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Fundamental mechanisms determining the performance of gas proportional detectors
Nuclear Instruments and Methods in Physics Research B 88 (1994) 465-469 North-Holland
Fundamental mechanisms determining the performance proportional detectors
NUMB
Beam Interactions with Materials & Atoms
of gas
A, Svensson a,b**,R.J. Allan b, J. Bordas b, E.A. Hughes b, R. Lewis b and G. Mant b aDept of Physics and Astronomy, University of Leicester, Leicester LEI 7RH, UK b SERC, Daresbury Laboratory, Daresbury, Warrington WA4 4AD, UK
Received 24 January 1994
The average ionic charge created in Ar, Kr and Xe as a result of X-ray photoabsorption has been determined using time-of-fligl$ mass spectroscopy in conjunction with synchrotron radiation (XTOFS). Measurements were carried out at the Ni K edge, 1.5 A. Calculations predicting the degree of electron multiplication expected from inelastic collisions in the gas at atmospheric pressures have been performed. Theory is found to be in agreement with present experimental findings. The estimated total electron yield in the gas is a guide in the dete~ination of the effkiency of a gas pro~~ional counter. Xenon gas is found to be the preferred candidate.
1. Introduction
The successful outcome of experiments where the info~ation is carried by X-rays depends on the availability of an efficient photon imaging detector. To date, the most widespread detector in use, which has found applications in many fields related to synchrotron radiation such as physics, biology, medicine and materials science, is the multiwire gas proportional counter (see, e.g., ref. 111).It is the interaction between matter and either ionising radiation or charged particles which determines the behaviour of this detector. We have studied the fundamental properties of a gas detector, both experimentally and theoretically, by considering the degree of ionisation taking place in some of the noble gases ~mmonly in use. The results are correlated with the electron multiplication “efficiency” found in a detector in operation.
2. Fundamental processes Provided that the energy of the photons is less than N 30 keV, the most probable process resulting from the interaction between electromagnetic radiation and atoms is the photoelectric effect. When an atom absorbs an X-ray it does so by converting nearly the entire photon energy into the ejection of a photoelectron, most commonly a core electron, and the remain-
* Corresponding
author, tel. + 44 533 523525.
0168-583X/94/$07.00
ing part into electronic excitation. Atomic readjustment to an initial vacancy is primarily achieved through two competing processes, radiative transitions and radiationless Auger decay, in which a vacancy from an inner shell is transferred to a higher one (see, e.g. ref. [2]). Also electron shakeoff, yielding more than one emitted electron for each vacancy transfer, can occur with low probability [3]. With the exception of the K and L shells of heavy atoms, Auger decay is the most likely process. Auger transitions lead to a definite final-charge state and the manifold of all possible routes results in a specific charge distribution. The electrons produced from photoionisation, the subsequent Auger processes and electron shakeoff are in this paper referred to as primary electrons. The gas pro~~ionai detector is operated at pressures of one or several atmospheres with a corresponding electron mean free path in the gas of only a few microns. Because the mean free path is short, many primary electrons will undergo inelastic collisions before they traverse the recording gas volume of the detector. Provided the electron energy is sufficient, the collision with an atom leads to ionisation and the production of secondary electrons (see, e.g. ref. [41 and references therein). As the average kinetic energy carried by a primary electron amounts to several keV it will participate in a series of inelastic ionising collisions before it loses ail its kinetic energy. Typically, the electron-atom inelastic ionisation cross section is of the order of 1O-2o m2 for electrons with a kinetic energy of a few keV and increases by an order of magnitude for electron energies of approximately 100
0 1994 - Elsevier Science B.V. All rights resewed
&SD1 0168-583X~94)00~47-N
466
A. Svensson et al. / Nucl. Instr. and Meth. in Phys. Res. B 88 (1994) 465-469
eV. Moreover, some ejected secondary electrons will also have a kinetic energy which is enough to ionise the gas and so contribute to the increasing number of electron-ion pairs. It is the generation of secondary electrons that is ultimately responsible for the electron multiplication in the gas itself.
