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Fine structure splitting in argon Kα X-ray emission spectra
Volume 145, number 8,9
FINE STRUCTURE
PHYSICS LETTERS A
SPLITTING IN ARGON &X-RAY
30 April 1990
EMISSION SPECTRA
I. REICHE, S. FRITZSCHE, G. MUSIOL and G. ZSCHORNACK Sektion Physik, Technische Universitiit Dresden, Mommsenstrasse 13, DDR-8027 Dresden, GDR
Received 18 December 1989; revised manuscript received 6 March 1990; accepted for publication 8 March 1990 Communicated by B. Fricke
K,,1,2X-my emission spectra of argon at various stages of outer shell ionization are calculated using the MCDF model. Conclusions concerning interpretation of spectra are obtained.
X-ray emission spectrometry is a method of growing importance for a number of problems in physics and applications in other fields, e.g. investigations of atomic collisions and heavy ion sources as well as plasma diagnostics in connection with fusion research and astrophysics. Recent discussion [ 1,2 ] has shown continuing interest in contributions to the interpretation of such spectra. In the present paper we analyze how the fine structure splitting influences the I& X-ray spectrum of argon at various stages of ionization. These calculations give a survey over spectra that are expected to be emitted by an electron beam ion source. Calculations on fine structure have been reported for the argon K, spectrum [ 31 and the K L” satellite lines in spectra of molybdenum, palladium, lanthanum and holmium [ 41, but not as a function of outer shell ionization. The method used in our calculations is essentially the same as in refs. [ 3,4]. The calculations are based on the multiconfiguration Dirac-Fock (MCDF) program of Grant et al. [ 5,6]. In the MCDF model configuration state functions (CSFs) designated by @(y:JM) are constructed in j-coupling as linear combinations of Slater determinants of the orbitals. Then an atomic state function (ASF) with angular momentum JM is obtained by
where n is the number of CSFs included in the calculation. The Dirac-Fock equations are solved it-
eratively by the self-consistent field method. The configuration mixing coefficients C’kican be optimized simultaneously with the radial wavefunctions.
2 3
131 2950
3000
3050
EleV
3100
Fig 1. &,,* X-ray transition energies and rates including fine structure splitting for argon ions at the ionization stages I from 0 to 13. (J? transition energy; IT transition rate.)
0375-9601/90/% 03.50 0 Elsevier Science Publishers B.V. (North-Holland )
441
Volume 145, number 8,9
evrt, ’ I:
30 April 1990
PHYSICS LETTERS A
r eX
Art+
010
2,960
2,662
2964
2,960
2,962
2,964 ElkeV
ElkeV
2.962
2666
2.690
ElkeV
1
36,ll
38,l6 37.7
Fig. 2. I(a,,* X-ray spectra of Ar+ ions. Upper part: transition energies and rates including tine structure splitting. The LSI-terms of the states before and after transition are given as well. Only transitions with an emission rate > lo-’ eV/fr are included. Central part: spectrum constructed by superposition of the single lines with an assumed width of 0.8 eV. Lower part: the above spectrum seen through a crystal diffraction spectrometer (calculated for a quartz ( I Oi 1) crystal of geometrical diffraction patterns with a width of 50 arcsec and a structure taken from ref. [ 81, in first diffraction order). (E: transition energy; I? transition rate; I: intensity; 8: spectrometer setting angle.)
442
37,6
I?/0
Fig . 3. &,,2 X-ray spectra of A?+ ions. For explanation see fig. 2.
Corrections to the MCDF energy levels are supplied by including the transverse Breit operator in first order perturbation theory, the second order vacuum polarization and an approximate estimate of the self-energy operator. The program was specially expanded to calculate
Volume145,number8,9
PHYSICSLETTERSA
X-ray emission rates including fine structure splitting. Gauge dependence of X-ray emission rates [ 7 ] was taken into account by obtaining all results in both Coulomb and length gauges. The calculations were carried out in a way requiring a comparably small size: The wavefunction used to describe an ion of a certain charge stage was optimized on a weighted sum of energy states before and after the K,, transition (EAL calculation). All states having equal occupation numbers of the nl orbitals as the minimal energy states with Is and 2p vacancies, respectively, were included. All transitions calculated in this way are shown in fig. 1. For X-ray emission rates values in Coulomb gauge have been selected. In fig. 1 all single transitions have the same weight independent of the initial state of transition, and the energies are truncated to integer values of eV for clarity of the figure. To get a suitable intensity scale, emission rate sums >O.l eV/fi had to be cut off. Figs. 2 and 3 show how a spectrum is obtained from these single lines in the cases of Ar+ and Ar9+, respectively. In the upper parts of these figures transitions between the possible states of the ions are shown in nearly the same way as in fig. I, but now with their correct energies and