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L X-ray intensity ratios for proton impact on selected rare-earth elements
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 261 (2007) 153–156 www.elsevier.com/locate/nimb
L X-ray intensity ratios for proton impact on selected rare-earth elements Sam J. Cipolla
*
Physics Department, Creighton University, Omaha, NE 68178, USA Available online 27 March 2007
Abstract L X-rays excited by 75–300 keV protons impacting thick targets of Gd, Tb, Dy, Ho, Er, Tm and Yb were measured with a highresolution Si(Li) detector equipped with an ultra-thin window. The intensities of the La(L3M4,5) and Lb2,15(L3N4,5) X-rays relative to the L‘(L3M1) X-rays were compared with theoretical predictions. Discrepancies in the results are attributed to multiple vacancy production by various mechanisms. M4,5 and N4,5 ionization probabilities in these collisions are deduced from the results. Ó 2007 Elsevier B.V. All rights reserved. PACS: 32.80.Hd; 32.70.Fw Keywords: Multiple ionization; Inner-shell ionization; Relative X-ray intensities
1. Introduction X-ray transition rates are used to convert X-ray production cross sections into ionization cross sections. However, X-ray transition rates calculated from theory [1] assume a single initial vacancy in the radiating atom, which may be an understatement of the actual situation. If multiple vacancies exist in the atom, it is expected that the transitions rates will be altered. Multiple vacancies can arise from various mechanisms, either concurrent with or subsequent to the production of a particular inner-shell ionization. Subsequent effects include outer-shell ionization due to energy transfer from Coster–Kronig (CK) radiation-less transitions within the inner sub-shells where the primary ionization takes place. Another mechanism is the shake effect following an inner-shell ionization [2]. A concurrent effect in the case of X-ray emission produced by ion–atom collisions is multiple vacancy production from direct Coulomb excitation.
In this work, inner-shell ionization in atoms with Z = 64–70 is accomplished by 75–300 keV proton impact, and relative X-ray transition rates are measured for electron transitions filling a vacancy in the L3 shell. After estimating the contribution of Coster–Kronig transitions to the relative rates, multiple vacancy production from a combination of collision and shake effects can be determined by comparing the results with theory. Multiple ionization resulting from 75 to 300 keV proton collisions with selected 4d transition elements have been previously reported by us [3]. Kavcic et al. [4–6] have shown evidence of simultaneous K and L shell ionization for proton bombardment of selected elements up through Fe. With regards to rare-earths, similar results to those reported here have been obtained by calculating L‘/La and Lb2,15/La from the X-ray production cross sections reported by Fazinic et al. [7]. 2. Experimental system
*
Tel.: +1 402 280 2133; fax: +1 402 280 2140. E-mail address: [email protected]
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.03.019
The experimental system is the same one used in previous work [3]. A mass-analyzed proton beam produced in a Cockcroft–Walton accelerator impacts thick target foils.
154
S.J. Cipolla / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 153–156
A secondary-electron suppression cage surrounds the target holder, which is connected to a current integrator to measure the proton charge. The targets are oriented at 45° to the beam direction and to a high-resolution Si(Li) X-ray detector equipped with an ultra-thin window. An additional 6-lm aluminized-Mylar absorber was used to reduce the count rate from softer X-rays. 3. Data analysis The peak-fitting procedure allowed separation of the L‘(L3M1), Lg(L2M1), La (L3M4,5), Lb1 (L2M4), Lb3 (L1M2), Lb4 (L1M3), Lb2,15 (L3N4,5), Lc1(L2N1), Lc2 (L1N2), Lc3 (L1N3) and Lc4(L1O2,3) major peaks. However, for Gd, Tb, and Dy, the Lg and La peaks could not be resolved. Instead, a small correction to the combined La,g yield, based on the Lg/La ratio obtained from the other spectrum analyses, where these peaks could be separated, was applied to obtain the La yield. Preliminary to the calculation of the relative L X-ray transition rates, the X-ray production cross sections for protons of incident energy E were determined from the