Measurement of electron multiplication and ionization coefficients in high-pressure xenon

Nuclear Inst. and Methods in Physics Research, A 937 (2019) 53–58

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Measurement of electron multiplication and ionization coefficients in high-pressure xenon Hiroki Kusano a,b ,∗, José A. Matias Lopes c,d , Nobuyuki Hasebe b a

Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan c Department of Physics, University of Coimbra, 3004-516, Coimbra, Portugal d Coimbra Polytechnic - ISEC, 3030-199 Coimbra, Portugal b

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Keywords: High-pressure xenon Electron multiplication First Townsend ionization coefficient Proportional counter Electron avalanche

ABSTRACT Electron multiplication in high-pressure pure xenon was studied in the 0.5–3.0 MPa pressure range using a cylindrical proportional counter. The electron multiplication factor and the first Townsend ionization coefficient were determined, thus expanding collective knowledge beyond the previous studies, which were limited to 1.0 MPa. The measured electron multiplication factor falls between 15 and 2400 for the investigated pressure range. The density-reduced first Townsend ionization coefficient in this work is larger than that obtained for low-pressure xenon. In addition, the density-reduced first Townsend ionization coefficient was found to be density dependent. It was also found that the energy resolution deteriorates with increasing pressure. However, when the electron multiplication factor is several hundred, the energy resolution in high-pressure pure xenon was found to be better than that in commonly used xenon-based gas mixtures.

1. Introduction High-pressure xenon is utilized to build detectors for use in various applications, such as neutrinoless double 𝛽 decay search [1,2] and MeV 𝛾-ray detection [3–5]. One of the distinctive applications of high-pressure xenon is the time projection chamber, which became a reality thanks to the availability of ionization charge and scintillation light signals. Although the event topology of ionizing particles can be recorded in a high-pressure xenon time projection chamber, the ionization signal amplification is often desirable to reconstruct topological information. This amplification is possible in xenon detectors through either proportional scintillation or electron multiplication. In this study, we focus on electron multiplication in high-pressure xenon. Electron multiplication in gaseous xenon has been studied for several decades, and it was also applied in various devices, such as the proportional counter (PC), gas electron multiplier, and Micromegas. These applications are typically used with xenon at pressures less than 10 bar (1 MPa) mixed with a small amount of additive gas (e.g., CH4 , CF4 , or TMA) to provide stable operation at high charge gain, increased electron drift velocity, and reduced electron diffusion. The fundamental quantity in electron multiplication is the first Townsend ionization coefficient 𝛼, which is defined as the average number of electron–ion pairs per unit length generated by a primary electron on its collisions with gas atoms. The first Townsend ionization

coefficient was studied in xenon gas for pressures below 1 atm using parallel electrodes [6–8]. It was shown that the reduced first Townsend ionization coefficient 𝛼∕𝑝 or 𝛼∕𝑁 can be described over a wide pressure range as a function of only the reduced electric field 𝐸∕𝑝 or 𝐸∕𝑁, where 𝑝, 𝑁, and 𝐸 denote the gas pressure, number density of gas molecules, and electric field, respectively. Both reduced quantities are widely used as a reference to develop xenon detectors based on electron multiplication, even for pressures above 1 atm. In contrast, 𝛼∕𝑝 for xenon was also measured up to 10 atm using a cylindrical PC [9]. It was reported that 𝛼∕𝑝 at pressures ranging from 1–10 atm is larger than the value reported by Kruithof [6]. The difference in 𝛼∕𝑝 was not fully explained, thus the electron multiplication mechanism in xenon is still unclear. Therefore, it is important to investigate electron multiplication in xenon at pressures above 1 MPa in order to understand the basic properties of xenon as a radiation detection medium, not only for fundamental knowledge of the relevant physics processes, but also for the development of new detectors. Furthermore, electron multiplication was also observed in liquid xenon [10–12], and the difference in 𝛼 values in gas and liquid xenon was determined [10]. It would be also interesting to study the behavior of electron multiplication in environments ranging from high-pressure gas to liquid xenon. In the present study, we further investigated electron multiplication in high-pressure xenon following our preliminary paper [13] using

∗ Corresponding author at: Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan. E-mail address: [email protected] (H. Kusano).

https://doi.org/10.1016/j.nima.2019.05.016 Received 24 November 2018; Received in revised form 29 April 2019; Accepted 5 May 2019 Available online 11 May 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.

