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Relative intensities of L X-rays excited by 75–300 keV proton impact on elements with Z = 39–50
Nuclear Instruments and Methods in Physics Research B 241 (2005) 129–133 www.elsevier.com/locate/nimb
Relative intensities of L X-rays excited by 75–300 keV proton impact on elements with Z = 39–50 Sam J. Cipolla *, Brian P. Hill Physics Department, Creighton University, 2500 California Plaza, Omaha, NE 68178, USA Available online 15 August 2005
Abstract L X-rays excited by 75–300 keV protons impacting thick targets of Y, Zr, Nb, Mo, Rh, Pd, Ag and Sn were measured using an ultra-thin window Si(Li) detector. The intensities of the L‘ and Lb2,15 X-ray transitions relative to the La(L3M4,5) X-rays were derived from the data and compared with theoretical predictions. Discrepancies in the results are attributed to multiple vacancy production due to the collisions. Vacancy fractions for the M and N shells of the target atoms are deduced from the results. Ó 2005 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 calculated from theory [1] assume a single initial vacancy in the radiating atom. If multiple vacancies exist in the atom, it is expected that the transitions rates will change. Multiple vacancies can arise from Coster–Kronig
*
Corresponding author. Tel.: +1 402 280 2133; fax: +1 402 280 2140. E-mail address: [email protected] (S.J. Cipolla).
radiation-less transitions. In the case of collisionally produced X-ray emission, additional multiple vacancies can occur directly by Coulomb excitation. In this work, inner-shell ionization in selected atoms with Z = 39–50 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. By comparing the results with theory, multiple vacancy effects can be deduced. After estimating the effect of Coster–Kronig transitions on the relative rates, the collisionally produced multiple vacancy effects can be determined.
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2. Experimental system The experimental system, located at the University of Nebraska – Lincoln, is the same as that used in previous work [2]. A mass-analyzed proton beam produced in a Cockcroft–Walton accelerator impacts thick target foils arranged on a vertical ladder. A secondary-electron suppression cage surrounds the ladder, which is connected to a calibrated current integrator to measure the proton charge. The targets are oriented at 45° to the beam direction and to a Si(Li) X-ray detector equipped with an ultra-thin window. An additional 6-lm aluminized-Mylar absorber was used to reduce the high 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), Lb3,4,6(L1M2,3 + L3N1), Lb2,15(L3N4,5), Lc1,5(L2N1 + L2N4), and Lc2,3(L1N2,3) peaks. Preliminary to the calculation of the relative L X-ray transition rates, the X-ray production cross-sections for protons of incident energy E0 were determined from the thick-target equation [3], Y ðE0 Þ dY SðE0 Þ l þ ; rðE0 Þx ¼ ð1Þ N e dE0 Y ðE0 Þ q where Y(E0) = NX-ray/Nproton is the X-ray yield, N is the target atom density, e is the detector efficiency, S(E0) is the proton stopping power in the target (from TRIM [4]), l/q is the mass absorption coefficient for X-ray self absorption in the target (from XCOM [5]), and dY/dE0 is the slope of the measured Y(E0) versus E0 curve. The yield slope dY/dE0 was obtained by fitting the yield data to Y(E0) = A(E0 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 [6]) as a standard [7]. The efficiency data were separately fitted below and above the Si–K edge using e(E) = Xexp(aEb)(1 exp (cEd)), where E is the X-ray energy and X, a, b, c, d are fitted parameters.
