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A study of the M-shell fluorescence yields of lead
132
Physica 115C (1982) 132-136 North-Holland Publishing Company
A STUDY OF THE M-SHELL FLUORESCENCE M. HRIBAR,
A. KODRE
YIELDS OF LEAD
and J. PAHOR
Department of Physics and Institute J. Stefan, E. Kardelj University, Ljubljana, Yugoslavia Received 8 July 1980 Received in final form 20 March 1982
The modes of decay of the M-shell vacancies in lead atoms were studied by means of a wall-less proportional counter spectrometer with lead in the form of lead-tetraethyle admixed to the working gas of the counter. The vacancies in consecutive M-subshells of the lead atoms were produced by the photoelectric absorption of the characteristic K-radiation of elements from Cl to V. The following M-shell fluorescence yields were extracted: & = 0.032~0.003, 02-s = 0.030~0.003, 0F5=0.030~0.002, 04,5>0.029.
1. Introduction The deexcitation of the M-shell vacancies in lead atoms has been studied by several authors. Jopson et al. [l] have reported the average WLM fluorescence yield as wLM= 0.032 * 0.006. The value has been corrected for the contribution from double M-shell vacancies by Bambynek et al. [2] to uLM = 0.0262 0.005. The average fluorescence yield WM= 0.029 2 0.002 has been determined by Konstantinov [3]. Theoretical values for the subshell fluorescence yields and Auger yields as well as for the Coster-Kronig transition probabilities have been calculated by McGuire [4] for the elements in the vicinity of Z = 80. These theoretical results indicate that only w and MS subshells can effectively contribute to the fluorescent mode of deexcitation. The aim of the present work is to verify this conjecture by experiment.
2. Experimental
procedure
The proportional counter is known to be a convenient device for the study of X-ray fluorescence, particularly in the low-energy region. The target atoms admixed to the counter gas are ionized by an external beam and the 037%4363/82/000&0000/$02.75
@ 1982 North-Holland
spectrometer can discern radiative and nonradiative modes of deexcitation provided that the gas is sufficiently dilute to let the fluorescence photons escape. Thus, the formation of a vacancy by photoelectric absorption is always detected by the presence of the ejected photoelectron: in the case of the subsequent nonradiative decay of the vacancy the full energy of excitation is transferred to the ejected electrons and consequently detected by the spectrometer. In the case of a radiative decay the energy imparted to the escaping photon is missing. The energy spectra of the events exhibit two peaks: the full energy peak and the escape peak. We used a wall-less proportional counter of 400 mm length: the active volume (diameter 56 mm) of the counter is defined by a cylindrical arrangement of thin wires at the cathode potential. The space between this cathode and the vessel wall (width 14 mm) is equipped with another set of counting wires and serves as an anticoincidence ring to eliminate the wall effects. A thin mylar window in the vessel wall at the middle of the counter length serves to admit a narrow beam of X-rays into the counter along its diameter. Monochromatic X-ray beams are produced by irradiation of suitable elemental targets in the X-ray tube: The characteristic Ka radiation of the target is isolated by the use of
M. Hribar et al. / M-shell
fluorescence
133
yields of lead
MAIN
_---___-__ P H. ANAL
J-
_---____ COUNTER
RING Fig. 1. The wiring of the spectrometer
using the wall-less
collimating slits and X-ray filters where possible. The experimental setup is shown in fig. 1. To study the M-shell fluorescence of lead the counter was filled with methane at 66 mbar and lead tetraethyle at its saturated vapour pressure (less than 0.15 mbar). Characteristic radiation of metallic targets of V, Ti and SC was used to induce fluorescence. Since all M-subshells of lead could be ionized with the K-series radiation of these elements and since escape of photons from various subshells could not be resolved by the
proportional
counter as a sensor.