3. Experimental The X-ray time-of-flight mass spectrometer, XTOFS, fulfils the conditions given by Wiley and McLaren [5]. It has been used to record multiply charged atomic ions formed as a result of X-ray photoabsorption and consists of an ionisation source, acceleration region and a field-free drift tube. The configuration of the system is such that almost 100% collection efficiency is ensured. The Auger cascade takes place within lo-i5 s, while collecting and analysing the ions takes approximately 10e6 s which leads to the observation of only final ionic states. Detection of ions is made in real time by using a time to digital converter, TDC, Le Croy 4208 with a time resolution of 1 ns. The electrons supply start pulses, and the mass analysed positive ions provide stop pulses to the TDC. The white X-ray beam is monochromatised following four reflections on a Si(l,l,l) crystal surface on line 2.2 of the Synchrotron Radiation Source, SRS, Daresbury Laboratory, using the electron beam in the storage ring as a virtual point source. With the use of two sets of slits, the two sets placed on either side of the silicon crystal, the resolution of the monochromatic beam was chosen to be approximately 1 eV [6]. Finally, the experimental chamber is aligned so that the beam of X-rays is made to interact with a diffuse gas jet in its centre.
4. Theoretical In modelling the primary electron production in the Auger process it is important to get the correct statistical distribution of relative ion charges, as measured in this work, as well as a good approximation to the energy distribution of emitted electrons in each primary event (see, e.g., ref. [7]). The latter will affect the ability of the electrons to penetrate further into the gas cell and undergo secondary collisions before being detected. In earlier studies a Hartree-Fock treatment was used to model the experimentally recorded ion charge spectra. The probabilities of vacancy transfer with ionisation were calculated in a number of possible configurations including multiple electron shakeoff [8,3,9]. These were then fed into a stochastic Monte Carlo
treatment of the vacancy cascade using a sudden approximation [lo]. In the present work, we are using known relative photoelectric cross sections for the subshells of the rare gases involved and a simple model of the cascade process [11,12]. The most important mechanisms identified earlier have been taken into account. Especially the Coster-Kronig transitions have been included. They may be a factor of 10 more likely than other Auger processes and are characterised by having both the vacancy and the electron filling it in shells with the same principle quantum number. To obtain a spectrum in reasonable accord with experiment we have also found it necessary to allow electrons to be emitted with a greater probability to the near continuum, that is the kinetic energy released should not be much larger than the ionisation energy of the electron, or equivalently that most Auger processes concern electrons lying energetically about half way between the vacancy site and the continuum. We have found that including shakeoff or radiative transitions does not influence the shape of the spectrum, implying that if they occur at all in the experiment it is with low probability. The present treatment is then sufficient to yield abundances in reasonable, but not perfect, accord with the experiment. Secondary electron production is modelled using the (e, 2e) collision cross sections over a wide range of energy given by Rapp and Englander-Golden [13]. If the cross section is known at a given energy the mean free path of an electron in the gas cell at given pressure can be calculated. The two secondary electrons have energies in the range zero to E eV, E = (E, - Z), where E, is the energy of the colliding electron and Z is the ionisation potential of the atom. It is assumed that secondary ionisation is from the valence shell only and that the total energy is conserved, presuming the ion recoil is negligible. Furthermore it is assumed that the electrons are emitted isotropically on average, since detailed collision dynamics would be hard to introduce into the simple model suggested ([see, e.g., ref. [4]). The path of an individual electron through the gas cell was followed, again using a Monte Carlo process, and it is found that the energy is exhausted, i.e E, falls below I, before the electrons reach the edge of the cell at pressures around 1 atm and this happens in about lo-” s, well within the experimental collection time.
5. Results and discussion The absorption cross section for any subshell is energy dependent and peaks near its edge. As a result the X-ray cross section is generally dominated by one or two subshells, where the greatest relative absorption is that of the shell whose energy is closest to that of the X-ray. The operation of proportional gas counters are
467
A. Svensson et al. / Nucl. Instr. and Meth. in Phys. Res. B 88 (1994) 465-469
Table 1 The relative abundances of ions formed as a consequence of photoionisation in primarily the K shell of argon and the L shells of krypton and xenon through X irradiation with an energy of 8.265 keV are listed. The estimated statistical mean error for each ion is given in percent Charge 4
Argon [%I
1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+
1.4 6.2 14.8 31.4 29.2 13.1 3.3 0.6
qave
Mean error
Krypton
Mean error
[%I
[%I
[%I
[%I
+0.5 k1.9 +1.3 +3.0 f 1.8 +0.7 *0.3 +0.03
1.1 1.6 2.2 11.9 16.4 27.1 23.2 11.2 3.7 1.2 0.6
f0.4 0.2 0.9 +0.5 1.5 +0.9 4.1 *3.7 f 6.3 4.7 + 10.1 9.8 15.3 f7.0 +2.1 21.7 f 1.3 18.2 *0.5 13.2 f0.7 6.7 2.5 1.2
f 0.003 f0.1 f0.2 *0.1 f 0.3 +0.1 *0.9 f0.4 f 1.4 + 0.8 f0.4 f 0.6 f0.3
4.36
Xenon [%I
Mean error
are based on the accuracy with which the integrated area under each peak in the mass spectrum could be determined. Vacancies were primarily created in the K shell of argon and the L shells of krypton and xenon. The total average charges, qave, are given also in where a, Table 1. qave is defined as Qz,,qn/Cnun, corresponds to the relative abundance of the nth ion having charge q,,, It should be noted that the values for qave are consistently higher than those previously found [3,14,9]. We attribute this discrepancy to the highly monochromatic X-rays used for our measurements (see also ref. Ml). The calculated charge distributions in the noble gases (see theoretical model) are shown in Table 2. Comparison with the experimental findings (Fig. 1) shows a good qualitative agreement in the distribution of charges. The agreement between theory and experiment is excellent in the case of qaV, (compare Tables 1 and 2), thus testifying for the validity of our theoretical treatment.