H. Kusano, J.A.M. Lopes and N. Hasebe

Nuclear Inst. and Methods in Physics Research, A 937 (2019) 53–58

resistance, yielding a decay time constant of 1 ms. Then, output signals from the CSA were fed to a shaping amplifier (CLEAR PULSE 4417) with the shaping time constant set to 5 μs for all measurements. The pulse height of output signals from the shaping amplifier were digitized using a multi-channel analyzer (MCA) (Labo 2100C/MCA). The induced charge at the anode was derived using pulses of known amplitude from a precision pulse generator (ORTEC 419) and a calibrated charge terminator as described below.

Fig. 1. Schematic drawing of the cylindrical proportional counter used for experiments.

2.2. Determination of the electron multiplication factor a cylindrical PC filled with pure xenon gas. In particular, the first Townsend ionization coefficient was measured up to 3.0 MPa, which extended the applicable range compared to previous studies. The experimental and data analysis methods are summarized in Section 2, and the electron multiplication factor, first Townsend ionization coefficient, and energy resolution results are presented and discussed in Section 3. 2. Experimental method

The electron multiplication factor is defined as the ratio of the total number of electrons collected in the anode to the number of initial electrons produced by the ionizing radiation. In the present work, the electron multiplication factor was determined using the so-called pulse matching method. The relationship between the induced charge and MCA channel was calibrated using the pulses of known amplitude produced by the pulse generator. Then, the electron multiplication factor 𝑀 can be calculated using the following equation:

2.1. Experimental setup

𝑀=

This investigation was carried out using a cylindrical PC, as shown in Fig. 1. The PC had an internal diameter of 30 mm, a length of 363 mm, and a wall thickness of 5 mm. The PC was made of stainless steel without radiation windows such that it could maintain high pressure. A gold-plated tungsten wire with a nominal diameter of 10 μm was used as an anode, which was soldered on feedthroughs welded at the both ends of the PC. To accurately evaluate the electric field, the anode wire diameter was measured as 10.3 ± 0.16 μm by a scanning electron microscope. The anode wire was connected to a high voltage power supply (CAEN N471), whereas the wall of the PC was grounded. A 133 Ba 𝛾-ray source was placed on the wall at the center of PC. Before the experiment, the PC and gas system were evacuated during baking at a temperature of 120 ◦ C for more than 100 h. The vacuum reached approximately 3 × 10−5 Pa, and the outgassing rate in the PC was less than 3×10−6 Pa/s. Xenon gas was purified continuously for 72 h in a tower of barium–titanium getters held at 600 ◦ C [11] before filling. The purity of xenon was checked by measuring the lifetime of liberated electrons [14]. The electron lifetime was measured using a parallel plate ionization chamber, in which a 241 Am 𝛼-particle source was installed. This apparatus is described in detail in a previous paper [15]. The electron lifetime was determined by analyzing the shape of pulses from a charge-sensitive preamplifier induced by drifting electrons. In this investigation, the electron lifetime was estimated to be longer than 1 ms at a pressure of 3.0 MPa. In contrast, the electron drift time in the PC from the cathode to the anode was estimated to be shorter than 20 μs at that pressure. Thus, the electron lifetime in purified xenon was sufficiently long, which means that the electron attachment due to electronegative impurities was negligible in this experiment. The impurity level is expected to be less than the order of ppb in oxygen equivalent, which is typically achievable with the chemical purification method such as the getter system used in this work [14,16]. The PC was filled with xenon at different pressures of 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 MPa to observe electron multiplication. The pressure was measured using a Bourdon gauge with an accuracy of ±0.0525 MPa. All measurements were carried out at room temperature (298 ± 1 K). The corresponding number density values of xenon for each pressure were (1.26, 2.58, 3.96, 5.43, 6.93, and 8.68) ×1020 cm−3 , respectively, which were derived from the van der Waals equation of state. The van der Waals constants are 𝑎 = 0.4192 Pa m6 /mol2 and 𝑏 = 5.16 × 10−5 m3 /mol for xenon gas [17]. The uncertainty in the xenon number density was evaluated from the uncertainty in pressure as the temperature uncertainty has a negligible contribution. Signals from the anode were fed to a charge-sensitive preamplifier (CSA) with a 2 pF feedback capacitance and a 500 MΩ feedback

where 𝑄, 𝑒, 𝐸𝛾 , and 𝑊 are the total induced charge, elementary electric charge, 𝛾-ray energy, and 𝑊 -value, respectively. The 𝑊 -value is defined as the average energy expended per electron–ion pair, and was assumed to be 21.9 eV [18]. Determining the electron multiplication factor with the pulse matching method requires accounting for the difference in pulse rise times between signals from the PC and pulses from the pulse generator. The pulse height attenuation of the cylindrical PC signals due to ballistic deficit after pulse shaping was studied previously [19–22]. The total induced charge corresponding to MCA channel 𝑚 can be calculated using the following expression [23]:

𝑄 , 𝑒𝐸𝛾 ∕𝑊

𝑄 = 𝐶0 𝑉 0

𝜁0 𝑚 , 𝜁 𝑚0

(1)

(2)

where 𝐶0 , 𝑉0 , and 𝑚0 are the input capacitance to the CSA from the pulse generator, the pulse amplitude from the pulse generator, and the corresponding MCA channel, respectively. In addition, the factors 𝜁 and 𝜁0 denote the attenuation coefficients of pulses from the PC and from the pulse generator, respectively. The attenuation coefficients were calculated in the same way, as shown in Ref. [21]. Because the pulse rise time from a cylindrical PC mainly depends on the motion of positive ions, the positive ion mobility is required to estimate the factor 𝜁. The ion mobility 𝜇 is given by 𝑁0 , (3) 𝑁 where 𝑆 is the reduced electric field 𝐸∕𝑁, defined as the electric field normalized by the number density of gas molecules. The units of 𝑆 are in Td, where 1 Td = 10−17 V cm2 . 𝜇0 (𝑆) is the reduced mobility corresponding to the standard number density 𝑁0 = 2.687 × 1019 cm−3 . In this work, experimental 𝜇0 data for Xe+ /Xe+ ions in xenon [24] was 2 3 + used because molecular ions of Xe+ and Xe would instantly form in 2 3 xenon from Xe+ ions above 1 atm [25]. Although the mobility of xenon ions was not studied at high-pressures, the relationship in Eq. (3) was assumed to apply to the investigated pressure range. As a result, the correction factors 𝜁0 ∕𝜁 were calculated to be approximately 2.1–2.4. 𝜇(𝑆) = 𝜇0 (𝑆)

2.3. Determination of the first Townsend ionization coefficient In cylindrical PCs, the relationship between the electron multiplication factor and the first Townsend ionization coefficient is 𝑟c

ln 𝑀 =

∫𝑎

𝛼 𝑑𝑟,

(4)

where 𝑎, 𝑟c , and 𝑟 denote the anode radius, the critical radius where electron multiplication begins, and the radial distance from the central axis. In many previous studies, the first Townsend ionization coefficient 54

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Nuclear Inst. and Methods in Physics Research, A 937 (2019) 53–58

was considered to depend only on the reduced electric field. The reduced electric field in cylindrical PCs is given by 𝑆(𝑟) = 𝐸(𝑟)∕𝑁 =

𝑉a , 𝑁𝑟 ln(𝑏∕𝑎)

(5)

where 𝑉a is the anode voltage and 𝑏 is the cathode radius. Then, the electron multiplication factor can be obtained as a function of the reduced electric field from Eqs. (4) and (5) as follows [26]: 𝑆a 𝛼(𝑆) ln 𝑀 = 𝑑𝑆, 𝑁𝑎𝑆a ∫𝑆c 𝑁𝑆 2

(6)

where 𝑆a and 𝑆c are the values of 𝑆 at the anode surface and critical radius, respectively. Despite many experimental and theoretical studies, the dependence of 𝛼 on 𝑆 in cylindrical PCs is still not fully understood. Various expressions for 𝛼 were proposed, e.g., as listed in Ref. [27]. The original Townsend formula was used here, which is given by 𝛼∕𝑁 = 𝐴 exp(−𝐵∕𝑆),

Fig. 2. Typical pulse height distribution for the anode voltage is 3.08 kV.