spectrometer, only the average fluorescence yield could be extracted from the data. A typical spectrum of pulses from the counter is shown in fig. 2 for the experiment with the scandium radiation. The fluorescence spectrum is compared to the spectrum of events in pure methane which shows the contribution of photoabsorption by carbon in the working gas. Evidently a larger part of the events in the main peak is of the latter origin, and only the difference of the two spectra can be attributed to
Scandium Energy
target 109
keV
CHANNEL
NUMBER
Fig. 2. The spectrum of pulses from the counter with (0) and without (0) the admixture of lead tetraethyle, irradiation of the counter by the scandium characteristic radiation, with all M-subshells excited.
obtained
during the
134
M. Hribar et al. 1 M-shell fluorescence
the events involving lead atoms. Since the admixture of the lead tetraethyle is known to decrease the resolution of the proportional counter, a series of spectra is recorded with part of the gas mixture repeatedly replaced by the pure methane. Thus the admixture of lead tetraethyle is gradually decreased, causing a corresponding improvement of the resolution and, of course, a corresponding loss of lead fluorescence events. A good compromise is usually achieved at 0.07 mbar of lead tetraethyle, the exact amount being deduced from the ratio of lead/carbon events. The fluorescence of consecutive subshells is suppressed by lowering the energy of the incident photons below the corresponding ionization thresholds. Thus, calcium KLY radiation was used to induce fluorescence in the MrMs subshells, and potassium Ka radiation to induce fluorescence in the M3-M5 subshells. Metallic targets in a hydrogen atmosphere were employed. The KP radiation of both targets reaches above the corresponding thresholds, however it represents less than 10% of the total intensity so that its effect can be subtracted as a small numerical correction. Finally, the chlorine radiation from the NaCl target was used to ionize the m and M5 subshells. Due to the low energy of the events the resolution of the spectrometer only allowed us to extract a lower limit for the fluorescence yield. No simple target is available to induce the fluorescence in the M5 subshell alone.
3. Results After subtraction of the carbon photoabsorption contribution determined in a separate experimental run on methane, the spectrum of the lead fluorescence is decomposed into the main peak of the spectrum, the fluorescence responding numbers of pulses N,,, and N, are extracted. Small corrections are applied to the numbers to account for the effects of fluorescent photon reabsorption and the escape of ejected electrons to the anticoincidence ring: in the first case the events are transferred from the escape
yields of lead
to the main peak, while in the second case the events are lost owing to the vetoing of the anticoincidence circuit. The corrections amount to less than 5% for the main peak and less than 1.5% for the escape peak. The Coster-Kronig transitions do not contribute observable effects: the fluorescence of separate subshells cannot be resolved in the escape peak and the energy of the Coster-Kronig electrons is so low that their escape is negligible. The observed fluorescence yield is defined as the ratio of the number of M-fluorescence photons to the number of primary vacancies in the M-shell. Since the photoabsorption events in the higher shells of lead atoms also contribute to the main peak of the spectrum, the fluorescence yield is calculated as W;-5= N,IPP,~N, +
W ,
with PM the relative probability of photoabsorption in the M-shell. These fluorescence yields are averages over subshells from i to 5, defined by the distribution of primary vacancies as produced in a particular experiment. In the derivation of the formula it has been taken into account that the radiative transitions from N- and higher shells, which carry a negligible amount of energy anyhow, lead to an escape peak less than 1 keV below the main peak, so close that it is effectively hidden in the low-energy tail and thus it is included in the signal. The results together with the relevant experimental data are given in table I. Theoretical calculations usually provide the subshell fluorescence yields mi which represent quantum mechanical characteristics of the atom independent of the excitation mode. The experimental and theoretical quantities are connected by the set of equations 5
wi-5 =
2
nkvk
9
i=1,2,3,4
k=i
k=i+l
where
ni denotes
the relative
number
of primary
M. Hribar et al. / M-shell fluorescenceyields of lead
Table
I Exciting
Absorption edge
MS
radiation Energy
Target
(keV)
h/I4
135
2.484 2.586
NI(N
+ Nm)
(keV)
Exp.