8.01
6.07
carried out in the X-ray region at photon energies where absorption predominantly occurs in one subshell. The experimentally determined relative intensities of differently charged ions in Ar, Kr and Xe following X-ray irradiation are given in Table 1. All mean errors Table 2 Results of theoretical model prediction of relative ion abundances and statistical standard deviation in the Monte Carlo process Charge 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 4 ave
Argon
[%I 4.17 0.33 21.50 19.67 42.50 11.83
4.32
Mean error
Ktypton
Mean error
[%I
[%I
[%I
+0.17 f 0.33 +2.17 f1.33 +0.83 +0.17
3.60 6.30 2.30 5.10 13.20 30.20 21.40 4.7 6.10 4.30 2.20 0.60
+0.6 +O.l +O.l *0.5 f 1.4 k3.0 kO.4 *0.5 fO.l *0.1 f0.4 f0
6.07
Xenon [%I
Mean error
[%I 0.17 1.50 2.67 6.50 6.83 10.50 11.17 14.17 14.83 11.50 9.50 4.33 3.17 1.50 0.50 0.17 8.08
f0.17 f 0.50 f 0.33 f 0.500 f 0.50 f 1.50 + 0.83 f 0.83 *0.50 f 0.50 f 1.17 f 0.67 f 0.50 *0.17 *0.17 *0.17
0
2
4
6
8
10
12
14
16
/rqewedwP,q
Fig. 1. Charge spectrum of Ar, Kr and Xe. Comparison between experiment and theoretical model (0: experimental values, + : theoretical values).
468
A. Svensson et al. /Nucl. Instr. and Meth. in Phys. Res. B 88 (1994) 465-469
Table 3 The absolute photoabsorption cross sections for Ar, Kr and Xe are given at a fixed X-ray energy Argon Krypton Xenon
a(hv = 9.24 keV) = 0.0052 Mb a c+(hv = 8.25 keV) = 0.0132 Mb b cr(hv = 8.25 keV) = 0.059 Mb b
a From ref. [18]. Note, no correction to this of the coherent and incoherent scattering been made, but this amounts to no more photon energies according to Vuilleumier b From ref. [19].
value for the sum cross section has than 2% at these [19].
6
1600
g
1400
c
1200
5 g
1000
1
800 600
H
g
400
:
200
1 e
:
I
_:'
t
;.*.'
-
-
/"
.-'
........_._,.___. __........--....-...-.. .----" ._.______ ............. _._.___._...._,~ _
o-,.;, 0
0.8
0.4
I.6
1.2
2
taa1 Fig. 2. Total electron yield as a function of pressure exhibiting a linear dependence. p
The transmission of X-rays through a layer of gas in which photoabsorption occurs, is given by Z = I, e --(rn7,
(1)
where I, is the initial photon intensity; n is the density of atoms. We assume here that we are dealing with an ideal gas, i.e. n =p/kT and T = 293 K; T is the length of the interaction region; and u is the absolute photoabsorption cross section (see Table 3). The experimentally determined primary electron signal was normalised to the photon flux and extrapolated to 1 atm assuming r = 1 cm and using the absolute cross sections of Ar, Kr and Xe (see Table 3). This gave per photon 0.03, 1.47 and 11.77 electrons/(scm) in Ar, Kr and Xe, respectively. These numbers are to be compared with the equivalent theoretical ones of 0.673, 3.27 and 13.90 electrons/& cm> (see Table 4). In this case, the agreement between the experiment and theory is relatively good for Kr and Xe. However, the experimentally determined primary signal for Ar is several orders of magnitudes smaller than the theoretical predictions. This discrepancy can be reconciled by considering the fact that the experimental recording of the Ar data is very inefficient because of the very small cross-section of the process and, consequently, we
