ࡱ> G bjbjَ ]a]$@@@@PlT@l$(LLLLLL;'5$!#YLLLLLYLLlL&LL@@LtLPr_ӛ@@rionization yield formation in argon-isobutane mixtures as measured by a proportional-counter method Ines KRAJCAR BRONIC1, Bernd GROSSWENDT2 1 Rudjer Boskovic Institute, P.O.Box 1016, 10001 Zagreb, CROATIA 2Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, GERMANY C-768 revised version address for correspondence (since Feb. 1, 1996): Dr. Ines Krajcar Bronic Abt. 6.11 Physikalisch-Technische Bundesanstalt Bundesallee 100 38116 BRAUNSCHWEIG GERMANY phone: +49 531 592 6252 fax: +49 531 592 6015 e-mail: KRAJCAR@OLIMP.IRB.HR or: broni616@n8402.bs.ptb.de ionization yield formation in argon-isobutane mixtures as measured by a proportional-counter method Ines KRAJCAR BRONIC1, Bernd GROSSWENDT2 1 Rudjer Boskovic Institute, P.O.Box 1016, 10001 Zagreb, CROATIA 2Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, GERMANY Abstract By using the proportional-counter method, mean ionization yields produced by 5.9keV photons in argon-isobutane mixtures were measured as a function of the mixture composition, total gas pressure, and gas gains between about 103 and 2(104. It was found that the yield for a given mixture is gain dependent: an initial increase of the yield at low gas gains is followed by almost constant yield values for gains between about 2(103 and 8(103; at still higher gains the yield decreases. Moreover it was observed that the ionization yield at constant gas gain depends on the total pressure of the gas mixture. This dependence leads to a rather clear correlation between yields and isobutane partial pressure. To explain the measurements a simple model of the mean energy W per ion-pair formed in Penning gas mixtures is also given. A direct comparison of calculated W values and measured data showed that the results of our proportional-counter experiments performed at high gas gains were strongly influenced by secondary effects induced during the formation of avalanches in the counter when using low isobutane partial pressures. Therefore, Penning mixtures with incomplete quenching should not be used as a counting gas in proportional counters if both high gas gain and good energy resolution are required, as for instance, in high-resolution low-energy (sub-keV) X-ray spectroscopy. 1. Introduction The complete understanding of ionization yields produced by ionizing radiation in gas-filled detectors, such as ionization chambers and proportional counters, is of main importance for their application in radiation fields because, as far as the measurement of energy deposited is concerned, a conversion of ionization yields into absorbed energy is necessary. The conversion coefficient commonly used for this purpose is the so-called W value, which is defined as the mean energy required per ion pair formed upon the complete slowing-down of ionizing particles in matter and depends on the particle type, on its energy and is a characteristic quantity of the stopping gas. If N(T0) is the mean number of ion pairs produced in a gas during the complete dissipation of the energy T0 of an ionizing particle, the corresponding W value is given by Eq.(1).  EMBED Equation.2  (1) Because of its definition, the applicability of W must be carefully checked in practice with respect to the required complete slow-down of the primary particles and of all their secondaries. The fulfillment of this requirement depends on particle ranges, on the dimensions of the sensitive volume of a detector, and on the properties of the used stopping gas. The applicability of W for converting ionization yields into absorbed energy is to be questioned, for instance, if UV photons could be produced during particle degradation because such photons, if not completely absorbed within the sensitive gas volume, could cause secondary electrons in its surroundings and therefore additional ion pairs not contained in the W value for the stopping gas. UV photons are usually produced in rare gases, and a certain amount of a polyatomic gas (quenching gas) should be added to the rare gas to quench (absorb) the UV photons. In this case the applicability of W may depend on the composition of a gas mixture and also on its total pressure. This fact is of particular importance from the practical point of view since a variety of different regular and irregular gas mixtures are commonly used in proportional counter experiments. Regular gas mixtures are those mixtures in which the total number of ion pairs (Nreg) formed by an ionizing particle is a weighted sum of the number Ni of ion pairs produced in each gas component of type i. For binary gas mixtures Nreg is given by Eq.