Eq. (1) can be recast as Y ðEÞ 1 ; rx ðEÞ ¼ N e qtðEÞ
ð2Þ
where, qtðEÞ ¼
1 SðEÞ dY ðEÞ l þ Y ðEÞ dE q
ð3Þ
is the effective thick-target thickness at incident energy, E. The X-ray production cross-section for a particular transition, rxi, is related to the sub-shell ionization cross-section, rs, according to Ci rxi ðEÞ ¼ rs ðEÞxs F s ; ð4Þ Cs where C represents the corresponding transition rate, xs is the sub-shell fluorescence yield and Fs is the Coster–Kronig vacancy enhancement factor, given by r2 r1 F s ¼ 1 þ f23 þ ðf13 þ f12 f23 Þ; ð5Þ r3 r3 where the fij are the Coster–Kronig yields [8]. From Eqs. (2) and (4), the relative transition rate for two X-ray transitions arising from the same sub-shell vacancy can be obtained experimentally as Y ðEÞi 1 Ci ei qtðEÞi ¼ . Cj Y ðEÞj 1 ej qtðEÞj
ð6Þ
In this formulation, thick target effects on the X-ray production are taken into account via the effective thickness terms. In deriving Eq. (6) the X-ray and non-radiative transition rates are, to a good approximation [9], changed by the same factor, so that the fluorescence yield, xs, is unaffected by the multiple ionization (MI) processes and thus cancels out in the ratio. 4. Results Eq. (6) was used to calculate the relative transition rates for L‘/La, Lb2,15/L‘, and Lb2,15/La averaged over all proton impact energies for each target, and the results were compared with
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131
theoretical values [1]. From these results, an estimation can be made of multiple vacancies produced in the sub-shell from which the electrons make transitions. It is assumed here that multiple vacancy production in the M1 is negligible compared with M4,5 due to the large difference in binding energies, and Coster–Kronig (CK) vacancy production in the M1 shell is energetically prohibited. If we assume transition rates are proportional to the number of electrons in the sub-shell from which electrons make a transition [10], we can write, ðCi =Cj Þexp N V V ¼1 ; ¼ N N ðCi =Cj Þtheory
ð7Þ
where N is the normal population of electrons and V is the number of electron vacancies in the subshell; V/N is the vacancy fraction. Furthermore, V can be decomposed as V = VCK(L) + VMI, where MI denotes direct MI in addition to CK effects that result in M4,5 or N4,5 vacancies. VCK(L) can be determined by finding the fraction of F3 that results in CK vacancy transfer to the M4,5 shell (for La) and the N4,5 shell (for Lb2,15) prior to the X-ray emissions, as V CKðLÞ ¼
1
r2 S f þ rr13 ðf13S þ f12S f23S Þ r3 23 ; þ rr23 f23 þ rr13 ðf13 þ f12 f23 Þ
ð8Þ
where the fS are the CK yields for S = M4,5 or N4,5[11]. Table 1 and Figs. 1–4 present the results of these analyses. The experiment to theory ratios, as expressed in Eq. (7), are rather constant for L‘/La, ranging from 0.75 to 0.91. The vacancy
Fig. 1. Theory/experiment ratio of the L‘(L3M1)/La(L3M4,5) relative intensities.
fractions were calculated according to Eq. (7) and the VCK(L) contribution was calculated from Eq. (8), leaving a vacancy fraction of VMI/N ranging from 0.14 to 0.20 for the M4,5 shells which are normally filled with N = 10 for these targets. The exception is Zr, for which VMI/N 0.01. The Lb2,15/L‘ intensity ratio comparisons with theory are larger than unity, ranging from 1.25 to 1.61, which reflects the collisional MI occurring in the N4,5 shell along with negligible ionization of the M1 shell. The Lb2,15/La intensity ratio comparisons with theory, ranging from 0.94 to 1.27, are affected by the MI occurring in both the M4,5 and N4,5 shells. In calculating the VMI/N for N4,5, the M4,5 vacancies from the L‘/La analysis
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)
Theory/experiment intensity ratios L‘/La
Y (39) Zr (40) Nb (41) Mo (42) Rh (45) Pd (46) Ag (47) Sn (50)
0.810 ± 0.014 0.910 ± 0.099 0.745 ± 0.037 0.755 ± 0.038 0.814 ± 0.044 0.791 ± 0.043 0.792 ± 0.042 0.846 ± 0.046
Lb2,15/La