speculate that much of our signal was buried in the background. Table 4 shows the predicted total number of primary and secondary electrons, e,,,, for a range of gas pressures calculated with the Monte Carlo simulation (Fig. 2). Whilst every primary electron participates in the generation of secondary electrons, it should be noted that their interaction will almost exclusively occur with neutral gas atoms. This is because the neutral atoms significantly outnumber the positive ions. The theoretically predicted yield of secondary electrons for each primary electron is gas dependent, and it is approximately 76 in Ar, 43 in Kr and 53 in Xe (Table 4). The total electron current, etot (also referred to as the the total electron-ion yield), generated by the gas in a proportional gas chamber per second is often calculated from the empirical relationship = aI X_w
etot
0
enerm[eVl 27[eV]
(2)
’
where IO is as defined above; and a is a correction factor (g 1; with dimensions of electrons/(photoncm) of gas at a given pressure)
Table 4 Simulated average numbers of primary and total electrons produced per incident photon in a 1 cm3 gas cell at given pressure Pressure
Argon
latml
primary
total
0.1 0.2 0.5 1.0 2.0
0.0672 0.134 0.342 0.673 1.35
5.08 f 10.2 f 25.8 + 51.4 f 104.0 f
Gas amplification (average number of secondary eproduced per primary e - )
Xenon
Krypton
76.0
0.505 1.02 2.56 5.17 10.3
primary
total
0.346 0.675 1.650 3.27 6.42
13.9* 28.5* 71.3* 145.0 f 289.0+
43.0
1.39 2.85 7.13 14.3 28.9
primary
total
1.42 2.85 7.09 13.9 28.9
74.7* 7.39 152.0* 15.1 381.0+ 37.9 764.0 f 75.8 1524.0* 151.0
53.0
A. Svensson et al. / Nucl. Instr. and Meth. in Phys. Res. B 88 (1994) 465-469
It takes into account the absolute cross section of the gas and is found to be for Ar, Kr and Xe: aAr m 0.31, ati _ 0.65 and axe u 1 (see, e.g., ref. [16]). In comparison with our results (Table 4), we find that the application of Eq. (2) to the case, for example, of a chamber at atmospheric pressure and with a depth of 1 cm, overestimates the total electron charge in the case of Ar, whilst it underestimates that for Xe. This is simply because Eq. (2) implicitly assumes that the only difference between the various gases normally used in proportional gas chambers is in their photoabsorption cross sections and it does not make allowance for their different electronic structure which is responsible for the different numbers of primary and secondary electrons emitted. In this context it is important to note that in our X-ray range, the total electron yield for xenon gas is much higher than for argon or krypton even though argon is the most efficient amplifier gas. A rough estimate of gas amplification A = 100 used by SipilP [17] in predicting the resolution of a proportional counter is of the same order of magnitude as our theoretical values which average around 64. However, when the amplification is multiplied by the primary electron yield it is xenon which gives the highest total yield, mainly due to its much higher photoionisation cross section and high primary electron yield. In considering mixed-gas proportional detectors these differences should be born in mind. To be noted is that from all points of view Kr is not a good candidate for proportional gas chambers.
6. Conclusions We have shown above that the electron amplification processes occurring following photoabsorption in some noble gases used in proportional counters can be predicted, at least to a first approximation, from first principles. The relative merits of Ar, Kr and Xe have been evaluated.
469
Acknowledgements The Monte Carlo simulations in this work were run on a parallel Meiko i860 Computing Surface at Daresbury Laboratory. The cooperation from the staff of the SRS is gratefully acknowledged.
