Multiple ionization effects on total L-shell X-ray production cross sections by proton impact

ARTICLE IN PRESS

Radiation Physics and Chemistry 69 (2004) 257–263

Multiple ionization effects on total L-shell X-ray production cross sections by proton impact J. Miranda*, O.G. de Lucio, E.B. Te! llez, J.N. Mart!ınez ! Instituto de F!ısica, Universidad Nacional Autonoma de M!exico, Apartado Postal 20-364, M!exico D.F. 01000, Mexico Received 10 March 2003; accepted 14 August 2003

Abstract The effect of multiple ionization on total L-shell X-ray production cross sections by proton impact, with energies below 1 MeV, on elements with atomic numbers in the range 26–55 was studied. Measurements of those cross sections for several elements were also done to enlarge the experimental database. Several tables for atomic parameters (fluorescence yields and Coster–Kronig transition probabilities) were used. The agreement between theory and experiment was optimized when average fluorescence yields given by Hubbel et al. (J. Phys. Chem. Ref. Data 23(2) (1994) 339) and a multiple ionization model proposed by Lapicki et al. (Phys. Rev. A 34(5) (1986) 5813) were used together. Thus, improvements to theoretical predictions for ionization cross sections should consider first a correct set of atomic parameters. r 2003 Elsevier Ltd. All rights reserved. Keywords: Ion–atom collision; Multiple ionization; Fluorescence yield; X-ray production cross sections; PIXE

1. Introduction The accurate knowledge of X-ray production cross sections by ion impact is necessary to adequately apply the analytical technique known as particle-induced Xray emission (PIXE) (Johansson and Campbell, 1988). As characteristic X-ray emission involves several atomic inner-shell processes, from primary ionization by the incoming radiation, up to the subsequent vacancy filling from outer-shell electrons, including intrashell transitions, it is necessary to describe all of them appropriately. The description of K-shell X-ray emission is already satisfactory, so even reference cross sections have been published (Paul and Sacher, 1989). However, due to their increased complexity, L- and M-shell X-ray emissions have not been properly taken into account. Therefore, much effort has been dedicated to this task (Miranda and Lugo-Licona, 2001; Lapicki, 2002). *Corresponding author. Tel.: +52-55-5622-5073; fax: +5255-5622-5009. E-mail address: miranda@fisica.unam.mx (J. Miranda).

However, the models proposed to explain, for example, the L-shell ionization, show an increasing sophistication (Balsamo et al., 1999), and are difficult to use in any analytical applications. In previous work, Miranda et al. (2001) showed that total L-shell X-ray production cross sections are acceptably described by the ECPSSR theory of Brandt and Lapicki (1981). This model improves the plane wave Born approximation by taking into account projectile energy loss (E), Coulomb deflection of the incident ion (C), polarization and change in electron binding energies through a perturbed stationary states method, and relativistic values of target electron mass (R). Nevertheless, Miranda et al. (2002) demonstrated that the use of different databases for atomic parameters, namely emission rates, fluorescence yields and Coster–Kronig transitions, has a significant effect on the theoretical predictions for the L-shell X-ray emission. There is still a question about the role of multiple ionization effects on this process. Several authors (Mehta et al., 1995; Semaniak et al., 1995; Yu et al., 1997) have considered this effect when heavier projectile ions are used, such as

0969-806X/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2003.08.014

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performed for selected elements in the aforementioned atomic number range and for proton energies between 250 and 700 keV.

