for example a Mg spectrum from our own work, which are compared with the calculation of Maurer and Watson [6] (Fig. 1.) The overlapping bar-structures represent the theoretical values. The numbers on the right side of the bar spectra give the number of the spectator vacancies. However it is seen, that most of the calculated energies are in the range of the traditional KLi groups, and only some of them are in the neighbouring groups. Probably this overlapping is one of the reasons why some theoretical intensity distributions are not in good agreement with the experimental ones. The ®ngers many times can be resolved at lower Z region to some distinct transitions or smaller groups of transitions. Some papers give the average energy of these transitions e.g. Ref. [7], weighted by the relative intensities. These intensities are a function of the energy of the incident particles. Higher Z projectiles of the same energy produce more and more vacancies with increasing Z. The same projectile with increasing bombarding energy ®rst is producing satellites with increasing
intensity, and after a smooth wide peak, the excitation begins to decrease with further increasing bombarding energy, at even higher energies almost without producing vacancies. A maximum of the ionization probability occurs if the projectile velocity matches the electron velocity in the given subshell. The calculations of the X-ray energies in most cases are done for free atoms, but the experimenter often makes measurements on solid samples. Numerous investigators dealt with the eects of the chemical environment on the dierent satellite lines. This eect is up to several eV depending on the material. We attempted to compile data from pure elemental solid samples. It means, that most of our data originates from metallic samples. When it was not possible to ®nd such sample it is noted in the compilation. 3. The eect of satellites in PIXE spectra In certain target and projectile Z and energy ranges the satellites in PIXE spectra can be rather intensive (several %, relative to their diagram lines) and can limit the accuracy of analytical data. The application of projectiles in excess to protons, like helium-ions, and even heavier ions can result quite large energy shifts and intensity increase of the peaks. Despite of the above mentioned ambiguities we think, that for the PIXE community it is advan-
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
tageous to know more about this problem. It is true, that in many cases the satellite data are not too accurate, but the relatively large intensity and energy shift of the satellites in some cases can eect the concentration data obtained by this method. 4. Our database Many new experimental data were obtained by dierent groups all over the world, in most cases with ion excitation. Therefore we began to compile the available data. The whole compilation will be published elsewhere. The newer measurements extended the studied Z, DE, Li ranges covered in Ref. [1]. Fig. 2 shows the Z and energy shift limits for the KaL satellites graphically. We began the collection of new data in several ways. One of them was to search papers citing the Bearden X-ray line energy tables [8] based on the Science Citation Index. From 168 papers, where the title suggested, that it probably contains satellite data, 42 gave tables of absolute or relative (to the diagram lines) satellite energies or spectra, from which we could graphically determine the shifts. Many papers were emphasizing on the intensity distribution of the dierent KLi satellites, so energy values were not reported. This method
11
proved to be a good start. Also the search of the references in the found satellite related papers was useful. At the moment we have over 100 papers with new data in our ®les. 5. A new semi-empirical description of the KaLi satellite energy shifts Here we report a new, improved linear description of the satellite shifts, which we obtained from the large amount of old and new data. A simple linear expression was in use for the description of the KL X-ray satellite energy shifts [2]. The original paper suggests to use the Slater rule for calculating the screening and gives equidistant shifts per spectator holes. For the shift of the KaL X-ray satellites they give shifts per vacancy as a function of the atomic number of the emitting species: D KaL 1:66ZL 1:66 Z ÿ 4:15:
1
Here ZL (Zÿ4.15) is the eective charge at the L shell determined from the Slater screening rules [9], and for i spectator holes one has to multiply this D value by i. Fig. 3. shows Eq. (1) superimposed on the experimental values. At low Z the ®rst shift is overestimated by this formula with about 50%. At
Fig. 2. Atomic number and energy shift limits of data in Ref. [1] and present data for KaL satellites. Light columns: status 1978 [1]; Dark columns: present status.
12
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
Fig. 3. Experimental energy shifts of KaL satellites and the calculated values after [8] (Eq. (1)).