1.164 ± 0.105 1.125 ± 0.061 0.938 ± 0.057 1.285 ± 0.068 1.272 ± 0.067 1.260 ± 0.066 1.092 ± 0.057
VMI/N Lb2,15/L‘
1.252 ± 0.102 1.505 ± 0.083 1.237 ± 0.076 1.576 ± 0.083 1.611 ± 0.089 1.592 ± 0.083 1.282 ± 0.069
M4,5
N4,5
L‘/La
Lb2,15/La
Lb2,15/L‘
0.139 ± 0.037 0.045 ± 0.087 0.200 ± 0.034 0.189 ± 0.034 0.127 ± 0.039 0.195 ± 0.038 0.201 ± 0.036 0.154 ± 0.046
0.228 ± 0.097 0.344 ± 0.046 0.217 ± 0.060 0.362 ± 0.043 0.377 ± 0.042 0.368 ± 0.042 0.199 ± 0.052
0.198 ± 0.058 0.344 ± 0.034 0.217 ± 0.047 0.362 ± 0.030 0.377 ± 0.030 0.368 ± 0.030 0.199 ± 0.037
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Fig. 2. Theory/experiment ratio of the Lb2,15(L3N4,5)/ La(L3M4,5) and Lb2,15(L3N4,5)/L‘(L3M1) relative intensities.
Fig. 3. Average vacancy fraction in M4,5 due to proton collisions as determined from L‘(L3M1)/La(L3M4,5) relative intensities.
Fig. 4. Average vacancy fraction in N4,5 due to proton collisions as determined from Lb2,15(L3N4,5)/La(L3M4,5) and Lb2,15(L3N4,5)/L‘(L3M1) relative intensities.
were accounted for in the analysis of the Lb2,15/La data. The N4,5 vacancy fractions, derived from both the Lb2,15/L‘ and Lb2,15/La data, are consistent and range from 0.19 to 0.38. The variability of these results, as contrasted with those for M4,5, are due to the gradual build-up of the N4,5 electron population in going from Y to Sn (only Pd, Ag, and Sn have the maximum number of 10 electrons in the N4,5 shells). The transition rate ratios for L‘/La and L‘/Lb2,15 are equivalent to the reduced transition rates due to multiple ionization for La and Lb2,15, assuming the rate for L‘ is unchanged in these collisions. Relative transition rates for L‘/ L3, La/L3, and Lb2,15/L3 can then be determined from the X-ray production cross-section results, as follows:
Table 2 Transition rate branching ratios modified by multiple ionization in the M4,5 and N4,5 shells Element
Y Zr Nb Mo Rh Pd Ag Sn
C‘/C3
Ca/C3
Cb2,15/C3
Experiment
Theory
Experiment
Theory
Experiment
Theory
0.0451 ± 0.0022 0.0384 ± 0.0044 0.0467 ± 0.0024 0.0456 ± 0.0024 0.0415 ± 0.0021 0.0411 ± 0.0020 0.0413 + 0.0021 0.0380 ± 0.0019
0.0367 0.0357 0.0349 0.0343 0.0329 0.0326 0.0324 0.0318
0.955 ± 0.047 0.944 ± 0.116 0.928 ± 0.048 0.928 ± 0.048 0.902 ± 0.046 0.893 ± 0.043 0.877 + 0.044 0.858 ± 0.041
0.958 0.943 0.930 0.921 0.881 0.879 0.870 0.849
0.0178 ± 0.0017 0.0250 ± 0.0014 0.0258 ± 0.0017 0.0557 ± 0.0028 0.0659 + 0.0033 0.0793 + 0.0039 0.104 ± 0.005
0.0207 0.0287 0.0249 0.0698 0.0824 0.0986 0.112
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Ci rxi ¼ x . C3 rl þ rxa þ rxb2;15
ð9Þ
This follows from Eqs. (4) and (6). There is a negligible error in ignoring the other L3 X-ray transitions as they contribute less than 1% of the total transition rate. The results are presented in Table 2. Because of the dominance of the La transition, the branching ratio Ca/C3 is not changed significantly relative to the other ratios. Thus, there is negligible error associated with using the theoretical Ca/C3 in converting a measured La X-ray production cross-section to the L3 sub-shell ionization cross-section, as had been done in previous work [12]. 5. Conclusion The enhancement of the relative intensities of L‘/La, L‘/Lb2,15, and Lb2,15/La is assumed to be attributable to MI of the M and N shell in these collisions involving 75–300 keV protons. The MI is likely caused by direct ionization of the M and N shells plus subsequent CK transitions among the M and N shells. No attempt has been made here to distinguish between these two effects. Although it is well known that MI can occur at very high proton energies and for projectiles heavier than protons, our results indicate that MI can also occur in low-Z atoms at lower proton collision energies. Similar results have been found by Campbell [13] who measured a 13% increase in
133
L‘/La and Lb2,15/La. Papp, et al. [14] measured a similar discrepancy for L3M1/L3M4,5 in Gd and U which they attributed to erroneous M1 level widths from theory.