thick-target equation Y ðEÞ dY SðEÞ l x þ ; rðEÞ ¼ ð1Þ N Ae dE Y ðEÞ q where Y(E) = NX-ray/Nproton is the X-ray yield, NA is the target atom density, e is the detector efficiency, S(E) is the proton stopping power in the target (from TRIM [8]), l/q is the mass absorption coefficient for X-ray self absorption in the target (from XCOM [9]), and dY/dE is the slope of the measured Y(E) versus E curve. The yield slope, dY/dE, was obtained by fitting the yield data to Y(E) = A(E C)B and differentiating; A, B and C are the fitted parameters. The detector efficiencies, e, were determined from a combination of radioactive standards and K X-ray yields from bombarded thick foils using calculated ECPSSR yields (from ISICS [10]) as a standard [11]. Efficiency data were separately fitted using eðEx Þ ¼ X expðaEbx Þð1 expðcEdx ÞÞ, where Ex is the X-ray energy and X, a, b, c, d are fitted parameters [12]. As shown in [3], the relative transition rate, Ci/Cj, for two X-ray transitions, i an j, arising from the decay of
the same sub-shell vacancy can be obtained experimentally from Y ðEÞi 1 Ci rxi ei qtðE3 Þi ¼ x ¼ Y ðEÞ ; j 1 Cj exp rj ej
ð2Þ
qtðEÞj
where qt(E) is the effective thick-target thickness at incident energy, E, which thereby takes into account thick target effects on the X-ray production. Eq. (2) was used to calculate the relative transition rates for L‘/La and L‘/Lb2,15 averaged over all impact energies from 75 to 300 keV in 25-keV steps for each target, and the results were compared with theory [1]. From these results, an estimation can be made of multiple vacancies produced in the sub-shell from which the electrons make transitions. The occurrence of vacancies in the M1 shell is negligible compared with M4,5 due to the large difference in binding energies, the high probability of an M1 vacancy being promoted to higher M sub-shells via the CK effects, and because vacancy production in the M1 shell due to CK rearrangement among the L sub-shells is energetically prohibited. Since transition rates are proportional to the number of electrons in the shell from which electrons make a transition, then [3] ðCi =Cj Þexp N V V ¼ 1 ¼ 1 p; ¼ N N ðCi =Cj Þtheory
ð3Þ
where N is the normal population of electrons and V is the average number of electron vacancies produced in a subshell. The vacancy fraction, V/N, is equivalent to the corresponding ionization probability, p, of the affected shell(s); i.e. V = pN. Furthermore, since the CK and MI mechanisms are assumed to be independent, we have p = pCK + pMI; or, equivalently, V = VCK(L) + VMI, where MI denotes all other MI in addition to CK effects that result in M4,5 or N4,5 vacancies. The quantity VCK(L) can be determined by finding the overall probability that the CK process causes a vacancy to occur in the M4,5 shell (for La) and the N4,5 shell (for Lb2,15) prior to the X-ray emissions, given by Eq. (4) where ri are L sub-shell ionization cross sections (calculated from ECPSSR theory using ISICS [10]), and the fijS are the CK yields for S = M4,5 or N4,5 [13], which represent the probabilities for an electron from the M4,5 or N4,5 shell to be ejected from the atom
Table 1 Results of determining the vacancy fractions from multiple ionization (MI) due to the collisions leading to L3 X-ray emission after correction for Coster–Kronig vacancy production in the M and N shells Element (Z)
Gd(64) Tb(65) Dy(66) Ho(67) Er(68) Tm(69) Yb(70)
Theory/Expt. relative intensity ratios
PMI = VMI/N
L‘/La
Lb2,15/La
Lb2,15/L‘
M4,5 L‘/La
Lb2,15/La
Lb2,15/L‘
0.955 ± 0.096 0.996 ± 0.168 0.944 ± 0.086 0.958 ± 0.064 0.925 ± 0.081 0.812 ± 0.071 0.900 ± 0.063
1.058 ± 0.110 1.136 ± 0.165 1.096 ± 0.091 1.034 ± 0.064 1.000 ± 0.101 1.017 ± 0.093 0.982 ± 0.070
1.120 ± 0.109 1.188 ± 0.220 1.215 ± 0.116 1.081 ± 0.084 1.100 ± 0.119 1.262 ± 0.122 1.129 ± 0.078
0.0451 ± 0.0045 0.0045 ± 0.0008 0.0563 ± 0.0051 0.0424 ± 0.0028 0.0750 ± 0.0066 0.1635 ± 0.0365 0.1129 ± 0.0319
0.0855 ± 0.0062 0.0666 ± 0.0067 0.1080 ± 0.0063 0.0765 ± 0.0034 0.0734 ± 0.0049 0.1804 ± 0.0103 0.0902 ± 0.0047
0.0962 ± 0.0069 0.0853 ± 0.0140 0.1089 ± 0.0087 0.0855 ± 0.0054 0.0849 ± 0.0070 0.1703 ± 0.0122 0.1091 ± 0.0056
N4,5
S.J. Cipolla / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 153–156
V CKðLÞ ¼
wtd. av. Lβ2,15/Ll
1.4
155
r2 S r1 S f þ ðf þ f12S f23O þ f12O f23S þ f12S f23S Þ r3 23 r3 13
ð4Þ
Ll/Lα 1.3
Lβ2,15/Lα
4. Results
Theory/Expt.