References [l] J.S. Worgan et al., Nucl. Instr. and Meth. A 291 (1990) 447. [2] F. Pleasonton and A.H. Snell, Proc. R. Sot. London 241 A (1957) 141. [3] T.A. Carlson and M.O. Krause, Phys. Rev. 137 (1965) A1655. [4] C.T. Whelan, H.R.J. Walters, A. Lahmam-Bennani and H. Ehrhardt (eds.), e-2e, and Related Processes, Proc. NATO Adv. Res. Workshop, Cambridge, 1992 (Kluwer, 1993). [5] W.C. Wiley and I.H. McLaren, Rev. Sci. Instr. 26 (1955) 1150. [6] G.P. Diakun and J.E. Harries, in: Synchrotron Radiation and Biophysics, ed. S.S. Hasnain (1990) p. 243. [7] M.H. Chen, B. Crasemann and H. Mark, Phys. Rev. A 21 (1980) 442. [8] T.A. Carlson, Phys. Rev. 130 (1963) 2361. [9] M.O. Krause and T.A. Carlson, Phys. Rev. 158 (1967) 18. [lo] T.A. Carlson, Photoelectron and Auger Spectroscopy (Plenum, New York, 1975). [ll] R.T. McGinnies and G.W. Grodstein, National Bureau of Standards, Supplement to Circ. 583 (NBS, Washington, 1959). [12] J.J. Yeh and I. Lindau, Atom. Data Nucl. Data Tables 32 (1985) 2. [13] D. Rapp and P. Englander-Golden, J. Chem. Phys 43 (1965) 1464. [14] T.A. Carlson, W.E. Hunt and M.O. Krause, Phys. Rev. 151 (1966) 41. 1153 N. Saito and I.H. Suzuki, J. Phys. B 25 (1992) 1785. [16] F. Sauli, Principles of operation of multiwire proportional and drift chambers, CERN 77-09 (1977). [17] H. Sipill, Nucl. Instr. and Meth. 133 (1976) 251. [18] J.H. McCrary, L.D. Looney, C.P. Constanten and H.F. Atwater, Phys. Rev. A 2 (1970) 2489. [19] F. Villeumier, Phys. Rev. A 6 (1972) 2067.
Fundamental mechanisms determining the performance proportional detectors
NUMB
Beam Interactions with Materials & Atoms
of gas
A, Svensson a,b**,R.J. Allan b, J. Bordas b, E.A. Hughes b, R. Lewis b and G. Mant b aDept of Physics and Astronomy, University of Leicester, Leicester LEI 7RH, UK b SERC, Daresbury Laboratory, Daresbury, Warrington WA4 4AD, UK
Received 24 January 1994
The average ionic charge created in Ar, Kr and Xe as a result of X-ray photoabsorption has been determined using time-of-fligl$ mass spectroscopy in conjunction with synchrotron radiation (XTOFS). Measurements were carried out at the Ni K edge, 1.5 A. Calculations predicting the degree of electron multiplication expected from inelastic collisions in the gas at atmospheric pressures have been performed. Theory is found to be in agreement with present experimental findings. The estimated total electron yield in the gas is a guide in the dete~ination of the effkiency of a gas pro~~ional counter. Xenon gas is found to be the preferred candidate.
1. Introduction
The successful outcome of experiments where the info~ation is carried by X-rays depends on the availability of an efficient photon imaging detector. To date, the most widespread detector in use, which has found applications in many fields related to synchrotron radiation such as physics, biology, medicine and materials science, is the multiwire gas proportional counter (see, e.g., ref. 111).It is the interaction between matter and either ionising radiation or charged particles which determines the behaviour of this detector. We have studied the fundamental properties of a gas detector, both experimentally and theoretically, by considering the degree of ionisation taking place in some of the noble gases ~mmonly in use. The results are correlated with the electron multiplication “efficiency” found in a detector in operation.
2. Fundamental processes Provided that the energy of the photons is less than N 30 keV, the most probable process resulting from the interaction between electromagnetic radiation and atoms is the photoelectric effect. When an atom absorbs an X-ray it does so by converting nearly the entire photon energy into the ejection of a photoelectron, most commonly a core electron, and the remain-
* Corresponding
author, tel. + 44 533 523525.
0168-583X/94/$07.00
ing part into electronic excitation. Atomic readjustment to an initial vacancy is primarily achieved through two competing processes, radiative transitions and radiationless Auger decay, in which a vacancy from an inner shell is transferred to a higher one (see, e.g. ref. [2]). Also electron shakeoff, yielding more than one emitted electron for each vacancy transfer, can occur with low probability [3]. With the exception of the K and L shells of heavy atoms, Auger decay is the most likely process. Auger transitions lead to a definite final-charge state and the manifold of all possible routes results in a specific charge distribution. The electrons produced from photoionisation, the subsequent Auger processes and electron shakeoff are in this paper referred to as primary electrons. The gas pro~~ionai detector is operated at pressures of one or several atmospheres with a corresponding electron mean free path in the gas of only a few microns. Because the mean free path is short, many primary electrons will undergo inelastic collisions before they traverse the recording gas volume of the detector. Provided the electron energy is sufficient, the collision with an atom leads to ionisation and the production of secondary electrons (see, e.g. ref. [41 and references therein). As the average kinetic energy carried by a primary electron amounts to several keV it will participate in a series of inelastic ionising collisions before it loses ail its kinetic energy. Typically, the electron-atom inelastic ionisation cross section is of the order of 1O-2o m2 for electrons with a kinetic energy of a few keV and increases by an order of magnitude for electron energies of approximately 100
0 1994 - Elsevier Science B.V. All rights resewed
&SD1 0168-583X~94)00~47-N
466
A. Svensson et al. / Nucl. Instr. and Meth. in Phys. Res. B 88 (1994) 465-469
eV. Moreover, some ejected secondary electrons will also have a kinetic energy which is enough to ionise the gas and so contribute to the increasing number of electron-ion pairs. It is the generation of secondary electrons that is ultimately responsible for the electron multiplication in the gas itself.