(7)

133

Ba. The xenon pressure is 1.5 MPa and

where 𝐴 and 𝐵 are constants. Eq. (7) is derived based on the general theory of electron motion in gases under a uniform electric field. It was suggested [28] that Eq. (7) can be used as a standard description for electron multiplication in cylindrical PCs. The following expression was derived from Eqs. (6) and (7): ln 𝑀 𝐴 = [exp(−𝐵∕𝑆a ) − exp(−𝐵∕𝑆c )] 𝑁𝑎𝑆a 𝐵 𝐴 exp(−𝐵∕𝑆a ). (8) ≈ 𝐵 The approximation is based on the assumption that 𝑆a ≫ 𝑆c , which is normally valid in cylindrical PCs. The constants 𝐴 and 𝐵 can be derived from 𝑀 and Eq. (8). Then, the first Townsend ionization coefficient is obtained from Eq. (7) using these derived constants. As described above, Eq. (7) was obtained under the assumption of a uniform electric field. The constants 𝐴 and 𝐵 in this expression depend only on the gaseous species. However, in nonuniform electric field conditions, such as those in cylindrical PCs, the behavior of electrons differs from that in a uniform electric field [29–32]. We assumed the constants 𝐴 and 𝐵 to also depend on the gaseous density as proposed for the nonuniform electric field conditions [30], thus these constants must be determined for each pressure value.

Fig. 3. Electron multiplication factor 𝑀 as a function of the anode voltage 𝑉a for pressures of 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 MPa.

factors of 100 and 1000. Both plots were obtained by applying a cubic spline interpolation to the 𝑀 vs. 𝑉a curves in Fig. 3. The solid lines in Fig. 4 show the results when the function 𝑐1 𝑁 𝑐2 was fit to the data, where 𝑐1 and 𝑐2 are fitting parameters. The fitted exponent 𝑐2 is 0.498 (𝑀 = 100) and 0.469 (𝑀 = 1000) for 𝑉𝑎 , and −0.502 (𝑀 = 100) and −0.531 (𝑀 = 1000) for 𝑆𝑎 . Therefore, 𝑉a and 𝑆a are approximately proportional to 𝑁 1∕2 and 𝑁 −1∕2 , respectively. One can conclude that the reduced electric field at the anode surface decreases with increasing density for a given electron multiplication factor.

3. Results and discussion A typical pulse height distribution obtained with 133 Ba is shown in Fig. 2, which was measured at a pressure of 1.5 MPa, 3.08 kV anode voltage, and data acquisition time of 1000 s. The photopeak (81.0 keV) and its X-ray escape peak (51.3 keV) are visible in the spectrum. The continuum is primarily due to Compton scattering of the 356 and 303 keV 133 Ba 𝛾 rays. The electron multiplication factor and energy resolution were derived by fitting the 81.0 keV photopeak to a Gaussian function superimposed on a linear continuum background. It was also confirmed that the electron multiplication factor derived from the X-ray escape peak was consistent with that derived from the photopeak.

3.2. First Townsend ionization coefficient The first Townsend ionization coefficient was determined from the electron multiplication factor results. Fig. 5 shows the density-reduced first Townsend ionization coefficient 𝛼∕𝑁 as a function of the reduced electric field at the anode surface 𝑆a . The uncertainty in 𝑆a is derived from the uncertainties in the anode voltage, anode and cathode radii, and gaseous density. The uncertainty in 𝛼∕𝑁 can be derived from the uncertainties in 𝑆a and the constants 𝐴 and 𝐵. The relatively large uncertainties, particularly at 0.5 MPa, are primarily due to the uncertainty in the gaseous density, which is derived from the uncertainty in pressure measurements. In Fig. 5, the experimental results from Kruithof [6] and Sakurai et al. [9] are also shown. The experiment of Kruithof was carried out in a parallel plate chamber at pressures ranging from 0.28–165 Torr (a number density of ≈ 9.9 × 1015 –5.8 × 1018 cm−3 ), and the experiment of Sakurai et al. was carried out in a cylindrical PC at

3.1. Electron multiplication factor Fig. 3 shows the electron multiplication factor 𝑀 derived from Eqs. (1) and (2) as a function of the anode voltage 𝑉a for each pressure. The minimum and maximum 𝑀 values for each pressure were found to be approximately 15 and 2400, respectively. The slope of the 𝑀 vs. 𝑉a curves decrease with pressure, which illustrates the dependence of the first Townsend ionization coefficient on the electric field and pressure. One can also see that the anode voltage required to obtain a specific multiplication factor is not proportional to the pressure in the PC. Fig. 4 shows the density dependence of the anode voltage 𝑉a and the reduced electric field at the anode surface 𝑆a at electron multiplication 55

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Nuclear Inst. and Methods in Physics Research, A 937 (2019) 53–58

Fig. 4. The anode voltage 𝑉a (left) and the reduced electric field at the anode surface 𝑆a (right) as a function of xenon density 𝑁 for an electron multiplication factor 𝑀 of 100 and 1000. Solid lines show the fitted curves to the data.