1.2
Table 1, along with Figs. 1 and 2, present the results of these analyses. Fig. 1 shows that the L‘/La versus Z experiment to theory ratios are generally between unity and 0.9 as Z increases, except for 0.81 ± 0.07 at Tm (Z = 69). This indicates a minimal or small M shell ionization probability that increases with Z in these experiments. The total ionization probabilities, p = V/N, were calculated according to Eq. (3) are shown in Fig. 2. The CK ionization probability of the M4,5 shells, pCK, energetically occurs only for Tm
1.1 1.0 0.9 0.8 0.7 64
65
66
67
68
69
70
Z
Fig. 1. Theory/experiment ratio of the L‘/La, Lb2,15/La and Lb2,15/L‘ relative intensities.
0.20
Wt'd Average
0.15 0.10
V/N
0.05 0.00 -0.05
M N LINEAR FIT TO M LINEAR FIT TO N
-0.10 -0.15 -0.20 64
65
66
67
68
69
70
Z Fig. 2. Ionization Probability for M4,5 and N4,5 sub-shells due to proton collisions.
fijO
during the i ! j CK transition in the L shell; represent the CK yields for which no electron from the M4,5 or N4,5 is ejected. The MI ionization probability is finally obtained as pMI = p pCK.
and Yb by means of f13M4;5 in Eq. (4). A linear fit to the MI ionization probabilities, pMI = p pCK, shows a gradual rise with Z, going from 0.02 to 0.13 for the M4,5 shells, with uncertainties in the data ranging from about 10 to 30%, respectively. From Fig. 1 it is seen that the Lb2,15/L‘ intensity ratio comparisons with theory are fairly constant at around 1.2, which reflects the collisional MI occurring in the N4,5 shell along with negligible occurrence of vacancies in the M1 shell. All of the CK processes expressed in (4) contributed to multiple ionization of the N4,5 shells. A linear fit to the MI ionization probabilities, pMI = p pCK, presented in Fig. 2, ranges from approximately 0.06 to 0.13, with about 8% uncertainty in the data throughout. We also considered the Lb2,15/La intensity ratio comparisons with theory, which are shown in Fig. 1. These are affected by the MI occurring in both the M4,5 and N4,5 shells. Within error limits, the Lb2,15/La ratio is in accordance with the theory ratio, indicating almost equal ionization probabilities for the N4,5 and M4,5 shells, which was also noted above from Fig. 2. The branching ratios, L‘/L3, La/L3 and Lb2,15/L3, can be determined from the X-ray production cross section results, as follows: Ci rxi ¼ x x C3 rl þ ra þ rxb2;15
ð5Þ
There is a negligible error in ignoring the other L3 X-ray transitions as they comprise less than 1% of the total
Table 2 Transition rate branching ratios modified by multiple ionization in the M4,5 and N4,5 shells Element
Gd Tb Dy Ho Er Tm Yb
C‘/C3
Ca/C3
Cb2,15/C3
Expt.
Theory
Expt.
Theory
Expt.