3. Experimental The X-ray time-of-flight mass spectrometer, XTOFS, fulfils the conditions given by Wiley and McLaren [5]. It has been used to record multiply charged atomic ions formed as a result of X-ray photoabsorption and consists of an ionisation source, acceleration region and a field-free drift tube. The configuration of the system is such that almost 100% collection efficiency is ensured. The Auger cascade takes place within lo-i5 s, while collecting and analysing the ions takes approximately 10e6 s which leads to the observation of only final ionic states. Detection of ions is made in real time by using a time to digital converter, TDC, Le Croy 4208 with a time resolution of 1 ns. The electrons supply start pulses, and the mass analysed positive ions provide stop pulses to the TDC. The white X-ray beam is monochromatised following four reflections on a Si(l,l,l) crystal surface on line 2.2 of the Synchrotron Radiation Source, SRS, Daresbury Laboratory, using the electron beam in the storage ring as a virtual point source. With the use of two sets of slits, the two sets placed on either side of the silicon crystal, the resolution of the monochromatic beam was chosen to be approximately 1 eV [6]. Finally, the experimental chamber is aligned so that the beam of X-rays is made to interact with a diffuse gas jet in its centre.
4. Theoretical In modelling the primary electron production in the Auger process it is important to get the correct statistical distribution of relative ion charges, as measured in this work, as well as a good approximation to the energy distribution of emitted electrons in each primary event (see, e.g., ref. [7]). The latter will affect the ability of the electrons to penetrate further into the gas cell and undergo secondary collisions before being detected. In earlier studies a Hartree-Fock treatment was used to model the experimentally recorded ion charge spectra. The probabilities of vacancy transfer with ionisation were calculated in a number of possible configurations including multiple electron shakeoff [8,3,9]. These were then fed into a stochastic Monte Carlo
treatment of the vacancy cascade using a sudden approximation [lo]. In the present work, we are using known relative photoelectric cross sections for the subshells of the rare gases involved and a simple model of the cascade process [11,12]. The most important mechanisms identified earlier have been taken into account. Especially the Coster-Kronig transitions have been included. They may be a factor of 10 more likely than other Auger processes and are characterised by having both the vacancy and the electron filling it in shells with the same principle quantum number. To obtain a spectrum in reasonable accord with experiment we have also found it necessary to allow electrons to be emitted with a greater probability to the near continuum, that is the kinetic energy released should not be much larger than the ionisation energy of the electron, or equivalently that most Auger processes concern electrons lying energetically about half way between the vacancy site and the continuum. We have found that including shakeoff or radiative transitions does not influence the shape of the spectrum, implying that if they occur at all in the experiment it is with low probability. The present treatment is then sufficient to yield abundances in reasonable, but not perfect, accord with the experiment. Secondary electron production is modelled using the (e, 2e) collision cross sections over a wide range of energy given by Rapp and Englander-Golden [13]. If the cross section is known at a given energy the mean free path of an electron in the gas cell at given pressure can be calculated. The two secondary electrons have energies in the range zero to E eV, E = (E, - Z), where E, is the energy of the colliding electron and Z is the ionisation potential of the atom. It is assumed that secondary ionisation is from the valence shell only and that the total energy is conserved, presuming the ion recoil is negligible. Furthermore it is assumed that the electrons are emitted isotropically on average, since detailed collision dynamics would be hard to introduce into the simple model suggested ([see, e.g., ref. [4]). The path of an individual electron through the gas cell was followed, again using a Monte Carlo process, and it is found that the energy is exhausted, i.e E, falls below I, before the electrons reach the edge of the cell at pressures around 1 atm and this happens in about lo-” s, well within the experimental collection time.