He or C. M-shell was studied by Yu et al. (1995) and by Braich et al. (1997). However, the case of protons is still largely unexplored, in spite of the explanation given by Lapicki (2002) about the possible disagreement of the theoretical predictions with experimental data. Lapicki et al. (1986) proposed a heuristic model to consider multiple ionization in order to correct the fluorescence yields. The adjustment considers a basic assumption: the fluorescence yields are modified by the creation of holes in the outer shells by the incoming projectiles, with an equal probability for each shell. This probability is calculated through the binary encounter approximation (Madison and Merzbacher, 1975) avoiding the cumbersome treatment of outer-shell ionization by other quantum or semiclassical theories. The equation for the corrected fluorescence yield reads os ¼

o0s ; 1  ðZ12 =2bv21 Þ ½1  ðb=4v21 Þ ð1  o0s Þ

2. Experimental Total X-ray production cross sections for elements Se, Br, Rb, Ru, Ag, Cd, Sb, I, and Cs were measured by means of the 0.7 MV Van de Graaff accelerator at the Instituto de F!ısica, UNAM. A diagram of the experimental setup is displayed in Fig. 1. A Canberra Si(Li) detector (resolution 190 eV at 5.9 keV) was located at a 90 angle from the incident beam direction and a 25 mm2 Canberra PIPS detector (placed at a 155 angle) was used to analyze backscattered protons. The beam had a 2 mm diameter and its incident direction formed an angle of 45 with the sample surface. Most targets were in the form of thin films (MicroMatter Co., Deer Harbor, WA, USA), with a nominal thickness of 50 mg/cm2 deposited onto 3.5 mm Mylar substrates. The Ru target (acquired from Goodfellow, Huntingdon, England), had a thickness of 53 (7) mg/cm2, which was measured using Rutherford backscattering with a 0.7 MeV He beam. Proton energies ranged between 200 and 700 keV. Typical proton beam currents were 5 nA. The signals from the detectors were processed by a 2024 Canberra amplifier (X-rays), and a 142-A Ortec preamplifier together with a 2022 Canberra amplifier (backscattered protons). Spectra were collected by two Ace-Ortec multichannel analyzers, attached to personal computers. The beam energy was determined using the 19 F(p, ag)16O resonant nuclear reaction, with the device developed by De Lucio and Miranda (1999).

ð1Þ

where o0s is the single-hole fluorescence yield, Z1 is the atomic number of the projectile, n1 is the ion velocity, and b is a parameter fixed from electron binding energies, that takes the value 0.9 for the L-shell. According to Lapicki et al. (1986), this formula is always useful for Z1 ¼ 1; but is limited to the range ðZ1 =n1 Þoð2bÞ1=2 for heavier ions. Therefore, the goal of this paper is to evaluate the influence of multiple ionization on total L-shell X-ray emission by proton impact on elements with 26pZp55; through the heuristic equation proposed by Lapicki et al. (1986), based on a comparison of the ECPSSR theory that utilized the Smit procedure (1989) with existing experimental results. To enlarge this database, measurements of total X-ray production cross sections were Multichannel analyzers

Si(Li) detector

Faraday cup

Current digitizer and integrator

A

Particle detector Proton beam

0.7 MV Van de Graaff accelerator

Thin film target

Switching magnet

Fig. 1. Diagram of the experimental setup for X-ray production cross section measurements.

ARTICLE IN PRESS J. Miranda et al. / Radiation Physics and Chemistry 69 (2004) 257–263

The Si(Li) detector efficiency was measured by means of K X-rays from elements Mg to Ge; the K-shell reference ionization cross sections given by Paul and Sacher (1989), and the atomic parameters (fluorescence yields and branching ratios) from Hubbell et al. (1994) and Scofield (1974) were used to calculate the K X-ray production cross sections. A 700 keV proton beam produced the primary excitation for the efficiency determination. X-ray production cross sections sX were obtained from peak areas YX through the equation sX ¼

YX OR sR F ðE0 Þ; eYR

ð2Þ

where OR is the solid angle subtended by the particle detector; sR is the backscattering cross section (Rutherford corrected by the L’Ecuyer electron screening effect); YR is the number of ions backscattered towards the particle detector, e is the X-ray detector efficiency for the measured line. The term F ðE0 Þ is a correction factor for X-ray self-absorption and ion stopping in the emitting film, which is important when low ion energies are used, as is the case in this work. This correction factor is given by (Braziewicz et al., 1994)

259

sections were calculated with the SRIM computer code (Ziegler et al., 1999), and the mass attenuation coefficients were evaluated using the XCOM program (Saloman et al., 1988).