intensities. The spectra drawn in the central part of each figure, which are expected to be emitted by ions of the given stage of ionization, were obtained by summing the single transition peaks with an assumed line width of 0.8 eV. The lower parts of the figures show spectra that would be measured by a crystal diffraction spectrometer. The spectrometer is assumed to have geometrical diffraction patterns with a width of 50 arcset and a typical structure obtained by statistical simulation studies on crystal diffraction spectrometers carried out by our group [ 8 1. From figs. 1, 2 and 3 it can be seen that even the X-ray spectrum emitted by only a single charge stage of an element is in most cases very complex. Furthermore, the broadening of the spectrum lines due to line structure splitting results in a strong overlap
30April1990
of the spectra from neighbouring charge stages. Therefore the identification of charge stages of a given element only by measuring the X-ray radiation emitted is very difficult and requires precise calculations of all possibly occurring spectra including their tine structure. Further complications arise from the occurrence of X-ray satellites, though in the considered case of electron-impact excitation the total intensity of K X-ray satellites is small compared with the intensity of the principal lines [ 9 1. According to our calculations an additional hole in the Lshell causes a shift of the mean argon K, X-ray energy of approximately 15 eV, whereas a hole in the M,-shell shifts the mean K, transition energy for the first ionization stages by about 0.5 eV. In addition the deexcitation through nonradiative electron transitions has been neglected here but should be taken into consideration. Unfortunately, we do not know any experimental study of the shape of argon K, X-ray emission spectra at various ionization stages. The authors would like to thank Professor I.P. Grant for making available his MCDF program package to us. References [ 1] LN. Timonova,V.V.Murakhtanovand L.N. MazaIov,in;
XXVIColloquiumSpectroscopicurn Intemationale,Vol.V, Abstracts,July2-9, 1989,Sofia,p. 105. [2] N. Saitch and Y. Gohshi, in: XXVI Colloquium Spectroscopicum Intemationale,Vol.I, Abstracts,July 2-9, 1989,Sofia,p. 256. [ 3] K.G. Dyall and I.P.Grant,PhysicaB 17 ( 1984) 1281. [4] M. Polasik,Phys.Rev.A 39 (1989) 616. [ 51I.P.Grant,B.J.McKenzie,P.H.Nonington,D.F.Mayersand N.C.Pyper,Comput.Phys.Commun.21 ( 1980)207. [ 61B.J. McKenzie,LP. Grant and P.H. Nor&ton, Comput. Phys. Commun. 21 (1980) 233. [7] I.P. Grant, J. Phys. B 7 (1974) 1458. [8] A. Reichmann, G. Musiol, W. Wagner and G. Zschomack, preprint Technische Universitit Dresden 05-01-87, Dresden (1987). [9] H.F. Beyer, GSI-Report 79-6, Darmstadt (1979).
443
FINE STRUCTURE
PHYSICS LETTERS A
SPLITTING IN ARGON &X-RAY
30 April 1990
EMISSION SPECTRA
I. REICHE, S. FRITZSCHE, G. MUSIOL and G. ZSCHORNACK Sektion Physik, Technische Universitiit Dresden, Mommsenstrasse 13, DDR-8027 Dresden, GDR
Received 18 December 1989; revised manuscript received 6 March 1990; accepted for publication 8 March 1990 Communicated by B. Fricke
K,,1,2X-my emission spectra of argon at various stages of outer shell ionization are calculated using the MCDF model. Conclusions concerning interpretation of spectra are obtained.
X-ray emission spectrometry is a method of growing importance for a number of problems in physics and applications in other fields, e.g. investigations of atomic collisions and heavy ion sources as well as plasma diagnostics in connection with fusion research and astrophysics. Recent discussion [ 1,2 ] has shown continuing interest in contributions to the interpretation of such spectra. In the present paper we analyze how the fine structure splitting influences the I& X-ray spectrum of argon at various stages of ionization. These calculations give a survey over spectra that are expected to be emitted by an electron beam ion source. Calculations on fine structure have been reported for the argon K, spectrum [ 31 and the K L” satellite lines in spectra of molybdenum, palladium, lanthanum and holmium [ 41, but not as a function of outer shell ionization. The method used in our calculations is essentially the same as in refs. [ 3,4]. The calculations are based on the multiconfiguration Dirac-Fock (MCDF) program of Grant et al. [ 5,6]. In the MCDF model configuration state functions (CSFs) designated by @(y:JM) are constructed in j-coupling as linear combinations of Slater determinants of the orbitals. Then an atomic state function (ASF) with angular momentum JM is obtained by
where n is the number of CSFs included in the calculation. The Dirac-Fock equations are solved it-
eratively by the self-consistent field method. The configuration mixing coefficients C’kican be optimized simultaneously with the radial wavefunctions.
2 3
131 2950
3000
3050
EleV
3100
Fig 1. &,,* X-ray transition energies and rates including fine structure splitting for argon ions at the ionization stages I from 0 to 13. (J? transition energy; IT transition rate.)
