Lβ 1 satellites in X-ray emission spectra of 4d transition elements

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1 Indian Journal of Pure & Applied Physics Vol. 45, February 2007, pp Lβ 1 satellites in Xray emission spectra of 4d transition elements Surendra Poonia a & S N Soni b a Division of Natural Resources and Environment, Central Arid one Research Institute, Jodhpur surendra_1975@yahoo.com, poonia.surendra@gmail.com b XRay Laboratory, Physics Department, Jai Narain Vyas University, Jodhpur Received 3 January 2006; revised 8 December 2006; accepted 12 December 2006 The Xray satellite spectra arising due to 2p 1/2 1 3x 1 3x 1 3d 1 (x s, p, d) transition array, in elements with = 40 to 50, have been calculated. The energies of various transitions of the array have been determined by using available HartreeFock Slater (HFS) data on 1s 1 2p 1 3x 1 and 2p 1/2 1 3x 1, 3x' 1 Auger transition energies and their relative intensities of all the possible transitions have been estimated by considering cross sections for the Auger transitions simultaneous to a hole creation and then distributing statistically the total crosssections for initial two hole states 2p 1/2 1 3x 1 amongst various allowed transitions from these initial states to 3x 1 3d 1 final states by CosterKronig (CK) and shake off processes. In both these processes, initial single hole creation is the prime phenomenon and electron bombardment has been the primary source of energy. Each transition has been assumed to give rise to a Gaussian line and the overall spectrum has been computed as the sum of these Gaussian curves. The calculated spectra have been compared with the measured satellite energies in Lβ 1 spectra. Their intense peaks have been identified as the observed satellite lines. The peaks in the computed satellite spectra have been compared with the experimentally reported satellites β 1 I, β 1 II, β 1 III and β 1 IV, which lie on the highenergy side of the Lβ 1 dipole line. Keywords: Lβ 1 satellites, M vacancy Lβ 1 transitions, Xray emission spectra IPC Code: G01J3/28 1 Introduction The identification of the transitions in doubly and triply inner shell ionized atoms, which can be assigned to various Xray satellites 17, has been in progress in this laboratory. The method adopted is more reliable than Wentzel's +1 approximation 8,9. The transition energies have been calculated using HartreeFockSlater (HFS) model 10 in the intermediate coupling scheme and their relative intensities have been estimated in the LS coupling scheme. In continuation of the same work, we present here the transition assignments to the satellites named β 1 I, β 1 II, β 1 III and β 1 IV in the Lemission spectra of 4d transition elements. A survey of the literature reveals that in Lβ 1 spectra, a maximum of four satellites have been reported in the elements with = 26 to 69 only, with a few gaps 11. These are named β 1 I, β 1 II, β 1 III and β 1 IV in order of increasing energy. These data have been graphically presented in Fig. 1, in which the energies of satellites relative to the respective β 1 lines have been plotted against. The transition assignments to all these lines have been reported by Soni 12, in which these lines are emitted by the superposition of all the intense 2p 1 1/2 3d 1 transitions taking place in the atom when an additional core hole in Mshell is present. In this paper, the relative transition probabilities are calculated by considering 2s 1 1/2 2p 1 1/2 3x 1 Coster Kronig transition probability and also by considering 1 shake off probabilities associated with a 2p 1/2 ionization, such that a 2p 1 1/2 3x 1 state may be generated. In these processes, the probability of formation of singly ionized state, 2s 1 1/2 or 2p 1 1/2, plays a very important role. These two probabilities were taken equal 12, which may not be true. The transition assignment to these satellites has, therefore, been reinvestigated presently by adding two features in the calculations over those used earlier 12. The first one is calculations of the 2s 1/2 1 and 2p 1/2 1 ionization probabilities, needed as base states for Coster Kronig probabilities and shake off processes, respectively. Secondly, each transition is assumed to give rise to a Gaussian line and the theoretical spectrum is obtained as the superposition of such Gaussian lines. The results for the elements = 40 to 50 are presented below. The measured data are taken from the tables of Bearden and Burr 13 and other many reports published so far covering the