References [1] J.H. Scofield, Atom. Data Nucl. Data Tables 14 (1974) 121. [2] S.J. Cipolla, Nucl. Instr. and Meth. B 99 (1995) 22. [3] E. Merzbacher, H. Lewis, Hand. d. Phys. 34 (1958) 166. [4] J. Ziegler, Transport of Ions in Matter, Ver. 91.07, IBM, Yorktown Heights, NY, 1991. [5] M. Berger, H. Hubbell, XCOM: Photon Cross-Section on a Personal Computer, NBS, Gaithersburg, USA, Report NBSIR 87-3595, July 1987. [6] Z. Liu, S.J. Cipolla, Comp. Phys. Commun. 97 (1996) 315. [7] W.J. Gallagher, S.J. Cipolla, Nucl. Instr. and Meth. 122 (1974) 405; S. Cipolla, S. Watson, Nucl. Instr. and Meth. B 10/11 (1985) 946. [8] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [9] R.J. Fortner, R.C. Der, T.M. Kavanagh, J.D. Garcia, J. Phys. B: At. Mol. Opt. Phys. 5 (1972) L73. [10] F.P. Larkins, J. Phys. B: At. Mol. Opt. Phys. 4 (1971) L29. [11] S.T. Perkins, D.E. Cullen, M.H. Chen, J.H. Hubbell, J. Rathkopf, J. Scofield, UCRL-50400 30 (October) (1991) 31. [12] S.J. Cipolla, AIP Conf. Proc. CP 680 (2003) 15; S.J. Cipolla, M.J. Dolezal, L.O. Casazza, AIP Conf. Proc. CP 392 (1997) 113; S.J. Cipolla, AIP Conf. Proc. CP 392 (1997) 117. [13] J.L. Campbell, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 3219. [14] T. Papp, J.L. Campbell, S. Raman, J. Phys. B 26 (1993) 4007.
Relative intensities of L X-rays excited by 75–300 keV proton impact on elements with Z = 39–50 Sam J. Cipolla *, Brian P. Hill Physics Department, Creighton University, 2500 California Plaza, Omaha, NE 68178, USA Available online 15 August 2005
Abstract L X-rays excited by 75–300 keV protons impacting thick targets of Y, Zr, Nb, Mo, Rh, Pd, Ag and Sn were measured using an ultra-thin window Si(Li) detector. The intensities of the L‘ and Lb2,15 X-ray transitions relative to the La(L3M4,5) X-rays were derived from the data and compared with theoretical predictions. Discrepancies in the results are attributed to multiple vacancy production due to the collisions. Vacancy fractions for the M and N shells of the target atoms are deduced from the results. Ó 2005 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 calculated from theory [1] assume a single initial vacancy in the radiating atom. If multiple vacancies exist in the atom, it is expected that the transitions rates will change. Multiple vacancies can arise from Coster–Kronig
*
Corresponding author. Tel.: +1 402 280 2133; fax: +1 402 280 2140. E-mail address: [email protected] (S.J. Cipolla).
radiation-less transitions. In the case of collisionally produced X-ray emission, additional multiple vacancies can occur directly by Coulomb excitation. In this work, inner-shell ionization in selected atoms with Z = 39–50 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. By comparing the results with theory, multiple vacancy effects can be deduced. After estimating the effect of Coster–Kronig transitions on the relative rates, the collisionally produced multiple vacancy effects can be determined.