3. Results and discussion The experimental cross sections measured in this work are presented in Table 1. In order to estimate their accuracy, the results for Ru are plotted in Fig. 2, as an example, compared with predictions from the ECPSSR theory. Fluorescence yields from Krause (1979) were used to compute the predictions. The agreement is very good, although in the high-energy region there is a slight overestimation of the cross sections by the theory. A further evaluation of the data can be carried out following the same line taken in the work of Miranda et al. (2001), using the ratios of experimental to theoretical cross sections, S; as a function of the reduced velocity parameter xR L ; which was defined by Rodr!ıguezFern!andez et al. (1993). This parameter is thoroughly explained in Appendix A.



2 1 þ 12 ð2 þ bÞ DE=E0 þ 16 ð2 þ bÞ ð3 þ bÞ DE=E0 F ðE0 Þ ¼

2 1  12 ða  b þ mxÞ % DE=E0 þ 16 ðða  bÞ ða  b  1Þ þ ð2a  3bÞmx% þ ðmxÞ % 2 Þ DE=E0 in which E0 is the ion incident energy, DE is the ion energy loss in the film, m is the mass attenuation coefficient, x% is defined as a mean thickness given by x% ¼ ½E0 =SðE0 Þ=ðcos g=cos dÞ; with SðE0 Þ the ion stopping cross section, g is the angle between the target normal and the beam axis, d is the angle between the target normal and the detection direction, while a and b are exponents calculated when expressions of the type sX pE p and SðEÞpE b are used as approximations. To compute this correction factor, the stopping cross

ð3Þ

The data set from the present work keeps close to the general trend of the rest of the experimental results, which comprise the 530 experimental points used previously, as observed in Fig. 3. Again, fluorescence yields and Coster–Kronig transition probabilities from Krause (1979) were employed. Now, as discussed in the work by Miranda et al. (2002), it is useful to evaluate the effect of using different databases for the atomic parameters. Considering that total L X-ray production cross sections were calculated,

Table 1 Total L-shell X-ray production cross sections by proton impact (barns) Energy (keV) 200 250 300 350 400 450 500 550 600 650 700 a

Se

Br a

98.8 (10) 134 (14) 164 (17) 184 (19)

40.1 (4.1) 74.0 (7.5) 109 (11) 153 (15) 176 (18) 228 (23) 274 (28) 326 (33) 369 (37) 436 (44) 470 (47)

Rb 38.6 (3.9) 57.6 (5.8) 86.2 (8.7) 119 (12)

Ru

23.7 (3.3) 34.1 (4.6) 47.1 (6.3) 60.7 (8.8) 66.5 (8.8) 94.4 (13) 113 (15) 131 (17) 159 (20)

Numbers in parenthesis are the combined uncertainties.

Ag

Cd 11.0 16.9 22.7 28.0

35.7 (2.4) 46.0 (3.1) 58.8 (3.8) 72.4 (4.7) 86.9 (5.7) 104 (6.8) 119 (7.6)

Sb

I

(0.73) (1.2) (1.5) (1.9) 19.3 25.6 33.4 41.7 51.0 60.7 70.4

(1.3) (1.7) (2.2) (2.7) (3.3) (4.0) (4.6)

2.03 3.78 6.77 10.5

Cs (0.51) (0.95) (1.7) (2.6)

0.46 1.37 2.76 4.61 6.03 8.34 11.5 14.8 18.4 23.0 26.5

(0.03) (0.09) (0.18) (0.30) (0.40) (0.55) (0.76) (0.98) (1.2) (1.5) (1.7)

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Table 2 Average L-shell fluorescence yields for elements not listed in Hubbell et al. (1994) tables

200 180 160

σX (b)

140

+

H > Ru σExp σECPSSR

120 100 80 60 40

Z

oL

34 35 27 43 44 54 55

0.0175 0.0193 0.0077 0.0415 0.0456 0.097 0.104

20 0 200

300

400

500

600

700

800

3.5

Proton Energy (keV) 3.0

Fig. 2. Total L-shell X-ray production cross sections for Ru, as a function of proton incident energy. A comparison with the predictions of the ECPSSR theory is also shown.