2 120 INDIAN J PURE & APPL PHYS, VOL. 45, FEBRUARY 2007 Fig. 1 Measured energies of various satellites on highenergy side of Lβ 1 line relative to their respective β 1 energies satellites 1419 of Lβ 1, paying attention particularly to the relative intensities of Lβ lines and to their widths and relative energies. The intermediate coupling is the most suitable for the middle elements, while jj coupling should be applied for the elements near the end of the periodic table. 2 Theory We have undertaken the studies of all those transitions of 2p 1 1/2 3x 1 3x 1 3d 1 (x s, p, d) array which are allowed according to selection rules 10 L = 0, ±1, S = 0 and J = 0, ±1. We have calculated their Hartree Fock Slater (HFS) energies in intermediate coupling and their relative probabilities in LS coupling scheme. We have computed the spectra arising out of the superposition of these transitions in the spectra of an element by assuming each transition to give rise to a Gaussian line. Finally, these computed spectra have been compared with the observed satellite spectra Transition energies The energies of the transitions, used in the present study, have been calculated by the combination formula: E (2p 1/2 1 3x 1 3x 1 3d 1 ) = E(Kα 1 ) E(1s 1 2p 1/2 1 3x 1 ) + E(2p 1/2 1 3x 1 3d 1 ) (1) where E(Kα 1 ) is the energy of Kα 1 line. Its values have been taken from the tables of Bearden and Burr 13. E(1s 1 2p 1 1/2 3x 1 ) and E(2p 1 1/2 3x 2 ) are the Auger electron energies for the 1s 1 2p 1 1/2 3x 1 and 2p 1 1/2 3x 2 transitions, respectively. These energies have been taken from the tables of Larkins 20, who has calculated various twohole state energies of atoms with = in the intermediate coupling approximation and has, also, corrected them for adiabatic relaxation 21 of the orbitals due to a sudden creation of an inner hole as well as for the solidstate effect 22 of the sample. The values are in good agreement with the available experimental Auger electron energy data in the region of values, presently under study, as claimed by Larkins Transition probabilities For the emission of Lβ 1 satellites, in hand, those transitions are being considered in which the initial states are doubly ionized, one vacancy lying in 2p 1/2 subshell and second one in any of Msubshells. Such states are formed by two processes. (i) 2s 1 2p 1/2 1 3x 1 CosterKronig transitions, namely conversion of onehole state 2s 1 to a two hole state 2p 1/2 1 3x 1 (x s, p, d) through the Auger transition 2s 1 2p 1/2 1 3x 1. This theory revolutionized the ideas in the field of Xray satellites.

3 POONIA & SONI: Lβ 1 SATELLITES IN XRAY EMISSION SPECTRA 121 (ii) By shakeoff process, namely an electron from Mshell of the atom may escape out simultaneous to the formation of a 2p 1/2 vacancy. This additional vacancy is created due to shaking of the atomic orbits caused by a sudden change in the potential field in the atom, taking place when a 2p 1/2 electron leaves the atom with a fast speed. The CosterKronig transition probability can be written as σ.