Theory
0.0359 ± 0.0030 0.0335 ± 0.0044 0.0380 ± 0.0031 0.0362 ± 0.0025 0.0391 ± 0.0021 0.0439 ± 0.0038 0.0407 ± 0.0024
0.0336 0.0340 0.0344 0.0347 0.0353 0.0355 0.0359
0.823 ± 0.078 0.835 ± 0.118 0.826 ± 0.056 0.821 ± 0.043 0.813 ± 0.072 0.812 ± 0.066 0.810+0.050
0.811 0.811 0.811 0.810 0.814 0.809 0.808
0.148 ± 0.014 0.140 ± 0.013 0.136 ± 0.010 0.143 ± 0.008 0.148 ± 0.014 0.144+0.011 0.149+0.009
0.146 0.145 0.146 0.145 0.147 0.146 0.146
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S.J. Cipolla / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 153–156
transition rate. The results are presented in Table 2. The branching ratios are not changed significantly relative to theory, except for C‘/C3, which tends to exceed theory as Z increases. This follows from the dominance of La and Lb2,15 along with the ionization probability of the M and N shells being approximately equal in these collision systems.
5. Conclusion After accounting for outer-shell ionization due to the CK effect, the remaining enhancement of the relative intensities of L‘/La, L‘/Lb2,15 and Lb2,15/La is assumed to be attributable to direct ionization of the M and N shells, shake effects, plus subsequent CK rearrangements among the M and N shells. Higher resolution work would be needed to distinguish among these effects. It should be noted that the L‘ X-ray emission can be anisotropic such that a directional correlation of the L‘ X-ray emission [14] also could lower the L‘/La and Lb2,15/L‘ ratios.
References [1] J.H. Scofield, Atomic Data Nucl. Data Table. 14 (1974) 121. [2] A. Kupliauskiene, K. Glemza, J. Phys. B: At. Mol. Opt. Phys. 35 (2002) 4637. [3] S.J. Cipolla, B.P. Hill, Nucl. Instr. and Meth. B 241 (2005) 129. [4] M. Kavcic, M. Tokesi, Phys. Rev. A 72 (2005) 062704. [5] M. Kavcic, M. Budnar, J.L. Campbell, Nucl. Instr. and Meth. B 196 (2002) 16. [6] M. Kavcic, M. Budnar, Z. Smit, in: J.L. Duggan, I.L. Morgan (Eds.), Applications of Accelerators in Research and Industry, AIP Conf. Proc. CP45, 1999, p. 40. [7] S. Fazinic, I. Bogdanovic, M. Jaksic, I. Orlic, V. Valkovic, Nucl. Instr. and Meth. B 94 (1994) 363. [8] J. Ziegler, Transport of Ions in Matter, version 91.07, IBM, Yorktown Heights, NY, July 26, 1991. [9] M. Berger, H. Hubbell, 1987, XCOM: Photon Cross-section on a Personal Computer, NBS, Gaithersburg, USA, Report NBSIR 873595 (July 1987). [10] Z. Liu, S.J. Cipolla, Comput. Phys. Commun. 97 (1996) 315. [11] S. Cipolla, S. Watson, Nucl. Instr. and Meth. B 10/11 (1985) 946. [12] W.J. Gallagher, S.J. Cipolla, Nucl. Instr. and Meth. B 122 (1974) 405. [13] S.T. Perkins, D.E. Cullen, M.H. Chen, J.H. Hubbell, J. Rathkopf, J. Scofield, UCRL-50400 30, October 31, 1991. [14] S. Fazinic, Nucl. Instr. and Meth. B 109/110 (1996) 9.
Nuclear Instruments and Methods in Physics Research B 261 (2007) 153–156 www.elsevier.com/locate/nimb
L X-ray intensity ratios for proton impact on selected rare-earth elements Sam J. Cipolla
*
Physics Department, Creighton University, Omaha, NE 68178, USA Available online 27 March 2007
Abstract L X-rays excited by 75–300 keV protons impacting thick targets of Gd, Tb, Dy, Ho, Er, Tm and Yb were measured with a highresolution Si(Li) detector equipped with an ultra-thin window. The intensities of the La(L3M4,5) and Lb2,15(L3N4,5) X-rays relative to the L‘(L3M1) X-rays were compared with theoretical predictions. Discrepancies in the results are attributed to multiple vacancy production by various mechanisms. M4,5 and N4,5 ionization probabilities in these collisions are deduced from the results. Ó 2007 Elsevier B.V. All rights reserved. PACS: 32.80.Hd; 32.70.Fw Keywords: Multiple ionization; Inner-shell ionization; Relative X-ray intensities
1. Introduction X-ray transition rates are used to convert X-ray production cross sections into ionization cross sections. However, X-ray transition rates calculated from theory [1] assume a single initial vacancy in the radiating atom, which may be an understatement of the actual situation. If multiple vacancies exist in the atom, it is expected that the transitions rates will be altered. Multiple vacancies can arise from various mechanisms, either concurrent with or subsequent to the production of a particular inner-shell ionization. Subsequent effects include outer-shell ionization due to energy transfer from Coster–Kronig (CK) radiation-less transitions within the inner sub-shells where the primary ionization takes place. Another mechanism is the shake effect following an inner-shell ionization [2]. A concurrent effect in the case of X-ray emission produced by ion–atom collisions is multiple vacancy production from direct Coulomb excitation.