Fig. 4. Experimental energy shifts of KaL satellites and the calculated values after Eq. (2).
seven vacancies the agreement with the experiments is quite good. For better agreement other Z dependent eective charges were used by several authors e.g. Refs. [7,10], obtaining much better agreement for single vacancy shift. These investigators did not report the application of their results for more vacancies. From the graphical systematics of the KLi satellites and from a straight line of the case of a single spectator hole, we obtained another similar equation, again for equally spaced satellites:
for the ranges of Z up to 50 and of vacancy number up to 7. At higher Z the increasing multiple ionization on the higher shells, and changing coupling nature distorts the picture.
D KaL 1:530 Z ÿ 6:828:
2
Fig. 4. displays Eq. (2) superimposed on the experimental values. However it is seen, that there is a need for a ZL , depending on the number of the L spectator holes i. The following simple empirical calculation (with an improved eective Z) of the energy shift for the case of i spectator L vacancies was obtained: DE KaLi i 1:530Z 0:5 i ÿ 1 ÿ 6:828; i 1; 2; 3; . . . ; 7: 3 This formula describes the KaL satellite energy shifts better (Fig. 5.). This is valid within a few eV
Fig. 5. Experimental energy shifts of KaL satellites and the calculated values after Eq. (3).
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
In the case of the KaL satellites, the electrons ®lling the K vacancy come from the same L shell in which the spectator vacancies are. So the eect will be much stronger than for KbL satellites. Our formula suggests, that each next vacancy increases the eective charge seen by the L electron(s) by about 0.5. A similar improved description of the KbL satellite energy spacings and re®nement of Eq. (3) is in preparation. Acknowledgements This work was partly supported by the Hungarian Research Fund: OTKA No. T016636 and U28924, and OMFB 2127/98; and partly by the US Department of Energy under Contract No. DE-AC05-96OR22464 with Lockheed Martin Energy Research Corporation (Oak Ridge).
13
References [1] Y. Cauchois, C. Senemaud, Wavelengths of X-ray Emission Lines and Absorption Edges, Pergamon Press, Oxford, 1978. [2] D. Burch, L. Wilets, W.E. Meyerhof, Phys. Rev. A 9 (1974) 1007. [3] R. Jenkins, R. Manne, R. Robin, C. Senemaud, IUPAC. Nomenclature system for X-ray spectroscopy. E.g.: X-ray Spectrometry 20 (1991) 149. [4] Ch. Herren, B. Boschung, J.-Cl. Dousse, B. Galley, J. Hoszowska, J. Kern, Ch. Rh^eme, M. Polasik, T. Ludziejewski, P. Rymuza, Z. Sujkowski, Phys. Rev. A 57 (1998) 235. [5] M. Polasik, Phys. Rev. A 41 (1990) 3689. [6] R.J. Maurer, R.L. Watson, At. Data Nucl. Data Tables 34 (1986) 185. [7] M. Deutsch, Phys. Rev. A 39 (1989) 1077. [8] J.A. Bearden, Rev. Mod. Phys. 39 (1967) 78. [9] J.C. Slater, Phys. Rev. 36 (1930) 57. [10] J. Bhattacharya, U. Laha, B. Talukdar, Phys. Rev. A 37 (1988) 3162.