Corrected
PM
Fluorescence yield
2.62 (Ka)
> 0.021
> 0.022
0.741
&
Cl 2 0.029
2.82 (KP) M3
3.066
K
3.31 (Ko)
0.022
0.023 k 0.001
0.769
(s>s = 0.030 2 0.002
0.023
0.024 k 0.002
0.780
62-5 = 0.030 f 0.003
0.788
& = 0.032 k 0.003
3.59 (KjI) M2
3.554
Ca
3.69 (Ko) 4.01 (KP)
MI
3.851
SC
4.09 (Ka)
0.025
0.026 2 0.002
Ti
4.46 (Kp) 4.51 (Ka)
0.024
0.025 2 0.002
V
4.93 (KP) 4.95 (Ko)
0.024
0.025 -t 0.002
vacancies in the ith subshell and frk the known Coster-Kronig yields. It would be possible, in principle, to solve the set of equations with the given average yields for the various subshells. However, the calculation involves differences of experimental values leading to an ill-conditioned problem with an unstable solution. Instead, the comparison of the experiment to the theory is made by calculating the average yields from the theoretical subshell values where above relations are used explicitly. The results and all the relevant theoretical data are summarized in table II. The partial subshell yields Table
II
M-subshell fluorescence Coster-Kronig yields Subshell
oi
M5 M3
0.030 0.031 5.0 x lo-’
M2
5.9x
Ml
2.7
M4
and the Coster-Kronig yields are interpolated from McGuire’s data, while the probabilities PM are taken from the compilation of Storm and Israel [5]. The vacancy distribution numbers Iti are derived from the photoabsorption data of the same source. Although the authors only claim an overall 10% accuracy for their theoretical calculations in the energy region of our interest, the discussion in another big compilation of X-ray absorption data by Hubbell et al. [6] indicates that the jump values, i.e. the ratios of the photoabsorption coefficients above and below the edge, are more accurate than the coefficients
and Relative 6k
x
1o-3
lo-’
f& = 0.040 fx = 0.098 fjS = 0.77 fu=O.ll f24= 0.66 fis = 0.09 fi2 = 0.12 fix = 0.62 fi4 = 0.07 f,s = 0.10
number n2
_ -
_
of primary n3
vacancies n4
Average
fluorescence
n5
Theor.
Exp.
yields
1
_ 0.18
0.42 0.34
1 0.58 0.48
0s = 0.030 (54.5= 0.030 w>r = 0.031
04,s 2 0.029 6%5 = 0.030
-
0.07
0.16
0.32
0.44
&-s = 0.030
G,
0.05
0.07
0.16
0.30
0.42
WM= 0.031
&., = 0.032
= 0.030
136
M. Hribar et al. I M-shell
themselves. Thus, in the computation of the fluorescence yields we estimated the accuracy of the & values with a uniform 5%. Besides, we report the corrected ratios N,/(N,+ N,,,) with their proper experimental errors to be converted into ‘fluorescence yields when more accurate Pt,, values become available. The good agreement between the experimental and theoretical values presented in tables I and II supports the conclusion that higher M-subshell vacancies mainly decay by Coster-Kronig transitions to m and MS subshells. Thus, the M-shell fluorescence is governed by the w4 and w5 fluorescence yields and is nearly independent of the excitation mode and the corresponding vacancy distribution.
fluorescence
yields
of lead
References [l] R.C. Jopson, H. Mark, C.D. Swift and M.A. Williamson, Phys. Rev. 137 (l%S) A13.53. [2] W. Bambynek, B. Crasemann, R.W. Fink, H.U. Freund, H. Mark, C.D. Swift, R.E. Price and P. Venugopala Rao, Rev. Mod. Phys. 44 (1972) 716. [31 A.A. Konstantinov and T.E. Sazonova, Izv. Akad. Nauk SSSR, Ser. Fiz. 32 (1%8) 631. [41 E.J. McGuire, Phys. Rev. A5 (1972) 1043. [51 E. Storm and HI. Israel, Nucl. Data Tables A7 (1970) 565. 161J.H. Hubbell, W.H. McMaster, N. Kerr DelGrande and J.H. Mallett, International Tables for X-Ray Crystallography, Vol. 4, eds. J.A. Ibers and W.C. Hamilton (Kynoch Press, Birmingham, 1974) Sec. 2.1.