2.5 2.0

S

8

1.5

7

Previous Data Miranda et al. 2001 This work

6

S

Krause Puri Hubbell Hubbell + MI

1.0

5

0.5

4

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

R ξL

3 2 1 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 R

ξL

Fig. 3. Ratios S of experimental to theoretical total L X-ray production cross sections for elements with 26pZp55; by proton impact with energies below 1 MeV, as a function of the reduced velocity parameter xR L : A comparison of data from this work is done with results from Miranda et al. (2001), and the full database.

three main data sets are available: the tables published by Krause (1979), the re-evaluation published by Puri et al. (1993) of Chen et al. (1981) atomic parameters, and the compilation of fluorescence yields from Hubbell et al. (1994). The difference among these databases is that the latter uses only average L-shell fluorescence yields, while the other two include subshell data. A disadvantage of the Hubbell et al. tables is that some of the values required in this work are not tabulated. Thus, a second degree polynomial fit to these values was done (oL as a function of Z). The values missing in the Hubbell et al. work are given in Table 2. Moreover, the influence of multiple ionization on higher atomic shells can be taken

Fig. 4. Mean ratios of experimental to theoretical total L X-ray production cross sections, as a function of the reduced velocity parameter xR L : Different tables for atomic parameters are used (Krause, 1979; Puri et al., 1993; Hubbell et al., 1994), including the Hubbell et al. (1994) review with multiple ionization corrections following Lapicki et al. (1986) model.

into account, if the heuristic approach suggested by Lapicki et al. (1986) is followed. To carry out this comparison, it was better to calculate the average values of the ratios S; after dividing the xR L range in smaller intervals, having a width equal to 0.1. The results are displayed in Fig. 4. It should be noted that the multiple ionization correction was applied only to the data set providing the best results, namely, the Hubbell et al. average L fluorescence yields. The mean ratio for the complete data set is shown in Table 3, giving the data for every database. It is apparent that the Hubbell et al. tables, together with the multiple ionization correction, provide the best results, giving a value closer to unity. The improvement in the theoretical predictions is more dramatic for the lowest energy range. In particular, the mean ratio S for xR L ¼ 0:2 goes down from 3.08 (0.51) for Krause’s tables to 2.18 (0.38), where the number between parenthesis is the standard deviation of the mean. It can be seen that there

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Table 3 Mean ratios of total L-shell experimental to theoretical cross sections for the complete data set (593 points) Atomic parameters

Krause (1979)

Puri et al. (1993)

Hubbell et al. (1994)

Hubbell et al.+multiple ionization

Mean Standard deviation of the mean

1.18 0.021

1.13 0.020

1.10 0.019

1.03 0.016

is not only a reduction in the average, but also in the spread of the data. Furthermore, the differences among the average S ratios for xR L > 0:8 lie within the standard deviation of the data. All this is explained by the fact that the multiple ionization correction is more important in the low-energy range, precisely where the theoretical models have failed to predict the cross sections. These results suggest that the disagreement between theory and experiment may be due to the use of inappropriate atomic parameters in the comparisons, rather than to imperfect theoretical models. Therefore, it is recommended that multiple ionization corrections be used both for the evaluation of theories, as well as with total L-shell X-ray production cross sections computed for analytical applications with PIXE. However, it is necessary to point out that more experiments are necessary in the lowest energy range, to reduce the uncertainties in the average ratios of experimental to theoretical cross sections.

possible that the already existing theories, such as the ECPSSR, require no further refinements, but only a better knowledge of the atomic parameters involved. Finally, these results should be used in PIXE analytical applications, so more accurate quantitative results are obtained.