In this work, inner-shell ionization in atoms with Z = 64–70 is accomplished by 75–300 keV proton impact, and relative X-ray transition rates are measured for electron transitions filling a vacancy in the L3 shell. After estimating the contribution of Coster–Kronig transitions to the relative rates, multiple vacancy production from a combination of collision and shake effects can be determined by comparing the results with theory. Multiple ionization resulting from 75 to 300 keV proton collisions with selected 4d transition elements have been previously reported by us [3]. Kavcic et al. [4–6] have shown evidence of simultaneous K and L shell ionization for proton bombardment of selected elements up through Fe. With regards to rare-earths, similar results to those reported here have been obtained by calculating L‘/La and Lb2,15/La from the X-ray production cross sections reported by Fazinic et al. [7]. 2. Experimental system
*
Tel.: +1 402 280 2133; fax: +1 402 280 2140. E-mail address: [email protected]
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.03.019
The experimental system is the same one used in previous work [3]. A mass-analyzed proton beam produced in a Cockcroft–Walton accelerator impacts thick target foils.
154
S.J. Cipolla / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 153–156
A secondary-electron suppression cage surrounds the target holder, which is connected to a current integrator to measure the proton charge. The targets are oriented at 45° to the beam direction and to a high-resolution Si(Li) X-ray detector equipped with an ultra-thin window. An additional 6-lm aluminized-Mylar absorber was used to reduce the count rate from softer X-rays. 3. Data analysis The peak-fitting procedure allowed separation of the L‘(L3M1), Lg(L2M1), La (L3M4,5), Lb1 (L2M4), Lb3 (L1M2), Lb4 (L1M3), Lb2,15 (L3N4,5), Lc1(L2N1), Lc2 (L1N2), Lc3 (L1N3) and Lc4(L1O2,3) major peaks. However, for Gd, Tb, and Dy, the Lg and La peaks could not be resolved. Instead, a small correction to the combined La,g yield, based on the Lg/La ratio obtained from the other spectrum analyses, where these peaks could be separated, was applied to obtain the La yield. Preliminary to the calculation of the relative L X-ray transition rates, the X-ray production cross sections for protons of incident energy E were determined from the thick-target equation Y ðEÞ dY SðEÞ l x þ ; rðEÞ ¼ ð1Þ N Ae dE Y ðEÞ q where Y(E) = NX-ray/Nproton is the X-ray yield, NA is the target atom density, e is the detector efficiency, S(E) is the proton stopping power in the target (from TRIM [8]), l/q is the mass absorption coefficient for X-ray self absorption in the target (from XCOM [9]), and dY/dE is the slope of the measured Y(E) versus E curve. The yield slope, dY/dE, was obtained by fitting the yield data to Y(E) = A(E C)B and differentiating; A, B and C are the fitted parameters. The detector efficiencies, e, were determined from a combination of radioactive standards and K X-ray yields from bombarded thick foils using calculated ECPSSR yields (from ISICS [10]) as a standard [11]. Efficiency data were separately fitted using eðEx Þ ¼ X expðaEbx Þð1 expðcEdx ÞÞ, where Ex is the X-ray energy and X, a, b, c, d are fitted parameters [12]. As shown in [3], the relative transition rate, Ci/Cj, for two X-ray transitions, i an j, arising from the decay of