σ', where σ denotes the probability of formation of a vacancy in 2s 1/2 subshell of the atom and σ' is the probability of its decay through the CK transition 2s 1 2p 1 1/2 3x 1. Factor σ has been calculated by the formulas given by Moores et al 23., namely: σ nl = (π n 4 a 0 2 nl / 4 ) σ nl (R) (2) or, say σ nl = (1.628 * ) nl σ nl (R)/ E nl 2 (3) where n and l denote the subshell of the atom in which a hole is created, nl denotes the total number of electrons in this subshell and E nl denotes the binding energy of the electron in this subshell. σ nl (R) is known as Reduced crosssection, and is calculated by the formula given in Eq. (4): σ nl (R) = (1/u) [P ln u +Q (11/u) 2 + (r/u+s/u 2 ) (11/u)] (4) These formulae have been derived by Moores et al 23. and are applicable to single ionization of atoms in inner shell by electron bombardment. The P, Q, r and s are constants, whose values for ionization in 2s 1/2 subshell are P = 23, Q = 3.69, r = 2, s = 1.79 and in 2p 1/2 subshell are P = 30, Q = 5.07, r = 1.20 and s = 2.50 [Ref. 23]. The dimensionless parameter u denotes the ratio of incident energy of incoming electron (E 0 ) to binding energy of the nl electron (E nl ). Since different researchers, who have measured satellite spectra of various elements experimentally, have used different excitation energies, we have arbitrarily taken the value of u as 2.5, a practical value found 23 to give a measurable intensity of satellites. The value of σ(2s 1 ), so calculated, has been multiplied with CosterKronig transition probability σ', taken from table of McGuire 24. It should be noted that the CosterKronig transitions help in forming only 2p 1 1/2 3d 1 states, and that too only in the elements 24 up to = 47. The other 2p 1 1/2 3x 1 transitions are not allowed energetically in these elements. Further, no such Coster Kronig transitions take place in elements 24 with = 48 to 73. Coming to shakeoff process, we have first calculated the cross section σ(2p 1 3/2 ) using formulas given in Eqs (24) and have, then, multiplied it with the shakeoff probability of a Msubshell electron. This probability has been calculated by interpolation from the percentage probabilities of shakeoff processes occurring with a single photoionization in inert gases 25. Subsequently the total probability of creation of an initial state 2p 1 1/2 3x 1 has been determined by adding these two cross sections as calculated. The crosssection for a set of 2p 1 1/2 3x 1 levels with x denoting any one subshell of Mshell, so calculated, has been assumed as the total probability of all the transitions from this set. This has been distributed statistically among all the allowed transitions from this set of levels, considering first all the multiplets of supermultiplets from various (2S+1) (L) levels of the set and then using tables of White and Eliason for relative probabilities of the transitions of each multiplet, as presented in [Ref. 10]. The detailed method of this distribution have been used by Poonia and Soni Synthesis of the spectrum We have calculated energies and intensities of all the possible transitions of the 2p 1/2 1 3x 1 3x 1 3d 1 (x s, p, d) array. The transitions having intensity less than 1/10 th of the maximum intensity out of all of them have been ignored. A composite spectrum formed by spectral lines emitted by these transitions has been computed by taking each as a Gaussian line. The choice of a Gaussian shape has been favoured over the Lorentzian one as it is more suitable to satellite spectra, as discussed by Maskil and Deutsch 26. For this, we have taken energy on Xaxis and intensity on Yaxis. The peak height of each line is taken equal to the transition probability and the peak position on Xaxis is taken at the energy of the transition. The widths of all the lines in one element have been assumed equal and its value has been decided by trial and error method in such a way that the number of peaks obtained from the calculated spectrum is at least equal to or greater than the number of satellites observed experimentally in the