Physica 115C (1982) 132-136 North-Holland Publishing Company
A STUDY OF THE M-SHELL FLUORESCENCE M. HRIBAR,
A. KODRE
YIELDS OF LEAD
and J. PAHOR
Department of Physics and Institute J. Stefan, E. Kardelj University, Ljubljana, Yugoslavia Received 8 July 1980 Received in final form 20 March 1982
The modes of decay of the M-shell vacancies in lead atoms were studied by means of a wall-less proportional counter spectrometer with lead in the form of lead-tetraethyle admixed to the working gas of the counter. The vacancies in consecutive M-subshells of the lead atoms were produced by the photoelectric absorption of the characteristic K-radiation of elements from Cl to V. The following M-shell fluorescence yields were extracted: & = 0.032~0.003, 02-s = 0.030~0.003, 0F5=0.030~0.002, 04,5>0.029.
1. Introduction The deexcitation of the M-shell vacancies in lead atoms has been studied by several authors. Jopson et al. [l] have reported the average WLM fluorescence yield as wLM= 0.032 * 0.006. The value has been corrected for the contribution from double M-shell vacancies by Bambynek et al. [2] to uLM = 0.0262 0.005. The average fluorescence yield WM= 0.029 2 0.002 has been determined by Konstantinov [3]. Theoretical values for the subshell fluorescence yields and Auger yields as well as for the Coster-Kronig transition probabilities have been calculated by McGuire [4] for the elements in the vicinity of Z = 80. These theoretical results indicate that only w and MS subshells can effectively contribute to the fluorescent mode of deexcitation. The aim of the present work is to verify this conjecture by experiment.
2. Experimental
procedure
The proportional counter is known to be a convenient device for the study of X-ray fluorescence, particularly in the low-energy region. The target atoms admixed to the counter gas are ionized by an external beam and the 037%4363/82/000&0000/$02.75
@ 1982 North-Holland
spectrometer can discern radiative and nonradiative modes of deexcitation provided that the gas is sufficiently dilute to let the fluorescence photons escape. Thus, the formation of a vacancy by photoelectric absorption is always detected by the presence of the ejected photoelectron: in the case of the subsequent nonradiative decay of the vacancy the full energy of excitation is transferred to the ejected electrons and consequently detected by the spectrometer. In the case of a radiative decay the energy imparted to the escaping photon is missing. The energy spectra of the events exhibit two peaks: the full energy peak and the escape peak. We used a wall-less proportional counter of 400 mm length: the active volume (diameter 56 mm) of the counter is defined by a cylindrical arrangement of thin wires at the cathode potential. The space between this cathode and the vessel wall (width 14 mm) is equipped with another set of counting wires and serves as an anticoincidence ring to eliminate the wall effects. A thin mylar window in the vessel wall at the middle of the counter length serves to admit a narrow beam of X-rays into the counter along its diameter. Monochromatic X-ray beams are produced by irradiation of suitable elemental targets in the X-ray tube: The characteristic Ka radiation of the target is isolated by the use of
M. Hribar et al. / M-shell
fluorescence
133
yields of lead
MAIN
_---___-__ P H. ANAL
J-
_---____ COUNTER
RING Fig. 1. The wiring of the spectrometer
using the wall-less
collimating slits and X-ray filters where possible. The experimental setup is shown in fig. 1. To study the M-shell fluorescence of lead the counter was filled with methane at 66 mbar and lead tetraethyle at its saturated vapour pressure (less than 0.15 mbar). Characteristic radiation of metallic targets of V, Ti and SC was used to induce fluorescence. Since all M-subshells of lead could be ionized with the K-series radiation of these elements and since escape of photons from various subshells could not be resolved by the
proportional
counter as a sensor.