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.07.016
130
S.J. Cipolla, B.P. Hill / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 129–133
2. Experimental system The experimental system, located at the University of Nebraska – Lincoln, is the same as that used in previous work [2]. A mass-analyzed proton beam produced in a Cockcroft–Walton accelerator impacts thick target foils arranged on a vertical ladder. A secondary-electron suppression cage surrounds the ladder, which is connected to a calibrated current integrator to measure the proton charge. The targets are oriented at 45° to the beam direction and to a Si(Li) X-ray detector equipped with an ultra-thin window. An additional 6-lm aluminized-Mylar absorber was used to reduce the high 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), Lb3,4,6(L1M2,3 + L3N1), Lb2,15(L3N4,5), Lc1,5(L2N1 + L2N4), and Lc2,3(L1N2,3) peaks. Preliminary to the calculation of the relative L X-ray transition rates, the X-ray production cross-sections for protons of incident energy E0 were determined from the thick-target equation [3], Y ðE0 Þ dY SðE0 Þ l þ ; rðE0 Þx ¼ ð1Þ N e dE0 Y ðE0 Þ q where Y(E0) = NX-ray/Nproton is the X-ray yield, N is the target atom density, e is the detector efficiency, S(E0) is the proton stopping power in the target (from TRIM [4]), l/q is the mass absorption coefficient for X-ray self absorption in the target (from XCOM [5]), and dY/dE0 is the slope of the measured Y(E0) versus E0 curve. The yield slope dY/dE0 was obtained by fitting the yield data to Y(E0) = A(E0 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 [6]) as a standard [7]. The efficiency data were separately fitted below and above the Si–K edge using e(E) = Xexp(aEb)(1 exp (cEd)), where E is the X-ray energy and X, a, b, c, d are fitted parameters.
Eq. (1) can be recast as Y ðEÞ 1 ; rx ðEÞ ¼ N e qtðEÞ
ð2Þ
where, qtðEÞ ¼
1 SðEÞ dY ðEÞ l þ Y ðEÞ dE q
ð3Þ
is the effective thick-target thickness at incident energy, E. The X-ray production cross-section for a particular transition, rxi, is related to the sub-shell ionization cross-section, rs, according to Ci rxi ðEÞ ¼ rs ðEÞxs F s ; ð4Þ Cs where C represents the corresponding transition rate, xs is the sub-shell fluorescence yield and Fs is the Coster–Kronig vacancy enhancement factor, given by r2 r1 F s ¼ 1 þ f23 þ ðf13 þ f12 f23 Þ; ð5Þ r3 r3 where the fij are the Coster–Kronig yields [8]. From Eqs. (2) and (4), the relative transition rate for two X-ray transitions arising from the same sub-shell vacancy can be obtained experimentally as Y ðEÞi 1 Ci ei qtðEÞi ¼ . Cj Y ðEÞj 1 ej qtðEÞj
ð6Þ
In this formulation, thick target effects on the X-ray production are taken into account via the effective thickness terms. In deriving Eq. (6) the X-ray and non-radiative transition rates are, to a good approximation [9], changed by the same factor, so that the fluorescence yield, xs, is unaffected by the multiple ionization (MI) processes and thus cancels out in the ratio. 4. Results Eq. (6) was used to calculate the relative transition rates for L‘/La, Lb2,15/L‘, and Lb2,15/La averaged over all proton impact energies for each target, and the results were compared with
S.J. Cipolla, B.P. Hill / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 129–133