4 122 INDIAN J PURE & APPL PHYS, VOL. 45, FEBRUARY 2007 Fig. 2 Computed 2p 1/2 1 3x 1 3x 1 3d 1 (x s, p, d) spectrum of 44Ru. The position of measured satellites [Ref. 11] are marked as vertical lines on the top part of the figure Fig. 3 Computed 2p 1/2 1 3x 1 3x 1 3d 1 (x s, p, d) spectrum of 48Cd. The position of measured satellites [Ref. 11] are marked as vertical lines on the top part of the figure Table 1 Relative intensities of the transitions of 2p 1/2 1 3x 1 3x 1 3d 1 (x s, p, d) array for = The names are denoted in the text. In 40 r to 47 Ag, both the CosterKronig (CK) transitions and shakeoff probabilities are added, while in 48 Cd to 50 Sn, Coster Kronig transitions are not allowed energetically Transition (a) 3 F 3 3 F 3 (3d) 3 F 2 3 F 2 (3d) 3 P 2 3 P 2 (3d) 3 D 1 3 F 2 (3d) 3 P 2 3 P 1 (3d) 3 F 3 3 F 4 (3d) 3 F 2 3 F 3 (3d) 3 F 3 3 F 2 (3d) 1 D 2 1 F 3 (3p) 1 D 2 1 D 2 (3p) 3 D 1 3 F 2 (3p) 1 P 1 1 D 2 (3s) 3 P 0 3 D 1 (3s) 3 P 1 3 D 2 (3p) Symbol of Relative Intensity (b) the transition used in the = 40 = 41 = 42 = 44 = 45 = 46 = 47 = 48 = 49 =50 text A B C D E F H G (a) The spectator hole position is shown in the braces along with the transitions spectrum of the element. The computed spectra in this case of two representative elements, 44 Ru and 48 Cd, thus obtained, are shown in Figs 2 and 3. In these spectra, peaks of higher intensities have been recognized as the observed satellites. For the one to one correspondence between peaks and measured satellites, the relative energy separations of peaks and those of measured satellites have been taken into consideration. 3 Results Out of all the 28 transitions of 2p 1/2 1 3x 1 3x 1 3d 1 (x s, p, d) array, 8 belonging to x = d group, 3 to x = p and 2 to x = s, have appreciable intensities so as to warrant attention in the spectra of 4d transition elements. These are presented in Table 1, in order of decreasing intensity and first eight of them are named A through H. The main transitions responsible for the formation of such peaks with their relative intensities, calculated energy, computed peak data and measured energies are presented in Tables 25. All these transitions in the element 40 r have energies and intensities such that a superposition of corresponding Gaussian lines gives rise to a spectrum consisting of 4 peaks, the number increasing with rise in and becomes 6 in 50 Sn. The computed Lβ 1 satellites spectra in this case of two representative elements, 44Ru and 48 Cd, are shown in Figs 2 and 3. A comparison of the computed spectrum of an element with the measured satellite spectrum reveals that

5 POONIA & SONI: Lβ 1 SATELLITES IN XRAY EMISSION SPECTRA 123 Table 2 Calculated energy and relative intensity of peak1 and 2, and of the transitions C and E which gives rise to these peaks. The corresponding measured β 1 I energy are also shown C ( 3 P 2 3 P 2 ) Rel Int E ( 3 P 2 3 P 1 ) Rel Int Computed peak data Peak1 & 2 Rel Int Measured β 1 I energies Table 3 Calculated energy and relative intensity of transitions A, B and H and of corresponding peak2 and 3. The satellites β 1 II to which this peak is identified are also shown A ( 3 F 3 3 F 3 ) B ( 3 F 2 3 F 2 ) H ( 3 F 2 3 F 3 ) Computed peak data Peak2 and 3 Measured β 1 II energies Table 4 Calculated energy and relative intensity of transitions F and G and of computed peak3 and 4. The satellites β 1 III to which this peak is identified are also shown F ( 3 F 3 3 F 4 ) G ( 1 D 2 1 D 2 ) Computed peak data Peak3 and 4 Measured β 1 III energies

6 124 INDIAN J PURE & APPL PHYS, VOL. 45, FEBRUARY 2007 Table 5 Calculated energy and relative intensity of transition D and G and of computed peak4 and 5. The satellite β 1 IV to which this peak is identified are also shown D ( 3 D 1 3 F 2 ) G ( 1 D 2 1 D 2 ) Computed peak data Peak4 and 5 Measured β 1 IV energies Fig. 4 Variation of calculated transition energies with. The measured spectra of elements with = 4050 are also shown, as in Figs. 2(ab), such that these agree with the interpolated values of peak energies of calculated spectra whereas the measured satellite energies are close to those of intense peaks, their separations in the computed and measured spectra are in good mutual agreement. The computed Lβ 1 satellite spectra are presented in Figs 2 and 3, in each of which the measured satellite data are shown by vertical bars at the top of the figure. In Fig. 4, we have shown the energies of various intense transitions of