Energy systematics of the KaLi satellite transitions I. T or ok a
a,*
, T. Papp a, S. Raman
b
Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), Pf. 51, H-4001 Debrecen, Hungary b Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Abstract The presence of X-ray satellites is common in X-ray spectra. The last compilation of satellite lines, frequently cited in the open literature, is the X-ray energy collection of Cauchois and Senemaud, Wavelengths of X-ray Emission Lines and Absorption Edges, Pergamon, Oxford, 1978 [1], which is restricted to electron and photon excitations. In the last decades, many ion-induced satellite measurements have been performed, the range covered in Ref. [1] have been extended for 40 < Z < 92, spectator vacancy number from 2 to 7, and energy-shifts from 200 to 1200 eV. In analytical work and in basic atomic physics research one needs the best data available on the satellite lines. We are working on a new and comprehensive compilation of experimental values for the K-satellite, and K-hypersatellite energy shifts. Some problems encountered during this work are discussed. A new semi-empirical formula for the description of the KaLi satellite energy shifts is given. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 0785; 2930; 3220R; 3320R; 7870 Keywords: X-ray emission spectra; Multiple ionization satellites
1. Introduction A broad range of information, stretching from analytical work to neutrino mass studies and from star evolution to plasma temperatures, can be derived from X-ray spectra. To achieve maximum accuracy, all details of the X-ray spectra need to be understood. The intensive, so-called diagram lines often are accompanied at their high energy sides with weak (in the case of photon or electron excitation) or
* Corresponding author. Tel.: +36-52-417-266/1403; fax: +36-52-416-181; e-mail: [email protected]
stronger (in the case of ion excitation) satellite peaks, originating from multiple ionization. It means, that e.g. producing a K hole can be accompanied by producing further L, M, N, O, etc. hole(s) in the same collision process. The K hole will be ®lled sooner than the outer vacancies. The so-called spectator holes on the outer shell(s) shift the energy of the K line, due to reduced screening of the nucleus. The L holes give a shift in the order of 10 eV, the M holes do it in the range of 1 eV. So, if the hole resides in a higher main quantum number shell, then the energy shift will be lower. In the case of K lines the L satellites have the strongest shifts (several 10 eV up to a few 100 eV). Approximately an additional L hole produces an
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 1 0 4 5 - 3
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
additional satellite peak, in ®rst approximation, this results in a spectrum with equally spaced satellite peaks. The maximum number of spectator vacancies for KL satellites is 7. Such satellite spectra (obtained by heavy ion bombardment) look like a gloves shape, each ®nger meaning a given number of L spectator holes. These satellites can be resolved by crystal spectrometers. Additional M shell spectator holes shift the K diagram line and the KL satellite lines with additional few eV, generally unresolved even by crystal spectrometers, but shifting and widening the peaks. In the following we speak about KL satellites not regarding the possible M, N, etc. components. The last compilation of satellite lines, frequently cited in the open literature, is Ref. [1], which is restricted to electron and photon excitations. We are working on a new and comprehensive compilation of experimental values for the K-satellite, and K-hypersatellite energy shifts, including the results obtained by ion impact ionization. Some methodical problems encountered during this work are discussed. Diculties arising from the chemical eects, additional outer-shell ionization, large number of possible transitions, solid-liquid-gas effects, assignments, notations, projectile Z and energy dependence, energy calibration of the measurements, etc., are presented using a representative portion of our KaLi satellite database. The large number of new data made it possible to test a simple description of the KL satellite energy shifts [2], and we found that a new semiempirical formula improves the agreement between calculated and experimental energy shifts of KL satellites. 2. Methods used for compilation Unfortunately, a wide variety of notations are used by dierent authors. The Siegbahn notation to name the peaks of decreasing intensity within the group like Ka1 , Ka2 , Ka3 , Ka4 , Ka5 ; . . . ; Ka0 , Ka00 ; . . . ; Ka14 , were used in Ref. [1]. The Arabic numerals were combined with primes, Roman numerals, etc. This notation mixes the diagram lines and their satellites. For many cases the authors attempted to give the electron or hole con-
9
®gurations of the initial and ®nal states. The large number of possible real transitions makes these notations ambiguous. In most cases it is even not sure whether e.g. the L hole is on the 2s or 2p subshell. There is IUPAC Notation, published in 1991 [3], which requires the naming of transitions by level assignments, which in many cases still is ambiguous. Their proposed system of notation for the satellites of unknown origin repeats the disadvantages of the Siegbahn notation. In several papers the authors were not assigning real transitions, they rather gave special notations of the resolved peaks, e.g. A, B, C, D, E. The most frequently used notation is to name the gloves ®nger-like resolved KL satellites KL0 , KL1 , KL2 , KL3 , KL4 ; . . . ; KL7 , upwards from the diagram line; with the superscript giving the number of L spectator vacancies. The KLi notation proved to be the most usable in compilation. In the case of KL satellites, the most signi®cant eect of additional M, N, etc shell spectator holes is the additional M ionization. As we are interested in the eect of the L spectator holes, we regarded the energy shift relative to the average energy of the diagram lines shifted by the M ionization in the given spectrum, instead of the tabulated value of them. The eect of the additional M ionization on the sequence of the KLi satellites in a ®rst approximation can be regarded to be the same for the dierent i values. So spectra obtained from bombardment by projectiles of dierent energy and Z can provide similar energy shifts. The same eect is seen in MN satellites, etc. [4]. The large number of unresolved additional higher order satellites (e.g. M for L) wash these transitions into a common peak, and the experiment can determine only the average energy of the KLi group. Theoreticians try to calculate all, or at least many distinct transitions, but at higher Z region the number of these transition makes it complicated to get reliable energy and intensity values. Polasik [5] reports that the KaL1 M2 satellite band of a medium Z element has about 15 000 distinct possible transitions. In such cases the non well-resolved peaks are averaged by the spectrometer, producing the gloves-like structure. Assignment: Generally we accepted the line and transition assignments given by the original au-
10
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
Fig. 1. Some notations of KaL satellites. The example spectrum is from metallic Mg bombarded by 3.2 MeV He ions. Ei is the energy of the satellite, E0 the energy of its diagram line. The bar structures are the calculated satellite transition energies from Ref. [6].