5. Results and discussion The absorption cross section for any subshell is energy dependent and peaks near its edge. As a result the X-ray cross section is generally dominated by one or two subshells, where the greatest relative absorption is that of the shell whose energy is closest to that of the X-ray. The operation of proportional gas counters are
467
A. Svensson et al. / Nucl. Instr. and Meth. in Phys. Res. B 88 (1994) 465-469
Table 1 The relative abundances of ions formed as a consequence of photoionisation in primarily the K shell of argon and the L shells of krypton and xenon through X irradiation with an energy of 8.265 keV are listed. The estimated statistical mean error for each ion is given in percent Charge 4
Argon [%I
1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 12+ 13+
1.4 6.2 14.8 31.4 29.2 13.1 3.3 0.6
qave
Mean error
Krypton
Mean error
[%I
[%I
[%I
[%I
+0.5 k1.9 +1.3 +3.0 f 1.8 +0.7 *0.3 +0.03
1.1 1.6 2.2 11.9 16.4 27.1 23.2 11.2 3.7 1.2 0.6
f0.4 0.2 0.9 +0.5 1.5 +0.9 4.1 *3.7 f 6.3 4.7 + 10.1 9.8 15.3 f7.0 +2.1 21.7 f 1.3 18.2 *0.5 13.2 f0.7 6.7 2.5 1.2
f 0.003 f0.1 f0.2 *0.1 f 0.3 +0.1 *0.9 f0.4 f 1.4 + 0.8 f0.4 f 0.6 f0.3
4.36
Xenon [%I
Mean error
are based on the accuracy with which the integrated area under each peak in the mass spectrum could be determined. Vacancies were primarily created in the K shell of argon and the L shells of krypton and xenon. The total average charges, qave, are given also in where a, Table 1. qave is defined as Qz,,qn/Cnun, corresponds to the relative abundance of the nth ion having charge q,,, It should be noted that the values for qave are consistently higher than those previously found [3,14,9]. We attribute this discrepancy to the highly monochromatic X-rays used for our measurements (see also ref. Ml). The calculated charge distributions in the noble gases (see theoretical model) are shown in Table 2. Comparison with the experimental findings (Fig. 1) shows a good qualitative agreement in the distribution of charges. The agreement between theory and experiment is excellent in the case of qaV, (compare Tables 1 and 2), thus testifying for the validity of our theoretical treatment.
8.01
6.07
carried out in the X-ray region at photon energies where absorption predominantly occurs in one subshell. The experimentally determined relative intensities of differently charged ions in Ar, Kr and Xe following X-ray irradiation are given in Table 1. All mean errors Table 2 Results of theoretical model prediction of relative ion abundances and statistical standard deviation in the Monte Carlo process Charge 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 4 ave
Argon
[%I 4.17 0.33 21.50 19.67 42.50 11.83
4.32
Mean error
Ktypton
Mean error
[%I
[%I
[%I
+0.17 f 0.33 +2.17 f1.33 +0.83 +0.17
3.60 6.30 2.30 5.10 13.20 30.20 21.40 4.7 6.10 4.30 2.20 0.60
+0.6 +O.l +O.l *0.5 f 1.4 k3.0 kO.4 *0.5 fO.l *0.1 f0.4 f0
6.07
Xenon [%I
Mean error
[%I 0.17 1.50 2.67 6.50 6.83 10.50 11.17 14.17 14.83 11.50 9.50 4.33 3.17 1.50 0.50 0.17 8.08
f0.17 f 0.50 f 0.33 f 0.500 f 0.50 f 1.50 + 0.83 f 0.83 *0.50 f 0.50 f 1.17 f 0.67 f 0.50 *0.17 *0.17 *0.17
0
2
4
6
8
10
12
14
16
/rqewedwP,q
Fig. 1. Charge spectrum of Ar, Kr and Xe. Comparison between experiment and theoretical model (0: experimental values, + : theoretical values).
468
A. Svensson et al. /Nucl. Instr. and Meth. in Phys. Res. B 88 (1994) 465-469
Table 3 The absolute photoabsorption cross sections for Ar, Kr and Xe are given at a fixed X-ray energy Argon Krypton Xenon
a(hv = 9.24 keV) = 0.0052 Mb a c+(hv = 8.25 keV) = 0.0132 Mb b cr(hv = 8.25 keV) = 0.059 Mb b
a From ref. [18]. Note, no correction to this of the coherent and incoherent scattering been made, but this amounts to no more photon energies according to Vuilleumier b From ref. [19].
value for the sum cross section has than 2% at these [19].
6
1600
g
1400
c
1200
5 g
1000
1
800 600
H
g
400
:
200
1 e
:
I
_:'
t
;.*.'