spectrometer, only the average fluorescence yield could be extracted from the data. A typical spectrum of pulses from the counter is shown in fig. 2 for the experiment with the scandium radiation. The fluorescence spectrum is compared to the spectrum of events in pure methane which shows the contribution of photoabsorption by carbon in the working gas. Evidently a larger part of the events in the main peak is of the latter origin, and only the difference of the two spectra can be attributed to
Scandium Energy
target 109
keV
CHANNEL
NUMBER
Fig. 2. The spectrum of pulses from the counter with (0) and without (0) the admixture of lead tetraethyle, irradiation of the counter by the scandium characteristic radiation, with all M-subshells excited.
obtained
during the
134
M. Hribar et al. 1 M-shell fluorescence
the events involving lead atoms. Since the admixture of the lead tetraethyle is known to decrease the resolution of the proportional counter, a series of spectra is recorded with part of the gas mixture repeatedly replaced by the pure methane. Thus the admixture of lead tetraethyle is gradually decreased, causing a corresponding improvement of the resolution and, of course, a corresponding loss of lead fluorescence events. A good compromise is usually achieved at 0.07 mbar of lead tetraethyle, the exact amount being deduced from the ratio of lead/carbon events. The fluorescence of consecutive subshells is suppressed by lowering the energy of the incident photons below the corresponding ionization thresholds. Thus, calcium KLY radiation was used to induce fluorescence in the MrMs subshells, and potassium Ka radiation to induce fluorescence in the M3-M5 subshells. Metallic targets in a hydrogen atmosphere were employed. The KP radiation of both targets reaches above the corresponding thresholds, however it represents less than 10% of the total intensity so that its effect can be subtracted as a small numerical correction. Finally, the chlorine radiation from the NaCl target was used to ionize the m and M5 subshells. Due to the low energy of the events the resolution of the spectrometer only allowed us to extract a lower limit for the fluorescence yield. No simple target is available to induce the fluorescence in the M5 subshell alone.
3. Results After subtraction of the carbon photoabsorption contribution determined in a separate experimental run on methane, the spectrum of the lead fluorescence is decomposed into the main peak of the spectrum, the fluorescence responding numbers of pulses N,,, and N, are extracted. Small corrections are applied to the numbers to account for the effects of fluorescent photon reabsorption and the escape of ejected electrons to the anticoincidence ring: in the first case the events are transferred from the escape
yields of lead
to the main peak, while in the second case the events are lost owing to the vetoing of the anticoincidence circuit. The corrections amount to less than 5% for the main peak and less than 1.5% for the escape peak. The Coster-Kronig transitions do not contribute observable effects: the fluorescence of separate subshells cannot be resolved in the escape peak and the energy of the Coster-Kronig electrons is so low that their escape is negligible. The observed fluorescence yield is defined as the ratio of the number of M-fluorescence photons to the number of primary vacancies in the M-shell. Since the photoabsorption events in the higher shells of lead atoms also contribute to the main peak of the spectrum, the fluorescence yield is calculated as W;-5= N,IPP,~N, +
W ,
with PM the relative probability of photoabsorption in the M-shell. These fluorescence yields are averages over subshells from i to 5, defined by the distribution of primary vacancies as produced in a particular experiment. In the derivation of the formula it has been taken into account that the radiative transitions from N- and higher shells, which carry a negligible amount of energy anyhow, lead to an escape peak less than 1 keV below the main peak, so close that it is effectively hidden in the low-energy tail and thus it is included in the signal. The results together with the relevant experimental data are given in table I. Theoretical calculations usually provide the subshell fluorescence yields mi which represent quantum mechanical characteristics of the atom independent of the excitation mode. The experimental and theoretical quantities are connected by the set of equations 5
wi-5 =
2
nkvk
9
i=1,2,3,4
k=i
k=i+l
where
ni denotes
the relative
number
of primary
M. Hribar et al. / M-shell fluorescenceyields of lead
Table
I Exciting
Absorption edge
MS
radiation Energy
Target
(keV)
h/I4
135
2.484 2.586
NI(N
+ Nm)
(keV)
Exp.