Acknowledgements The authors thank the technical assistance of J.C. Pineda for accelerator operation. Work supported in part by IAEA (contract 9944-R), and CONACYT (contract 25085-E). The participation of E.B. T!ellez and J.N. Mart!ınez was possible through the program ! ! UNAM. Jovenes Hacia la Investigacion,

Appendix A. Definition of the reduced velocity parameter The reduced velocity parameter xR L ; defined by Rodr!ıguez-Fern!andez et al. (1993), and based on the work of Brandt and Lapicki (1981), is given by the following expressions:

4. Conclusions The total L X-ray production cross sections measured in this work are in full agreement with previous experiments, as shown in Fig. 3. The use of different databases for atomic parameters (fluorescence yields and Coster–Kronig transition probabilities) have an essential role in the accuracy of the theoretical predictions for these cross sections, showing a dramatic improvement in the lowest energy range. Multiple ionization corrections together with the average fluorescence yields published by Hubbell et al. (1994) offer more accurate theoretical predictions, when compared with the experimental database. This must be considered very thoroughly when evaluating theoretical models for L-shell ionization cross by proton impact. It is

R R 1 R xR L ¼ 4 ðxL1 þ xL2 þ 2xL3 Þ;

ðA:1Þ

xR Li

where is the relativistic reduced velocity parameter of the Li subshell (i ¼ 1; 2 or 3). This variable takes into account the number of electrons in every subshell. The relativistic velocity parameters are defined by  R 1=2 ms xs xs ; ðA:2Þ xR Ls ¼ zs  zs ¼ 1 þ

 2Z1 ½gs ðxs Þ  hs ðxs ; cs Þ Z2s ys

ðA:3Þ

with mR s the corrected relativistic electron mass:

80 0  2 12 1 0  2 1 > Z2s Z2s > > B C > B0:40 c C C B0:40 c C > B > B B C C > >B C C C; > B1 þ b0 B CþB > @ @ A A n x n x 2 2 > s s A > >@ > < 2 1=2 mR þ ys ¼ 0 0 s ¼ ð1 þ b0 ys Þ  2 12 1 0  2 1 > > Z2s Z2s > > B > B0:15 c C C B0:15 c C > B C > B C C B C > B > C CþB C; > > B1 þ b0 B @ A A @ A xs xs > @ > > :

s ¼ K; L1 ðA:4Þ s ¼ L2 ; L3

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and gL1 ðxs Þ ¼ ð1  xs Þ9 ð1 þ 9xs þ 31x2s þ 49x3s þ 162x4s þ 63x5s þ 18x6s þ 0:515x7s Þ;

ðA:5Þ

gL2;3 ðxs Þ ¼ ð1  xs Þ10 ð1 þ 10xs þ 45x2s þ 102x3s þ 331x4s þ 6:7x5s þ 58x6s þ 7:8x7s þ 0:888x8s Þ;

ðA:6Þ

!

hs ðxs ; cs Þ ¼

IðxÞ ¼

2n2 Iðcs n2 =xs Þ; ys x3s

8   3 1 > >  1 ; p ln > > > 4 x2 > > > > < e2x ð0:031 þ 0:21x1=2 þ 0:005x > 0:069x3=2 þ 0:324x2 Þ1 ; > > > > 2x > 2e x1:6 ; > > > : 0;

ðA:7Þ

0pxp0:035; 0:035pxp3:1; 3:1pxp11; x > 11;

ðA:8Þ which are functions that describe the electron cloud polarization during the ion–atom collision. In Eq. (A.4), b0 is a constant of the order of 1.1. Moreover, Z1 is the projectile atomic number; Z2s ¼ Z2  4:15; with Z2 the atomic number of the target; ns is the principal quantum number of the shell to be ionized, and c is the speed of light. The constant cs takes the value 1.5 for s ¼ L1 and 1.25 for s ¼ L2;3 : The non-relativistic reduced velocity xs can be calculated with the formula: v1 xs ¼ ; ðA:9Þ ð1=2Þys v2s where ys ¼

_o2s Z2s R

ðA:10Þ

is a reduced electron binding energy in shell s; while R ¼ 13:6 eV; is Rydberg’s constant. The variable n2s is the electron speed in the shell to be ionized, and n1 is the projectile speed before the collision.

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