the same sub-shell vacancy can be obtained experimentally from Y ðEÞi 1 Ci rxi ei qtðE3 Þi ¼ x ¼ Y ðEÞ ; j 1 Cj exp rj ej
ð2Þ
qtðEÞj
where qt(E) is the effective thick-target thickness at incident energy, E, which thereby takes into account thick target effects on the X-ray production. Eq. (2) was used to calculate the relative transition rates for L‘/La and L‘/Lb2,15 averaged over all impact energies from 75 to 300 keV in 25-keV steps for each target, and the results were compared with theory [1]. From these results, an estimation can be made of multiple vacancies produced in the sub-shell from which the electrons make transitions. The occurrence of vacancies in the M1 shell is negligible compared with M4,5 due to the large difference in binding energies, the high probability of an M1 vacancy being promoted to higher M sub-shells via the CK effects, and because vacancy production in the M1 shell due to CK rearrangement among the L sub-shells is energetically prohibited. Since transition rates are proportional to the number of electrons in the shell from which electrons make a transition, then [3] ðCi =Cj Þexp N V V ¼ 1 ¼ 1 p; ¼ N N ðCi =Cj Þtheory
ð3Þ
where N is the normal population of electrons and V is the average number of electron vacancies produced in a subshell. The vacancy fraction, V/N, is equivalent to the corresponding ionization probability, p, of the affected shell(s); i.e. V = pN. Furthermore, since the CK and MI mechanisms are assumed to be independent, we have p = pCK + pMI; or, equivalently, V = VCK(L) + VMI, where MI denotes all other MI in addition to CK effects that result in M4,5 or N4,5 vacancies. The quantity VCK(L) can be determined by finding the overall probability that the CK process causes a vacancy to occur in the M4,5 shell (for La) and the N4,5 shell (for Lb2,15) prior to the X-ray emissions, given by Eq. (4) where ri are L sub-shell ionization cross sections (calculated from ECPSSR theory using ISICS [10]), and the fijS are the CK yields for S = M4,5 or N4,5 [13], which represent the probabilities for an electron from the M4,5 or N4,5 shell to be ejected from the atom
Table 1 Results of determining the vacancy fractions from multiple ionization (MI) due to the collisions leading to L3 X-ray emission after correction for Coster–Kronig vacancy production in the M and N shells Element (Z)
Gd(64) Tb(65) Dy(66) Ho(67) Er(68) Tm(69) Yb(70)
Theory/Expt. relative intensity ratios
PMI = VMI/N
L‘/La
Lb2,15/La
Lb2,15/L‘
M4,5 L‘/La
Lb2,15/La
Lb2,15/L‘
0.955 ± 0.096 0.996 ± 0.168 0.944 ± 0.086 0.958 ± 0.064 0.925 ± 0.081 0.812 ± 0.071 0.900 ± 0.063
1.058 ± 0.110 1.136 ± 0.165 1.096 ± 0.091 1.034 ± 0.064 1.000 ± 0.101 1.017 ± 0.093 0.982 ± 0.070
1.120 ± 0.109 1.188 ± 0.220 1.215 ± 0.116 1.081 ± 0.084 1.100 ± 0.119 1.262 ± 0.122 1.129 ± 0.078
0.0451 ± 0.0045 0.0045 ± 0.0008 0.0563 ± 0.0051 0.0424 ± 0.0028 0.0750 ± 0.0066 0.1635 ± 0.0365 0.1129 ± 0.0319
0.0855 ± 0.0062 0.0666 ± 0.0067 0.1080 ± 0.0063 0.0765 ± 0.0034 0.0734 ± 0.0049 0.1804 ± 0.0103 0.0902 ± 0.0047
0.0962 ± 0.0069 0.0853 ± 0.0140 0.1089 ± 0.0087 0.0855 ± 0.0054 0.0849 ± 0.0070 0.1703 ± 0.0122 0.1091 ± 0.0056
N4,5
S.J. Cipolla / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 153–156
V CKðLÞ ¼
wtd. av. Lβ2,15/Ll
1.4
155
r2 S r1 S f þ ðf þ f12S f23O þ f12O f23S þ f12S f23S Þ r3 23 r3 13
ð4Þ
Ll/Lα 1.3
Lβ2,15/Lα
4. Results
Theory/Expt.