131
theoretical values [1]. From these results, an estimation can be made of multiple vacancies produced in the sub-shell from which the electrons make transitions. It is assumed here that multiple vacancy production in the M1 is negligible compared with M4,5 due to the large difference in binding energies, and Coster–Kronig (CK) vacancy production in the M1 shell is energetically prohibited. If we assume transition rates are proportional to the number of electrons in the sub-shell from which electrons make a transition [10], we can write, ðCi =Cj Þexp N V V ¼1 ; ¼ N N ðCi =Cj Þtheory
ð7Þ
where N is the normal population of electrons and V is the number of electron vacancies in the subshell; V/N is the vacancy fraction. Furthermore, V can be decomposed as V = VCK(L) + VMI, where MI denotes direct MI in addition to CK effects that result in M4,5 or N4,5 vacancies. VCK(L) can be determined by finding the fraction of F3 that results in CK vacancy transfer to the M4,5 shell (for La) and the N4,5 shell (for Lb2,15) prior to the X-ray emissions, as V CKðLÞ ¼
1
r2 S f þ rr13 ðf13S þ f12S f23S Þ r3 23 ; þ rr23 f23 þ rr13 ðf13 þ f12 f23 Þ
ð8Þ
where the fS are the CK yields for S = M4,5 or N4,5[11]. Table 1 and Figs. 1–4 present the results of these analyses. The experiment to theory ratios, as expressed in Eq. (7), are rather constant for L‘/La, ranging from 0.75 to 0.91. The vacancy
Fig. 1. Theory/experiment ratio of the L‘(L3M1)/La(L3M4,5) relative intensities.
fractions were calculated according to Eq. (7) and the VCK(L) contribution was calculated from Eq. (8), leaving a vacancy fraction of VMI/N ranging from 0.14 to 0.20 for the M4,5 shells which are normally filled with N = 10 for these targets. The exception is Zr, for which VMI/N 0.01. The Lb2,15/L‘ intensity ratio comparisons with theory are larger than unity, ranging from 1.25 to 1.61, which reflects the collisional MI occurring in the N4,5 shell along with negligible ionization of the M1 shell. The Lb2,15/La intensity ratio comparisons with theory, ranging from 0.94 to 1.27, are affected by the MI occurring in both the M4,5 and N4,5 shells. In calculating the VMI/N for N4,5, the M4,5 vacancies from the L‘/La analysis
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)
Theory/experiment intensity ratios L‘/La
Y (39) Zr (40) Nb (41) Mo (42) Rh (45) Pd (46) Ag (47) Sn (50)
0.810 ± 0.014 0.910 ± 0.099 0.745 ± 0.037 0.755 ± 0.038 0.814 ± 0.044 0.791 ± 0.043 0.792 ± 0.042 0.846 ± 0.046
Lb2,15/La
1.164 ± 0.105 1.125 ± 0.061 0.938 ± 0.057 1.285 ± 0.068 1.272 ± 0.067 1.260 ± 0.066 1.092 ± 0.057
VMI/N Lb2,15/L‘
1.252 ± 0.102 1.505 ± 0.083 1.237 ± 0.076 1.576 ± 0.083 1.611 ± 0.089 1.592 ± 0.083 1.282 ± 0.069
M4,5
N4,5
L‘/La
Lb2,15/La
Lb2,15/L‘
0.139 ± 0.037 0.045 ± 0.087 0.200 ± 0.034 0.189 ± 0.034 0.127 ± 0.039 0.195 ± 0.038 0.201 ± 0.036 0.154 ± 0.046
0.228 ± 0.097 0.344 ± 0.046 0.217 ± 0.060 0.362 ± 0.043 0.377 ± 0.042 0.368 ± 0.042 0.199 ± 0.052
0.198 ± 0.058 0.344 ± 0.034 0.217 ± 0.047 0.362 ± 0.030 0.377 ± 0.030 0.368 ± 0.030 0.199 ± 0.037
132
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Fig. 2. Theory/experiment ratio of the Lb2,15(L3N4,5)/ La(L3M4,5) and Lb2,15(L3N4,5)/L‘(L3M1) relative intensities.
