Systematization of L X-ray satellites I: Lα satellites

Transcription

1 Indian Journal of Pure & Applied Physics Vol. 42, December 2004, pp Systematization of L X-ray satellites I: Lα satellites U D Misra & N Kumar Department of Physics, Lucknow University, Lucknow udmisra@rediffmail.com Received 3 December 2003; revised 29 April 2004; accepted 21 June 2004 The iterative procedure, based on Hagström's method of the doubly modified Moseley plot, has been used for the first time for the systematization of Lα X-ray satellites for 48 < Z < 80. This has resulted in: (i) the identification of a number of satellites measured by certain researchers and (ii) removal of anomalies in the measurements of the wavelength of some satellite lines. [Keyword: Lα satellites, LX-ray satellites] IPC Code: G01J 3/443 1 Introduction It is well known that X-ray satellites are very weak lines which arise as a result of single electron transfers in atoms, which are doubly or multiply ionized in inner shells. Their frequencies do not conform to the known X-ray energy level diagrams for singly ionized atoms, for that reason they are also called non-diagram lines. Following their discovery 1, a large number of papers have appeared dealing with the measurement of their wavelengths in different series in different atoms (Kα and Kβ for Z = 3 to 53; Lα, Lβ and Lγ for Z = 12 to 92 and Mα, Mβ and Mγ for Z = 21 to 92). The relevant data can be found in various compilations 2-5. However, in none of these tabulations there appears any critical assessment of the accuracy of the wavelength measurements. The result is a near-chaotic situation where the measurements of the wavelength of the same line as measured by different researchers using different techniques show considerable disagreement. In this connection, it needs to be emphasized that the wavelengths of the satellites measured by different researchers depend upon (i) the wavelengths of the reference lines used, (ii) purity of the sample, namely, whether the target was the pure element or a chemical compound thereof. These conditions were different for different researchers and moreover, in some cases, the accuracy of the measurements could also be in doubt. The situation is similar regarding the interpretation of the origin of different lines. In earlier attempts 6,7 efforts were made to identify the inner levels AX XB which are involved in the emission of a satellite of the parent diagram line A B, with X as the spectator vacancy. However, as pointed out by Ray 8 the levels AX and XB should not be treated as single levels but as multiplets arising as a result of the exchange interaction between the electrons of the levels AX and XB. It must however be realized that the exact calculation of the individual levels of a multiplet is a very difficult task since such a calculation has to start from a knowledge of the relevant wave functions, which become increasingly complicated as the atomic number Z increases. Furthermore, such calculations deal with free atoms, and do not take into account the solid state effects. The experimental results obtained by X-ray spectroscopicts are invariably obtained from solid targets, which explain the disagreement between the theoretical calculations of different researchers as well as between theory and experiment. A practical wayout of this difficulty is provided by a method of calculation based on the Moseley plot and its modifications, namely, the modified Moseley plot of Idei 9 and the doubly modified Moseley plot first described and used by Hagström 10 which is applicable to limited ranges of atomic numbers in which a sub-shell is being filled up. Since the starting point of such calculations is provided by the experimental observations this avoids the difficulties mentioned above regarding the lack of knowledge of exact wave functions. A further improvement in this procedure is provided by the iterative method developed by Misra et al. 11,12 for which the starting point is Hagström's method of the doubly modified Moseley plot. This