Corrected
PM
Fluorescence yield
2.62 (Ka)
> 0.021
> 0.022
0.741
&
Cl 2 0.029
2.82 (KP) M3
3.066
K
3.31 (Ko)
0.022
0.023 k 0.001
0.769
(s>s = 0.030 2 0.002
0.023
0.024 k 0.002
0.780
62-5 = 0.030 f 0.003
0.788
& = 0.032 k 0.003
3.59 (KjI) M2
3.554
Ca
3.69 (Ko) 4.01 (KP)
MI
3.851
SC
4.09 (Ka)
0.025
0.026 2 0.002
Ti
4.46 (Kp) 4.51 (Ka)
0.024
0.025 2 0.002
V
4.93 (KP) 4.95 (Ko)
0.024
0.025 -t 0.002
vacancies in the ith subshell and frk the known Coster-Kronig yields. It would be possible, in principle, to solve the set of equations with the given average yields for the various subshells. However, the calculation involves differences of experimental values leading to an ill-conditioned problem with an unstable solution. Instead, the comparison of the experiment to the theory is made by calculating the average yields from the theoretical subshell values where above relations are used explicitly. The results and all the relevant theoretical data are summarized in table II. The partial subshell yields Table
II
M-subshell fluorescence Coster-Kronig yields Subshell
oi
M5 M3
0.030 0.031 5.0 x lo-’
M2
5.9x
Ml
2.7
M4
and the Coster-Kronig yields are interpolated from McGuire’s data, while the probabilities PM are taken from the compilation of Storm and Israel [5]. The vacancy distribution numbers Iti are derived from the photoabsorption data of the same source. Although the authors only claim an overall 10% accuracy for their theoretical calculations in the energy region of our interest, the discussion in another big compilation of X-ray absorption data by Hubbell et al. [6] indicates that the jump values, i.e. the ratios of the photoabsorption coefficients above and below the edge, are more accurate than the coefficients
and Relative 6k
x
1o-3
lo-’
f& = 0.040 fx = 0.098 fjS = 0.77 fu=O.ll f24= 0.66 fis = 0.09 fi2 = 0.12 fix = 0.62 fi4 = 0.07 f,s = 0.10
number n2
_ -
_
of primary n3
vacancies n4
Average
fluorescence
n5
Theor.
Exp.
yields
1
_ 0.18
0.42 0.34
1 0.58 0.48
0s = 0.030 (54.5= 0.030 w>r = 0.031
04,s 2 0.029 6%5 = 0.030
-
0.07
0.16
0.32
0.44
&-s = 0.030
G,
0.05
0.07
0.16
0.30
0.42
WM= 0.031
&., = 0.032
= 0.030
136
M. Hribar et al. I M-shell
themselves. Thus, in the computation of the fluorescence yields we estimated the accuracy of the & values with a uniform 5%. Besides, we report the corrected ratios N,/(N,+ N,,,) with their proper experimental errors to be converted into ‘fluorescence yields when more accurate Pt,, values become available. The good agreement between the experimental and theoretical values presented in tables I and II supports the conclusion that higher M-subshell vacancies mainly decay by Coster-Kronig transitions to m and MS subshells. Thus, the M-shell fluorescence is governed by the w4 and w5 fluorescence yields and is nearly independent of the excitation mode and the corresponding vacancy distribution.
fluorescence
yields
of lead
References [l] R.C. Jopson, H. Mark, C.D. Swift and M.A. Williamson, Phys. Rev. 137 (l%S) A13.53. [2] W. Bambynek, B. Crasemann, R.W. Fink, H.U. Freund, H. Mark, C.D. Swift, R.E. Price and P. Venugopala Rao, Rev. Mod. Phys. 44 (1972) 716. [31 A.A. Konstantinov and T.E. Sazonova, Izv. Akad. Nauk SSSR, Ser. Fiz. 32 (1%8) 631. [41 E.J. McGuire, Phys. Rev. A5 (1972) 1043. [51 E. Storm and HI. Israel, Nucl. Data Tables A7 (1970) 565. 161J.H. Hubbell, W.H. McMaster, N. Kerr DelGrande and J.H. Mallett, International Tables for X-Ray Crystallography, Vol. 4, eds. J.A. Ibers and W.C. Hamilton (Kynoch Press, Birmingham, 1974) Sec. 2.1.