calculated spectra (Figs 2 and 3), and have also presented in it the positions of measured satellites β 1 I, β 1 II, β 1 III and β 1 IV in these spectra. Figs 2 4 give a clear view of one to one correspondence between the measured satellites and intense transitions of calculated spectra p 1/2 1 3d 1 3d 2 array 3. A, B and H Out of these three most intense transitions 3 F 3 3 F 3, 3 F 2 3 F 2 and 3 F 2 3 F 3, named A, B and H, respectively of the complete 2p 1 1/2 3x 1 3x 1 3d 1 (x s, p, d) array, the A and B have energies very close to each other in all the elements 40 Mo to 50 Sn. Their superposition gives rise to the highest peak in each of the spectra, marked 2 in = 40 to 46 and marked 3 in = 47 to 50 (Figs 2 and 3). This is, hereby, identified as the II satellite β 1 in the spectra of 40 r to 50 Sn. The transition 3 F 2 3 F 3, namely H is the weakest transition of the eight transitions AH of the 2p 1 1/2 3x 1 3x 1 3d 1 array, considered in this study, and has energy close to those of A in the range = It, also, contributes in forming the peak2 in = 40 to 46 and peak no 3 in = 47 to 50, and hence it can be taken as the supporting origin for the line β II C and E In the elements = 40 to 50 the transitions C ( 3 P 2 3 P 2 ) and E ( 3 P 2 3 P 1 ) of the 2p 1/2 1 3d 1 3d 2 array and

7 POONIA & SONI: Lβ 1 SATELLITES IN XRAY EMISSION SPECTRA 125 some weaker ones contribute to peak1 in 40 r to 46 Pd and peak1 and 2 in 47 Ag to 50 Sn (Figs 2 and 3), in order of increasing energy. The transition E is closer to C in 42 Mo to 46 Pd, and gradually shifts towards peak2 as increases. It, therefore, adds to peak1 in 42Mo and 44 Ru, forms a shoulder in 46 Pd and, transition E gives rise to a well separated peak, marked 2 in 47 Ag to 50 Sn. The lines β 1 I in the spectra of 42Mo and 44Ru are identified with peak1, respectively. In the spectrum of 46 Pd, the measured position of β 1 I is between these peaks. While, in those of 47 Ag to 50 Sn, peak2 is identified as β 1 I. The peak1 merges with Lβ 1 line in the spectra of elements = 47 to 50 and hence is not observed independently Transition F The transition 3 F 3 3 F 4, namely F is the weakest transition of the 2p 1/2 1 3d 1 3d 2 array considered in this study. The measured β 1 III energies in the spectra of elements with 42 Mo to 50 Sn are in an excellent agreement with the calculated energies of the transition F. The peak formed by it has been marked 3 in 42 Mo to 46 Pd and marked 4 in 48 Cd to 50 Sn (Figs 2 and 3). This is, hereby, identified as the satellite β 1 III in the spectra of = Transition D and G The transition D, namely 3 D 1 3 F 2 has the highest energy of the 2p 1 1/2 3d 1 3d 2 array being considered in the present study. The peak formed by it has been marked 4 in 42 Mo to 46 Pd and peak5 in 47 Ag and 48 Cd in Figs 2 and 3. This is, hereby, identified as the satellite β IV 1 in the spectra of 42 Mo to 48 Cd. The transition G, namely 2p 1 3p 1 1 D 2 3p 1 3d 1 1 D 2 has energy close to it on its higher side. Hence, it can be taken as the supporting origin for the line β IV p 1 3p 1 3p 1 3d 1 array In this array, the strongest transition is 3 D 1 3 F 2 and 1 D 2 1 F 3 as presented in Table 1. The transition no. 9, namely 1 D 2 1 F 3 is the most intense transition of all the 2p 1 3p 1 3p 1 3d 1 ones falling in the Lβ 1 region of the spectra under study, and so has an intensity higher than that of the transition 1 D 2 1 D 2, namely G. Its calculated energy lies on lower energy side of β 1 line and hence the satellite structures corresponding to them cannot be expected to be resolved from it. The transition no 11, namely 3 D 1 3 F 2 has an intensity little less than that of transition G and has energy close to it and on its lower side of A. It, also, contributes in forming the peak2 in all the spectra and hence can be supporting origin for the line β 1 II in the range 40 r to 46Pd and β 1 I in the elements 47 Ag to 50 Sn. 3.3 Other transitions The transitions shown at sr no 8 to 14 in Table 1, have energies lying