thors, if the assignment of a transition in the source had been found to be contradictory, we made a new more probable assignment. Several times the original authors themselves or others corrected later the erroneous assignments. These satellites themselves are structured. There is a tradition, that the gloves-like spectra are regarded as if the distinct ``®ngers'' were representing a given KLi group. The reality is more complicated, the KLi groups are overlapping, see for example a Mg spectrum from our own work, which are compared with the calculation of Maurer and Watson [6] (Fig. 1.) The overlapping bar-structures represent the theoretical values. The numbers on the right side of the bar spectra give the number of the spectator vacancies. However it is seen, that most of the calculated energies are in the range of the traditional KLi groups, and only some of them are in the neighbouring groups. Probably this overlapping is one of the reasons why some theoretical intensity distributions are not in good agreement with the experimental ones. The ®ngers many times can be resolved at lower Z region to some distinct transitions or smaller groups of transitions. Some papers give the average energy of these transitions e.g. Ref. [7], weighted by the relative intensities. These intensities are a function of the energy of the incident particles. Higher Z projectiles of the same energy produce more and more vacancies with increasing Z. The same projectile with increasing bombarding energy ®rst is producing satellites with increasing
intensity, and after a smooth wide peak, the excitation begins to decrease with further increasing bombarding energy, at even higher energies almost without producing vacancies. A maximum of the ionization probability occurs if the projectile velocity matches the electron velocity in the given subshell. The calculations of the X-ray energies in most cases are done for free atoms, but the experimenter often makes measurements on solid samples. Numerous investigators dealt with the eects of the chemical environment on the dierent satellite lines. This eect is up to several eV depending on the material. We attempted to compile data from pure elemental solid samples. It means, that most of our data originates from metallic samples. When it was not possible to ®nd such sample it is noted in the compilation. 3. The eect of satellites in PIXE spectra In certain target and projectile Z and energy ranges the satellites in PIXE spectra can be rather intensive (several %, relative to their diagram lines) and can limit the accuracy of analytical data. The application of projectiles in excess to protons, like helium-ions, and even heavier ions can result quite large energy shifts and intensity increase of the peaks. Despite of the above mentioned ambiguities we think, that for the PIXE community it is advan-
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
tageous to know more about this problem. It is true, that in many cases the satellite data are not too accurate, but the relatively large intensity and energy shift of the satellites in some cases can eect the concentration data obtained by this method. 4. Our database Many new experimental data were obtained by dierent groups all over the world, in most cases with ion excitation. Therefore we began to compile the available data. The whole compilation will be published elsewhere. The newer measurements extended the studied Z, DE, Li ranges covered in Ref. [1]. Fig. 2 shows the Z and energy shift limits for the KaL satellites graphically. We began the collection of new data in several ways. One of them was to search papers citing the Bearden X-ray line energy tables [8] based on the Science Citation Index. From 168 papers, where the title suggested, that it probably contains satellite data, 42 gave tables of absolute or relative (to the diagram lines) satellite energies or spectra, from which we could graphically determine the shifts. Many papers were emphasizing on the intensity distribution of the dierent KLi satellites, so energy values were not reported. This method
11
proved to be a good start. Also the search of the references in the found satellite related papers was useful. At the moment we have over 100 papers with new data in our ®les. 5. A new semi-empirical description of the KaLi satellite energy shifts Here we report a new, improved linear description of the satellite shifts, which we obtained from the large amount of old and new data. A simple linear expression was in use for the description of the KL X-ray satellite energy shifts [2]. The original paper suggests to use the Slater rule for calculating the screening and gives equidistant shifts per spectator holes. For the shift of the KaL X-ray satellites they give shifts per vacancy as a function of the atomic number of the emitting species: D KaL 1:66ZL 1:66 Z ÿ 4:15:
1
Here ZL (Zÿ4.15) is the eective charge at the L shell determined from the Slater screening rules [9], and for i spectator holes one has to multiply this D value by i. Fig. 3. shows Eq. (1) superimposed on the experimental values. At low Z the ®rst shift is overestimated by this formula with about 50%. At
Fig. 2. Atomic number and energy shift limits of data in Ref. [1] and present data for KaL satellites. Light columns: status 1978 [1]; Dark columns: present status.