0375-9601/90/% 03.50 0 Elsevier Science Publishers B.V. (North-Holland )
441
Volume 145, number 8,9
evrt, ’ I:
30 April 1990
PHYSICS LETTERS A
r eX
Art+
010
2,960
2,662
2964
2,960
2,962
2,964 ElkeV
ElkeV
2.962
2666
2.690
ElkeV
1
36,ll
38,l6 37.7
Fig. 2. I(a,,* X-ray spectra of Ar+ ions. Upper part: transition energies and rates including tine structure splitting. The LSI-terms of the states before and after transition are given as well. Only transitions with an emission rate > lo-’ eV/fr are included. Central part: spectrum constructed by superposition of the single lines with an assumed width of 0.8 eV. Lower part: the above spectrum seen through a crystal diffraction spectrometer (calculated for a quartz ( I Oi 1) crystal of geometrical diffraction patterns with a width of 50 arcsec and a structure taken from ref. [ 81, in first diffraction order). (E: transition energy; I? transition rate; I: intensity; 8: spectrometer setting angle.)
442
37,6
I?/0
Fig . 3. &,,2 X-ray spectra of A?+ ions. For explanation see fig. 2.
Corrections to the MCDF energy levels are supplied by including the transverse Breit operator in first order perturbation theory, the second order vacuum polarization and an approximate estimate of the self-energy operator. The program was specially expanded to calculate
Volume145,number8,9
PHYSICSLETTERSA
X-ray emission rates including fine structure splitting. Gauge dependence of X-ray emission rates [ 7 ] was taken into account by obtaining all results in both Coulomb and length gauges. The calculations were carried out in a way requiring a comparably small size: The wavefunction used to describe an ion of a certain charge stage was optimized on a weighted sum of energy states before and after the K,, transition (EAL calculation). All states having equal occupation numbers of the nl orbitals as the minimal energy states with Is and 2p vacancies, respectively, were included. All transitions calculated in this way are shown in fig. 1. For X-ray emission rates values in Coulomb gauge have been selected. In fig. 1 all single transitions have the same weight independent of the initial state of transition, and the energies are truncated to integer values of eV for clarity of the figure. To get a suitable intensity scale, emission rate sums >O.l eV/fi had to be cut off. Figs. 2 and 3 show how a spectrum is obtained from these single lines in the cases of Ar+ and Ar9+, respectively. In the upper parts of these figures transitions between the possible states of the ions are shown in nearly the same way as in fig. I, but now with their correct energies and intensities. The spectra drawn in the central part of each figure, which are expected to be emitted by ions of the given stage of ionization, were obtained by summing the single transition peaks with an assumed line width of 0.8 eV. The lower parts of the figures show spectra that would be measured by a crystal diffraction spectrometer. The spectrometer is assumed to have geometrical diffraction patterns with a width of 50 arcset and a typical structure obtained by statistical simulation studies on crystal diffraction spectrometers carried out by our group [ 8 1. From figs. 1, 2 and 3 it can be seen that even the X-ray spectrum emitted by only a single charge stage of an element is in most cases very complex. Furthermore, the broadening of the spectrum lines due to line structure splitting results in a strong overlap
30April1990
of the spectra from neighbouring charge stages. Therefore the identification of charge stages of a given element only by measuring the X-ray radiation emitted is very difficult and requires precise calculations of all possibly occurring spectra including their tine structure. Further complications arise from the occurrence of X-ray satellites, though in the considered case of electron-impact excitation the total intensity of K X-ray satellites is small compared with the intensity of the principal lines [ 9 1. According to our calculations an additional hole in the Lshell causes a shift of the mean argon K, X-ray energy of approximately 15 eV, whereas a hole in the M,-shell shifts the mean K, transition energy for the first ionization stages by about 0.5 eV. In addition the deexcitation through nonradiative electron transitions has been neglected here but should be taken into consideration. Unfortunately, we do not know any experimental study of the shape of argon K, X-ray emission spectra at various ionization stages. The authors would like to thank Professor I.P. Grant for making available his MCDF program package to us. References [ 1] LN. Timonova,V.V.Murakhtanovand L.N. MazaIov,in;
XXVIColloquiumSpectroscopicurn Intemationale,Vol.V, Abstracts,July2-9, 1989,Sofia,p. 105. [2] N. Saitch and Y. Gohshi, in: XXVI Colloquium Spectroscopicum Intemationale,Vol.I, Abstracts,July 2-9, 1989,Sofia,p. 256. [ 3] K.G. Dyall and I.P.Grant,PhysicaB 17 ( 1984) 1281. [4] M. Polasik,Phys.Rev.A 39 (1989) 616. [ 51I.P.Grant,B.J.McKenzie,P.H.Nonington,D.F.Mayersand N.C.Pyper,Comput.Phys.Commun.21 ( 1980)207. [ 61B.J. McKenzie,LP. Grant and P.H. Nor&ton, Comput. Phys. Commun. 21 (1980) 233. [7] I.P. Grant, J. Phys. B 7 (1974) 1458. [8] A. Reichmann, G. Musiol, W. Wagner and G. Zschomack, preprint Technische Universitit Dresden 05-01-87, Dresden (1987). [9] H.F. Beyer, GSI-Report 79-6, Darmstadt (1979).
443