in the range of transitions A through H and, therefore, merge with one or other of the peaks formed by them. The transition no. 8, namely 2p 1/2 1 3d 1 3 F 3 3d 2 3 F 2 has energy value very close to the most intense transition A and has an intensity lower than one tenth of that of A. Therefore, this transition cannot be expected to be observed independent of the transition A. Hence, it can be taken as the supporting origin for the line β 1 II in the range of elements = 40 to Conclusion The present studies have revealed that all four satellites β 1 I, β 1 II, β 1 III and β 1 IV observed in Lβ 1 spectra of elements = 4050, with a few exceptions, arise mainly due to 2p 1/2 1 3d 1 transitions in the presence of a 3d spectator vacancy. The association of various intense transitions of the array with the measured satellites is presented in Table 6. On the basis of agreement between computed spectra and measured satellites, it is observed that the satellite β 1 I is emitted by the superposition of two intense transitions, 3 P 2 3 P 2 and 3 P 2 3 P 1, in order of decreasing contribution of intensity. It has been well established that the transition 3 F 3 3 F 3 is the main source of the emission of Table 6 Lβ 1 satellites and corresponding 2p 1/2 1 3x 1 3x 1 3d 1 (x s, p, d) transitions in elements 40 r to 50Sn Satellites I β 1 C, E C, E C, E C, E C, E C, E C, E E E E II β 1 A, B, H A, B, H A, B, H A, B, H A, B, H A, B, H A, B, H A, B, H A, B, H A, B, H III β 1 F F F F F F F F F, G F, G IV β 1 D, G D, G D, G D, G D, G D, G

8 126 INDIAN J PURE & APPL PHYS, VOL. 45, FEBRUARY 2007 the satellite β 1 II in the elements 42 Mo to 50 Sn. Coming to the other two satellites in this region of the spectra, the line β 1 III, observed in the spectra 42 Mo to 50 Sn, is assigned to the transition 3 F 3 F 4. The line β 1 IV, observed in the spectra of elements with = 4248, has, similarly, been assigned to the 1 D 2 1 D 2 transition. Unfortunately no experimental data are available on the intensities of these satellites. References 1 Soni S N, in: S K Joshi, B D Shrivastava and A P Deshpande (Eds.), Xray Spectroscopy and Allied Areas, Narosa Pub House, New Delhi, 1998, pp 59. This is a review report and contains a list of the papers published by the author on this subject in the period Poonia S & Soni S N, Indian J Pure & Appl Phys, 38 (2000) Soni S N & Poonia S, J Phys Chem Solids, 61 (2000) Poonia S & Soni S N, J Phys Chem Solids, 62 (2001) Poonia S & Soni S N, J Electron Spectrosc Relat Phenom, 122 (2002) Soni S N & Poonia S, Indian J Phys, 76B (2002) Poonia S & Soni S N, Indian J Pure & Appl Phys, 40 (2002) Wentzel G, Ann Phys NY, 66 (1921) Wentzel G, eits Physik, 31 (1925) Condon E U & Shortley G H, The Theory of Atomic Spectra, (1967) (Cambridge University Press) pp Cauchois Y & Senemaud C, 2 nd Edition, Wavelengths of X Ray Emission Lines and Absorption Edges, (1978), (Pergamon Press, Oxford), pp Soni S N, J Phys B: At Mol Opt Phys, 23 (1990) Bearden J A & Burr A F, Rev Mod Phys, 39 (1967) Krause M O, Wuilleumier F W & Nestor C W, Phys Rev A, 6 (1972) Chen M H, Crasemann B, Aoyagi M & Mark H, Phys Rev A, 15 (1977) Tulkki J & KeskiRahkonen O, Phys Rev A, 24 (1981) PutilaMantyla P, Ohno M & Graeffe G, J Phys B: At Mol Phys, 17 (1984) PutilaMantyla P & Graeffe G, Phys Rev A, 35 (1987) PutilaMantyla P & Graeffe G, Phys Rev A, 39 (1989) Larkins F P, At Data Nucl Data Tables, 20 (1977) Shirley D A, Phys Rev A, 7 (1973) Larkins F P, J Phys C (GB), 10 (1977) Moores D L, Golden L B & Sampson D H, J Phys B, 13 (1980) McGuire E J, Lshell Auger, CK and radiative Matrix elements, Report No. SCRR710075, Sandia Laboratories, (1971). 25 Carlson T A & Nestor Jr. C W, Phys Rev A, 8 (1972) Maskil N & Deutsch M, Phys Rev A, 38 (1988) 3467.

Systematization of L X-ray satellites I: Lα satellites

Indian Journal of Pure & Applied Physics Vol. 42, December 2004, pp. 891-895 Systematization of L X-ray satellites I: Lα satellites U D Misra & N Kumar Department of Physics, Lucknow University, Lucknow