Fig. 6. Ratio of the density-reduced first Townsend ionization coefficient 𝛼∕𝑁 obtained in this work to the results of Kruithof [6] as a function of the reduced electric field at the anode surface 𝑆a . Fig. 5. Density-reduced first Townsend ionization coefficient 𝛼∕𝑁 as a function of the reduced electric field at the anode surface 𝑆a . The solid and dashed lines show the previous experimental results obtained by Kruithof [6] and Sakurai et al. [9], respectively.

𝛼∕𝑁 in this work to the results of Kruithof. The ratio increases with increasing pressure, which clearly indicates the density dependence of the first Townsend ionization coefficient. Fig. 7 shows the ionization coefficient 𝜂 as a function of the reduced electric field at the anode surface 𝑆a . The ionization coefficient 𝜂 is defined as the average number of ion pairs created by an electron per volt, which is expressed as

pressures ranging from 1–10 atm (a number density of ≈ 2.5 × 1019 – 2.6 × 1020 cm−3 ). Although not shown in the figure, 𝛼∕𝑁 obtained from other experiments using parallel electrodes [7,8] is slightly smaller than the results reported by Kruithof. The 𝛼∕𝑁 reported here are consistent with the results from Sakurai et al. at 1.0 MPa pressure, but larger than that of Kruithof. One possible reason for the difference may be attributed to the purity of the xenon gas used in the different experiments. In this work, the xenon gas was purified as described in Section 2.1. Sakurai et al. also used pure xenon gas with less than 1 ppm of contamination, whereas Kruithof used xenon gas with up to 0.1% of contamination. Electronegative impurities cause signal loss due to electron attachment, which may explain the smaller value of 𝛼∕𝑁. In addition, 𝛼∕𝑁 would be affected by the different experimental conditions, namely the difference between the nonuniform electric field with high pressure and the uniform electric field with low pressure. It was noted that the spiral motion of electrons around the anode affects the ionization coefficient in a nonuniform electric field, such as in a PC [29,31]. This effect could be responsible for the large 𝛼∕𝑁 values obtained in this work compared to those obtained with a uniform electric field. As shown in Fig. 5, electron multiplication at high pressure occurs at a lower value of 𝑆a . Furthermore, the 𝛼∕𝑁 vs. 𝑆a curve in this work seems to be represented by multiple curves. Fig. 6 shows the ratio of

𝜂 = 𝛼∕𝐸 =

𝛼∕𝑁 . 𝐸∕𝑁

(9)

The results of Kruithof [6] are also shown. Derenzo et al. [10] also found 𝜂 to range from (0.12–2.24) ×10−2 V−1 for 𝑆 ranging from 2.86– 14.3 Td in liquid xenon. As shown in their work, the 𝜂 vs. 𝑆 curve in liquid xenon has a shape similar to that in gaseous xenon [6], but the range of 𝑆 values is smaller than that in gaseous xenon by a factor of approximately 27. Thus, electron multiplication in liquid xenon occurs at lower 𝑆 values compared to gaseous xenon. The 𝜂 results presented here would appear to be shifted with increasing pressure toward values that one would measure in liquid xenon. It was suggested that there are various density effects on the first Townsend ionization coefficient in liquid xenon [33]. Also, the density dependence of 𝑊 -value was investigated in high-pressure xenon [34]. As discussed in the previous studies, the ionization process in xenon depends on the gaseous density in the high-pressure region. Therefore, the density dependence of 𝛼∕𝑁 and 𝜂 obtained in this study can be attributed to the density effect. 56

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Nuclear Inst. and Methods in Physics Research, A 937 (2019) 53–58

Fig. 7. Ionization coefficient 𝜂 as a function of the reduced electric field at the anode surface 𝑆a . The solid line shows the previous experimental results from Kruithof [6].

Fig. 10. Energy resolution of the 81.0 keV photopeak as a function of the reduced electric field at the anode surface 𝑆a .