1.2
Table 1, along with Figs. 1 and 2, present the results of these analyses. Fig. 1 shows that the L‘/La versus Z experiment to theory ratios are generally between unity and 0.9 as Z increases, except for 0.81 ± 0.07 at Tm (Z = 69). This indicates a minimal or small M shell ionization probability that increases with Z in these experiments. The total ionization probabilities, p = V/N, were calculated according to Eq. (3) are shown in Fig. 2. The CK ionization probability of the M4,5 shells, pCK, energetically occurs only for Tm
1.1 1.0 0.9 0.8 0.7 64
65
66
67
68
69
70
Z
Fig. 1. Theory/experiment ratio of the L‘/La, Lb2,15/La and Lb2,15/L‘ relative intensities.
0.20
Wt'd Average
0.15 0.10
V/N
0.05 0.00 -0.05
M N LINEAR FIT TO M LINEAR FIT TO N
-0.10 -0.15 -0.20 64
65
66
67
68
69
70
Z Fig. 2. Ionization Probability for M4,5 and N4,5 sub-shells due to proton collisions.
fijO
during the i ! j CK transition in the L shell; represent the CK yields for which no electron from the M4,5 or N4,5 is ejected. The MI ionization probability is finally obtained as pMI = p pCK.
and Yb by means of f13M4;5 in Eq. (4). A linear fit to the MI ionization probabilities, pMI = p pCK, shows a gradual rise with Z, going from 0.02 to 0.13 for the M4,5 shells, with uncertainties in the data ranging from about 10 to 30%, respectively. From Fig. 1 it is seen that the Lb2,15/L‘ intensity ratio comparisons with theory are fairly constant at around 1.2, which reflects the collisional MI occurring in the N4,5 shell along with negligible occurrence of vacancies in the M1 shell. All of the CK processes expressed in (4) contributed to multiple ionization of the N4,5 shells. A linear fit to the MI ionization probabilities, pMI = p pCK, presented in Fig. 2, ranges from approximately 0.06 to 0.13, with about 8% uncertainty in the data throughout. We also considered the Lb2,15/La intensity ratio comparisons with theory, which are shown in Fig. 1. These are affected by the MI occurring in both the M4,5 and N4,5 shells. Within error limits, the Lb2,15/La ratio is in accordance with the theory ratio, indicating almost equal ionization probabilities for the N4,5 and M4,5 shells, which was also noted above from Fig. 2. The branching ratios, L‘/L3, La/L3 and Lb2,15/L3, can be determined from the X-ray production cross section results, as follows: Ci rxi ¼ x x C3 rl þ ra þ rxb2;15
ð5Þ
There is a negligible error in ignoring the other L3 X-ray transitions as they comprise less than 1% of the total
Table 2 Transition rate branching ratios modified by multiple ionization in the M4,5 and N4,5 shells Element
Gd Tb Dy Ho Er Tm Yb
C‘/C3
Ca/C3
Cb2,15/C3
Expt.
Theory
Expt.
Theory
Expt.
Theory
0.0359 ± 0.0030 0.0335 ± 0.0044 0.0380 ± 0.0031 0.0362 ± 0.0025 0.0391 ± 0.0021 0.0439 ± 0.0038 0.0407 ± 0.0024
0.0336 0.0340 0.0344 0.0347 0.0353 0.0355 0.0359
0.823 ± 0.078 0.835 ± 0.118 0.826 ± 0.056 0.821 ± 0.043 0.813 ± 0.072 0.812 ± 0.066 0.810+0.050
0.811 0.811 0.811 0.810 0.814 0.809 0.808
0.148 ± 0.014 0.140 ± 0.013 0.136 ± 0.010 0.143 ± 0.008 0.148 ± 0.014 0.144+0.011 0.149+0.009
0.146 0.145 0.146 0.145 0.147 0.146 0.146
156
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transition rate. The results are presented in Table 2. The branching ratios are not changed significantly relative to theory, except for C‘/C3, which tends to exceed theory as Z increases. This follows from the dominance of La and Lb2,15 along with the ionization probability of the M and N shells being approximately equal in these collision systems.
5. Conclusion After accounting for outer-shell ionization due to the CK effect, the remaining enhancement of the relative intensities of L‘/La, L‘/Lb2,15 and Lb2,15/La is assumed to be attributable to direct ionization of the M and N shells, shake effects, plus subsequent CK rearrangements among the M and N shells. Higher resolution work would be needed to distinguish among these effects. It should be noted that the L‘ X-ray emission can be anisotropic such that a directional correlation of the L‘ X-ray emission [14] also could lower the L‘/La and Lb2,15/L‘ ratios.
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