Fig. 3. Average vacancy fraction in M4,5 due to proton collisions as determined from L‘(L3M1)/La(L3M4,5) relative intensities.
Fig. 4. Average vacancy fraction in N4,5 due to proton collisions as determined from Lb2,15(L3N4,5)/La(L3M4,5) and Lb2,15(L3N4,5)/L‘(L3M1) relative intensities.
were accounted for in the analysis of the Lb2,15/La data. The N4,5 vacancy fractions, derived from both the Lb2,15/L‘ and Lb2,15/La data, are consistent and range from 0.19 to 0.38. The variability of these results, as contrasted with those for M4,5, are due to the gradual build-up of the N4,5 electron population in going from Y to Sn (only Pd, Ag, and Sn have the maximum number of 10 electrons in the N4,5 shells). The transition rate ratios for L‘/La and L‘/Lb2,15 are equivalent to the reduced transition rates due to multiple ionization for La and Lb2,15, assuming the rate for L‘ is unchanged in these collisions. Relative transition rates for L‘/ L3, La/L3, and Lb2,15/L3 can then be determined from the X-ray production cross-section results, as follows:
Table 2 Transition rate branching ratios modified by multiple ionization in the M4,5 and N4,5 shells Element
Y Zr Nb Mo Rh Pd Ag Sn
C‘/C3
Ca/C3
Cb2,15/C3
Experiment
Theory
Experiment
Theory
Experiment
Theory
0.0451 ± 0.0022 0.0384 ± 0.0044 0.0467 ± 0.0024 0.0456 ± 0.0024 0.0415 ± 0.0021 0.0411 ± 0.0020 0.0413 + 0.0021 0.0380 ± 0.0019
0.0367 0.0357 0.0349 0.0343 0.0329 0.0326 0.0324 0.0318
0.955 ± 0.047 0.944 ± 0.116 0.928 ± 0.048 0.928 ± 0.048 0.902 ± 0.046 0.893 ± 0.043 0.877 + 0.044 0.858 ± 0.041
0.958 0.943 0.930 0.921 0.881 0.879 0.870 0.849
0.0178 ± 0.0017 0.0250 ± 0.0014 0.0258 ± 0.0017 0.0557 ± 0.0028 0.0659 + 0.0033 0.0793 + 0.0039 0.104 ± 0.005
0.0207 0.0287 0.0249 0.0698 0.0824 0.0986 0.112
S.J. Cipolla, B.P. Hill / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 129–133
Ci rxi ¼ x . C3 rl þ rxa þ rxb2;15
ð9Þ
This follows from Eqs. (4) and (6). There is a negligible error in ignoring the other L3 X-ray transitions as they contribute less than 1% of the total transition rate. The results are presented in Table 2. Because of the dominance of the La transition, the branching ratio Ca/C3 is not changed significantly relative to the other ratios. Thus, there is negligible error associated with using the theoretical Ca/C3 in converting a measured La X-ray production cross-section to the L3 sub-shell ionization cross-section, as had been done in previous work [12]. 5. Conclusion The enhancement of the relative intensities of L‘/La, L‘/Lb2,15, and Lb2,15/La is assumed to be attributable to MI of the M and N shell in these collisions involving 75–300 keV protons. The MI is likely caused by direct ionization of the M and N shells plus subsequent CK transitions among the M and N shells. No attempt has been made here to distinguish between these two effects. Although it is well known that MI can occur at very high proton energies and for projectiles heavier than protons, our results indicate that MI can also occur in low-Z atoms at lower proton collision energies. Similar results have been found by Campbell [13] who measured a 13% increase in
133
L‘/La and Lb2,15/La. Papp, et al. [14] measured a similar discrepancy for L3M1/L3M4,5 in Gd and U which they attributed to erroneous M1 level widths from theory.
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