The energy resolution is shown as a function of 𝑀 for each pressure value in Fig. 8. The deterioration of the energy resolution in the lower 𝑀 region is due to electronic noise and primary electron–ion recombination. The contribution of the former effect is approximately constant while that of the latter effect becomes large with increasing pressure, as described later. Consequently, the intermediate 𝑀 region yielding an approximately constant energy resolution reduces as pressure increases, as shown in Fig. 8. In contrast, the deterioration of the energy resolution in the higher 𝑀 region is due to field distortion caused by the space charge of positive xenon ions and the large number of photons emitted by excited xenon molecules. The latter effect is presumably dominant because the larger electron multiplication factor was measured with superior energy resolution in the case of xenon doped with a suitable amount of quenching gases at pressures near 1 atm [35,36]. The energy resolutions at 𝑀 = 100 and 1000 shown in Fig. 9 were determined by applying a cubic spline interpolation to the data in Fig. 8. The energy resolution deteriorates with increasing xenon density, particularly when 𝑀 = 100. The density dependence of the energy resolution was measured in several studies [9,37–40]. Results from these studies suggest several causes of deterioration, such as electronegative impurities, nonuniformity of the anode wire diameter, and some deviation in the reduced electric field in which the PC was operated. The impurity effect was avoided in this experiment as described in Section 2.1. The nonuniformity of the anode wire diameter creates fluctuations in the electron multiplication factor because 𝑆 depends on 𝑎, as defined in Eq. (5). Assuming that electrons are collected at a point on the anode wire, the variations of 𝑀 corresponding to the variation of anode wire diameter used in this study were estimated to be 6.6%, 7.8%, 8.9%, 10%, 11%, and 12%, respectively, when 𝑀 = 100 for each pressure. In addition, the size of the electron swarms in the multiplication region becomes smaller as gaseous density increases. This fact results from a reduction in the range of primary photoelectrons, as well as transverse diffusion of electrons in high-pressure xenon. Therefore, the energy resolution is more sensitive to the anode nonuniformity at high pressure as electron swarms are collected in an increasingly narrower area of the anode wire. Another possible cause for the deterioration of the energy resolution is that the PC operates at increasingly lower reduced electric field values as pressure increases, as clearly shown in Fig. 10. This fact results in increased primary electron–ion recombination and excitation collisions of electrons with atoms. The recombination rate of the primary electron–ion pairs will become higher at lower electric field and higher gaseous density. It is reasonable to expect that the variation in the recombination fraction of primary electron–ion pairs, particularly those generated near the cathode, will cause fluctuations

Fig. 8. Energy resolution of the 81.0 keV photopeak as a function of the electron multiplication factor 𝑀.

Fig. 9. Energy resolution of the 81.0 keV photopeak as a function of xenon density 𝑁 for electron multiplication factors of 100 and 1000.

3.3. Energy resolution Figs. 8–10 show the energy resolution of the 81.0 keV photopeak as functions of the electron multiplication factor 𝑀, xenon density 𝑁, and reduced electric field at the anode surface 𝑆a , respectively. The energy resolution is expressed in terms of the full width at half maximum (FWHM) of the 81.0 keV photopeak. 57

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Nuclear Inst. and Methods in Physics Research, A 937 (2019) 53–58

in the charge induced at the anode. The latter effect will complicate the electron multiplication process, as pointed out in several prior studies [9,38,39]. Several different de-excitation channels occur after excitation collisions, such as photon de-excitation, Penning ionization between excited atoms and/or excited dimers, and stepwise ionization, which is electron-impact ionization with excited atoms or excited dimers. Penning ionization includes associative ionization, known as the Hornbeck–Molnar effect [41]. The deterioration of the energy resolution with increasing gaseous density could be attributed in part to stronger fluctuations in the above processes occurring during electron multiplication. Compared to xenon-based gas mixtures [40], higher energy resolution was obtained for pure xenon in the high-pressure region in this work. The energy resolution at 0.5 MPa was reported to be 9.2% at 59.5 keV for Xe + CH4 (98:2) gas mixtures. In the case of higher pressures, the energy resolution was reported to be 13.5% at 81.0 keV for Xe + Ar + CH4 (90:8:2) gas mixtures at 1.5 MPa, and 28.2% at 59.5 keV for Xe + C2 H4 (98:2) gas mixtures at 2.5 MPa. The energy resolution in pure xenon obtained in this investigation is better than the above results involving gas mixtures, even once the difference in the primary photon energy is considered. Therefore, pure xenon would be suitable for electron multiplication at high pressure, particularly when the electron multiplication factor is less than 1000.

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