12
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
Fig. 3. Experimental energy shifts of KaL satellites and the calculated values after [8] (Eq. (1)).
Fig. 4. Experimental energy shifts of KaL satellites and the calculated values after Eq. (2).
seven vacancies the agreement with the experiments is quite good. For better agreement other Z dependent eective charges were used by several authors e.g. Refs. [7,10], obtaining much better agreement for single vacancy shift. These investigators did not report the application of their results for more vacancies. From the graphical systematics of the KLi satellites and from a straight line of the case of a single spectator hole, we obtained another similar equation, again for equally spaced satellites:
for the ranges of Z up to 50 and of vacancy number up to 7. At higher Z the increasing multiple ionization on the higher shells, and changing coupling nature distorts the picture.
D KaL 1:530 Z ÿ 6:828:
2
Fig. 4. displays Eq. (2) superimposed on the experimental values. However it is seen, that there is a need for a ZL , depending on the number of the L spectator holes i. The following simple empirical calculation (with an improved eective Z) of the energy shift for the case of i spectator L vacancies was obtained: DE KaLi i 1:530Z 0:5 i ÿ 1 ÿ 6:828; i 1; 2; 3; . . . ; 7: 3 This formula describes the KaL satellite energy shifts better (Fig. 5.). This is valid within a few eV
Fig. 5. Experimental energy shifts of KaL satellites and the calculated values after Eq. (3).
I. T or ok et al. / Nucl. Instr. and Meth. in Phys. Res. B 150 (1999) 8±13
In the case of the KaL satellites, the electrons ®lling the K vacancy come from the same L shell in which the spectator vacancies are. So the eect will be much stronger than for KbL satellites. Our formula suggests, that each next vacancy increases the eective charge seen by the L electron(s) by about 0.5. A similar improved description of the KbL satellite energy spacings and re®nement of Eq. (3) is in preparation. Acknowledgements This work was partly supported by the Hungarian Research Fund: OTKA No. T016636 and U28924, and OMFB 2127/98; and partly by the US Department of Energy under Contract No. DE-AC05-96OR22464 with Lockheed Martin Energy Research Corporation (Oak Ridge).
13
References [1] Y. Cauchois, C. Senemaud, Wavelengths of X-ray Emission Lines and Absorption Edges, Pergamon Press, Oxford, 1978. [2] D. Burch, L. Wilets, W.E. Meyerhof, Phys. Rev. A 9 (1974) 1007. [3] R. Jenkins, R. Manne, R. Robin, C. Senemaud, IUPAC. Nomenclature system for X-ray spectroscopy. E.g.: X-ray Spectrometry 20 (1991) 149. [4] Ch. Herren, B. Boschung, J.-Cl. Dousse, B. Galley, J. Hoszowska, J. Kern, Ch. Rh^eme, M. Polasik, T. Ludziejewski, P. Rymuza, Z. Sujkowski, Phys. Rev. A 57 (1998) 235. [5] M. Polasik, Phys. Rev. A 41 (1990) 3689. [6] R.J. Maurer, R.L. Watson, At. Data Nucl. Data Tables 34 (1986) 185. [7] M. Deutsch, Phys. Rev. A 39 (1989) 1077. [8] J.A. Bearden, Rev. Mod. Phys. 39 (1967) 78. [9] J.C. Slater, Phys. Rev. 36 (1930) 57. [10] J. Bhattacharya, U. Laha, B. Talukdar, Phys. Rev. A 37 (1988) 3162.