-
-
/"
.-'
........_._,.___. __........--....-...-.. .----" ._.______ ............. _._.___._...._,~ _
o-,.;, 0
0.8
0.4
I.6
1.2
2
taa1 Fig. 2. Total electron yield as a function of pressure exhibiting a linear dependence. p
The transmission of X-rays through a layer of gas in which photoabsorption occurs, is given by Z = I, e --(rn7,
(1)
where I, is the initial photon intensity; n is the density of atoms. We assume here that we are dealing with an ideal gas, i.e. n =p/kT and T = 293 K; T is the length of the interaction region; and u is the absolute photoabsorption cross section (see Table 3). The experimentally determined primary electron signal was normalised to the photon flux and extrapolated to 1 atm assuming r = 1 cm and using the absolute cross sections of Ar, Kr and Xe (see Table 3). This gave per photon 0.03, 1.47 and 11.77 electrons/(scm) in Ar, Kr and Xe, respectively. These numbers are to be compared with the equivalent theoretical ones of 0.673, 3.27 and 13.90 electrons/& cm> (see Table 4). In this case, the agreement between the experiment and theory is relatively good for Kr and Xe. However, the experimentally determined primary signal for Ar is several orders of magnitudes smaller than the theoretical predictions. This discrepancy can be reconciled by considering the fact that the experimental recording of the Ar data is very inefficient because of the very small cross-section of the process and, consequently, we
speculate that much of our signal was buried in the background. Table 4 shows the predicted total number of primary and secondary electrons, e,,,, for a range of gas pressures calculated with the Monte Carlo simulation (Fig. 2). Whilst every primary electron participates in the generation of secondary electrons, it should be noted that their interaction will almost exclusively occur with neutral gas atoms. This is because the neutral atoms significantly outnumber the positive ions. The theoretically predicted yield of secondary electrons for each primary electron is gas dependent, and it is approximately 76 in Ar, 43 in Kr and 53 in Xe (Table 4). The total electron current, etot (also referred to as the the total electron-ion yield), generated by the gas in a proportional gas chamber per second is often calculated from the empirical relationship = aI X_w
etot
0
enerm[eVl 27[eV]
(2)
’
where IO is as defined above; and a is a correction factor (g 1; with dimensions of electrons/(photoncm) of gas at a given pressure)
Table 4 Simulated average numbers of primary and total electrons produced per incident photon in a 1 cm3 gas cell at given pressure Pressure
Argon
latml
primary
total
0.1 0.2 0.5 1.0 2.0
0.0672 0.134 0.342 0.673 1.35
5.08 f 10.2 f 25.8 + 51.4 f 104.0 f
Gas amplification (average number of secondary eproduced per primary e - )
Xenon
Krypton
76.0
0.505 1.02 2.56 5.17 10.3
primary
total
0.346 0.675 1.650 3.27 6.42
13.9* 28.5* 71.3* 145.0 f 289.0+
43.0
1.39 2.85 7.13 14.3 28.9
primary
total
1.42 2.85 7.09 13.9 28.9
74.7* 7.39 152.0* 15.1 381.0+ 37.9 764.0 f 75.8 1524.0* 151.0
53.0
A. Svensson et al. / Nucl. Instr. and Meth. in Phys. Res. B 88 (1994) 465-469
It takes into account the absolute cross section of the gas and is found to be for Ar, Kr and Xe: aAr m 0.31, ati _ 0.65 and axe u 1 (see, e.g., ref. [16]). In comparison with our results (Table 4), we find that the application of Eq. (2) to the case, for example, of a chamber at atmospheric pressure and with a depth of 1 cm, overestimates the total electron charge in the case of Ar, whilst it underestimates that for Xe. This is simply because Eq. (2) implicitly assumes that the only difference between the various gases normally used in proportional gas chambers is in their photoabsorption cross sections and it does not make allowance for their different electronic structure which is responsible for the different numbers of primary and secondary electrons emitted. In this context it is important to note that in our X-ray range, the total electron yield for xenon gas is much higher than for argon or krypton even though argon is the most efficient amplifier gas. A rough estimate of gas amplification A = 100 used by SipilP [17] in predicting the resolution of a proportional counter is of the same order of magnitude as our theoretical values which average around 64. However, when the amplification is multiplied by the primary electron yield it is xenon which gives the highest total yield, mainly due to its much higher photoionisation cross section and high primary electron yield. In considering mixed-gas proportional detectors these differences should be born in mind. To be noted is that from all points of view Kr is not a good candidate for proportional gas chambers.
6. Conclusions We have shown above that the electron amplification processes occurring following photoabsorption in some noble gases used in proportional counters can be predicted, at least to a first approximation, from first principles. The relative merits of Ar, Kr and Xe have been evaluated.
469
Acknowledgements The Monte Carlo simulations in this work were run on a parallel Meiko i860 Computing Surface at Daresbury Laboratory. The cooperation from the staff of the SRS is gratefully acknowledged.
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