2 892 INDIAN J PURE & APPL PHYS, VOL 42, DECEMBER 2004 method has already been successfully used 12 in the case of X-ray diagram lines for (i) prediction of wavelength positions of those lines which have not been reported for certain elements though they have been measured for others and (ii) removal of anomalies in the measurement of the wavelength of some lines. In the present paper, the application of the iterative method 11,12 to the calculation of the wavelength of the Lα satellites for the atomic numbers Z=48 to 80, has been extended. 2 Theory For the sake of completeness, a brief description of the iterative method of Misra et al. 11,12 has been given. It is well known that the Moseley plot 13,14 is a graph ev versus Z of where ev is either a level binding energy or a diagram line energy measured in electron volts, and Z is the atomic number. The resulting curve is a straight line ev =AZ+B where A and B are the slope and intercept of the line as obtained by the method of least squares respectively. Idei 9 modified the curve by plotting, ev AZ B versus Z which makes it possible to make even small errors in measurement discernible. This plot is generally of parabolic shape which by suitably choosing the constant B, is made to have its vertex lie on the Z- axis. Now, following Hagström s 10 when the square roots of the points lying on the parabola ( ev AZ B versus Z curve) are taken, these points lie on two different straight lines, both passing through the vertex of the parabola. If the parabola is symmetric and the straight line on the high Z side of the vertex is reflected in the Z-axis, then it would form a continuation of the straight line on the low Z-side of the vertex and the two will now have the same slope which would be determined by the constant C on the doubly modified Moseley plot ( ev AZ B) 1/2 =CZ+D. The plot of ( ev AZ B) 1/2 CZ against Z would then be a straight line parallel to the Z-axis at a distance D from it. If, however, the two limbs of the Moseley plot are unsymmetrical, then the constant C will have different values C 1 and C 2 for the two segments of the doubly modified Moseley plot. Separate least square fits are now made to the straight line segments as obtained from the doubly modified Moseley plot, their slopes being denoted by C 1 and C 2 respectively. Plots of ( ev AZ B) 1/2 C 1 Z and ( ev AZ B) 1/2 C 2 Z are then made against Z. These plots are found to be very nearly parallel to the Z-axis with two different intercepts D 1 and D 2 respectively. The actual values of the intercepts D 1 and D 2 are obtained by taking the average of the ordinates of the individual points. Using the individual averaged values of these separate intercepts and values of slopes of these two separate straight lines as well as the values of constant A and B as obtained before, it is found that the energy value thus calculated for each Z is modified and two different modified energy values are obtained for the point corresponding to the vertex of the parabola. The average of these is used along with the modified energy values of remaining Z, to start another cycle of calculation. The entire process is repeated till after a certain cycle of iterations a self consistent set of energy values is obtained. Further details may be obtained from the paper referred to earlier 11,12. This iterative self-consistent modification of the doubly modified Moseley plot can be profitably applied in different atomic number ranges to data which in the first approximation obey the Moseley law. With this end in view, we plotted ev versus Z graphs for a large number of satellites in the atomic number ranges 48 < Z < 56, 57 < Z < 71 and 72 < Z < 80. It was observed that these plots are very nearly straight lines which clearly demonstrate that satellite energies also obey the Moseley law, a fact which was pointed out for the first time by Deodhar and Rai 15,16. Consequently, the method of the iterative selfconsistent doubly modified Moseley plot can be used with confidence for systematization of X-ray satellite energies. It is hoped that this will lead to precise computation of the wavelengths of these satellites. 3 Results In Table 1, we list the wavelengths in x u as compiled by Cauchois and Sénémaud 5 for the satellite lines Lα 3, Lα 4, Lα 5, Lα 6 and Lα 7 in the atomic number range Z = 48 to 56. Table 2 contains similar data for Lα x line in the atomic number range Z = 57 to 80. Along with these values the wavelength values are given as obtained by us in the final cycle of iteration for these lines. For the first cycle of our calculation we have used the wavelength values given by Cauchois and Sénémaud 5 and the conversion factor λ (x u) V (kev) = for converting wavelength values into ev. The same factor was used to convert our calculated values in the final cycle of iteration from ev to x u. Some of the experimental values in Tables 1 and 2 do not figure in the Cauchois-Sénémaud tables. These values along with relevant references are marked with an asterisk.

3 MISRA & KUMAR: Lα SATELLITES 893 Table 1 Comparison of experimentally observed 5 and our calculated wavelengths of different Lα satellites for 48 < Z < 56 All values in xu Lines Satellite Lα 3 Satellite Lα 4 Satellite Lα 5 Satellite Lα 6 Satellite Lα 7 Experimentally Calculated Experimentally Calculated Experimentally Calculated Experimentally Calculated Experimentally Calculated Z observed by authors observed by authors observed by authors observed by authors observed by authors * * * * * * ,24* * * * Table 2 Comparison of experimentally observed 5 and our calculated wavelengths of the Lα x satellite for 57 Z 80. All values in x u Z Experimentally observed Calculated by authors * * *, * Discussion A scrutiny of the wavelengths given in Tables 1 and 2 shows that apart from very few exceptions there is a close agreement between the experimental wavelength values compiled by Cauchois and Sénémaud 5 and those calculated by us. We therefore, conclude that our iterative procedure for calculation of the wavelength values of all the lines studied in the present investigation is quite reliable. We now proceed to the discussion of certain salient features brought out by an examination of the wavelengths given in Tables 1 and 2. An examination of the Cauchois and Senemaud table reveals that wavelengths for the following satellites do not figure in the tabulation; Lα 3 for Z = 51, 52 and 54; Lα 4 for Z = 54, 55 and 56; Lα 5 for Z = 54 and 55; Lα 6 for Z = 54 and 55; Lα 7 for Z = 54 and 55; Lα x for Z = 57 to 61, 63, 65, 67 and 69. It also appears that the following satellites had in fact been measured by different researchers as given below: Lα x for Z = 60; x u, Srivastava et al. 17 ; Lα x for Z = 63; x u, Srivastava et al. 18 ; Lα x for Z = 67; x u, Nigam et al. 19 and also x u, Qapoor 20. It is not clear, why their data were not included in the Cauchois and Sénémaud tabulation. The agreement between our calculated wavelength values and the experimental values as reported by the above authors is fair for Z = 60, quite good for Z=63 and excellent for Z=67 (Table 2). Two workers have measured certain satellites but the Cauchois and Sénémaud tables list only the more recent of the two measurements without giving any reasons for doing so. These are:

4 894 INDIAN J PURE & APPL PHYS, VOL 42, DECEMBER 2004 Lα 6 satellite for Z = 48 The wavelength of this line is reported as x u by Randall and Parratt 21 and as x u by Richtmyer and Richtmyer 22. Reference to Table 1 shows that our calculated value of x u agrees much better with the value reported by Richtmyer and Richtmyer which has not been included in the Cauchois and Sénémaud tables, again without giving any reason. Lα 7 satellite for Z = 48 Here the experimental value of Randall and Parratt 21 is x u, while that reported by Richtmyer and Richtmyer 22 is x u. Our calculated value of x u is in excellent agreement with the value of Richtmyer and Richtmyer. Lα 5 satellite for Z = 49 In this case, the value reported by Randall and Parratt 21 is x u, while that of Richtmyer and Richtmyer 22 is x u. Again our calculated value of x u agrees more closely with that reported by Richtmyer and Richtmyer. The Lα 7 satellite for Z=49 In this case, Randall and Parratt 21 reported a wavelength of x.u. while that measured by Richtmyer and Richtmyer 22 is x.u. Here also our calculated value of x.u. is in excellent agreement with the experimental value of Richtmyer and Richtmyer. In case of Z = 55, Kelleström and Ray 23 have reported three spark lines at x u, x u and x u without identifying their origin. Cauchois and Sénémaud 5 classified these lines as nonidentified. Our calculations have led to the values of x u for Lα 4, x u for Lα 6 and x u for Lα 7 in fairly close agreement with the experimental values of Kelleström and Ray 23. Our work has thus led to the assignment of Lα 4, Lα 6 and Lα 7 for these spark lines. It is hoped that if these lines are measured once again, a closer agreement may result with our calculated values. It may also be mentioned that earlier Coster 24,25 in 1922 had measured a line at x u for Z = 55 and had identified it as Lα 3. However, much later in 1931, Doléjsék and Ruricék 26 reported the wavelength of Lα 3 as x.u. as given in the Cauchois and Sénémaud tables. The close agreement between our calculated value with the one identified by Coster as Lα 3 shows that the line measured by him was in reality Lα 6 and not Lα 3. In case of Z = 56, three spark lines reported by Kelleström and Ray 23 at x u, x u and x u, without any assignment, do not figure at all in the Cauchois and Sénémaud tables. Our calculations show that the line at x u (our calculated value x u) should be named Lα 3 while that at x u (our calculated value x u) should be named as Lα 4. It may be mentioned that Randall and Parratt 21 had later on reported a wavelength of x u for Z=56 and identified it as Lα 3 which supports our view that the "spark line" at x u, observed by Kelleström and Ray 23 should indeed be called Lα 3. Our calculated values are in better agreement with the values reported by researchers whose papers seem to have escaped the attention of Cauchois and Sénémaud. 5 Conclusion It is concluded that our method of iteration as applied to the doubly modified Moseley plot has led to the correct assignment of a number of satellite lines measured by various researchers but not included in the Cauchois and Sénémaud tables. As for the lines, which have not been measured so far, it is hoped that if these are carefully searched for, their wavelengths would be found to agree closely with the values calculated by us. Acknowledgement We wish to thank Prof B G Gokhale for critically going through the manuscript and for numerous helpful discussions. References 1 Siegbahn M & Stenström W, Z Physik 17 (1916) 48 & Siegbahn M, Spectroskopie der Röntgenstrahlen (Springer Berlin, 1931). 3 Cauchois Y & Hulubei H, Longuers d'onde des Emission X et des Discontinutie's d'absorption X (Herman, Paris), Sandström A E, Handbuch der Physik Vol. XXX, Cauchois Y & Sénémaud C. Longuers d'onde des Emission X et des Discontinuties d'absorption X. (Pergamon Oxford, 1978) 2 nd Ed. 6 Wentzel G, Ann Phys Lpz 66 (1921) Druyvesteyn M J, Z Phys 43 (1928) Ray B B, Philos Mag, 3 (1929) Idei S, Sci Rep Tohoku Univ Ser I, 19 (1930) Hagström S, Z Phys, 178 (1964) Misra U D, Mathew S & Gokhale B G, Z Phys D, 37 (1996) Misra U D, Mathew S & Gokhale B G, Indian J Pure & Appl Phys, 37 (1998) Moseley H G J, Philos Mag, 26 (1913) Moseley H G J, Philos Mag, 27 (1914) Deodhar G B & Rai S J, Phys B, 3 (1970) Deodhar G B & Rai S J, Phys B, 2 (1969) 1402.

5 MISRA & KUMAR: Lα SATELLITES Srivastava B D, Jain R K & Dubey V S, Can J Phys 55 (1977) Srivastava B D, Jain R K & Dubey V S, Phys Lett, 54A (1975) Nigam A N, Mathur R B & Gokhale B G, Phys Rev, A13 (1976) Kapoor Q S, PhD Thesis, (University of Rajasthan, Jaipur), Randall C A & Parratt L G, Phys Rev 57 (1940) Richtmyer F K & Richtmyer R D, Phys Rev 34 (1929) Kelleström G & Ray B B, Arkiv Mate Astrono Fysik, 24B (1934) No Coster D, Philos Mag, 43 (1922) Coster D, Philos Mag, 44 (1922) Doléjsék V & Ruricék J, C R Acad Sci (Paris), 192 (1931) 1369.