(2).  EMBED Equation.2  (2) Here, z is the energy partition parameter. It is a function of the mixture composition and depends on the approach used to describe the energy partition between the gas components [1-5]. Several models for W value calculation in regular mixtures were recently summarized and analyzed [6]. According to the conclusions in Ref. [6] we will apply a model of Inokuti and Eggarter [5] which gives the following expression for z:  EMBED Equation.2  (3) where si, Ci, and Wi, i=1,2, are the total ionization cross section, the concentration fraction, and the W value of the component i, respectively. Irregular gas mixtures are those in which the energy spent on excitation of one gas component can be efficiently transferred to the other gas producing additional new ion pairs [1]. The total number of ion pairs is higher than it would be without the energy transfer, and consequently the W value is smaller. The models for regular mixtures cannot be applied any more because they do not take into account the additional ion pairs. The energy transfer is possible in a mixture of a rare gas with an admixing gas which may be another (heavier) rare gas (for He and Ne as the main gases), or, as in most cases, a molecular gas. The ionization potential of the admixed gas must be lower than the metastable state of the main rare gas. The effect of additional ionization of the admixture was first discovered in neon-argon mixtures by Penning [7,8] and is called the Penning effect. The effect of lower W values for certain concentration ratios in the mixtures due to the Penning effect is usually called the Jesse effect [9]. It should be noted that smaller W values were observed also in mixtures in which the admixture had an ionization potential above the metastable state, but still lower than a resonant state of the main rare gas [2,10]. In such a case we talk about the non-metastable Penning effect, as opposed to the formerly mentioned metastable Penning effect. The lowest W value in a gas mixture with Penning effect is given in ref. [11] by  EMBED Equation.2  (4) where Wreg=T0/Nreg is the W value for the regular mixture neglecting the Penning effect, and Nreg is defined in Eq.(2). N*/N is the ratio of the number of excited states and the number of ion pairs in the main rare gas. In Eq.(4) h is the ionization efficiency of the admixed molecules. Its value is 1 for a rare-gas admixture, and h<1 for molecular gases which after absorption of energy higher than the ionization energy may either dissociate or autoionize [12]. It was found experimentally (by measuring ionization produced by alpha particles in ionization chambers) [9,10] that the W value has a minimum, given approximately by Eq.(4), for a certain concentration fraction of the admixture. In mixtures with the metastable Penning effect these concentration fractions are of the order of 0.1 - 1%, and the W value is lowered by up to 20%. In mixtures with the non-metastable Penning effect [2,10] the changes in W value (the Jesse effect) are much smaller (not more than 5%) and the required concentration fraction of the admixture is higher (3-5%). The experiment by Parks et al. [13] showed for the first time that the Jesse effect depends on the total pressure of the mixture. Jarvinen and Sipila [14] observed a small increase of W value for several irregular mixtures with increasing total pressure and pointed out that this effect could be explained by a pressure dependence of the destruction of metastable rare gas states. Using the proportional-counter method, Krajcar-Bronic et al. [15] found that in argon - butane mixtures W value depends on the partial pressure of butane. Excepting these (fragmentary) experimental results, no systematic study of W value in Penning gas mixtures at various pressures and over a wide range of mixture compositions exists. Motivated by this lack of data and by the practical importance of irregular gas mixtures for proportional-counter applications, it was the aim of the present work to study the pressure dependence of ionization yield formation in Penning gas mixtures in more detail. This was done in two parts. In the first parts we developed a simple model with respect to the pressure dependence of W in argon-based Penning gas mixtures taking into account the most important energy-transfer interaction mechanisms which influence the ionization yield formation. This model can simply be applied also to other irregular mixtures consisting of rare gases and admixtures of molecular gases. In the second part we measured the ionization yield produced by 5.89 keV photons within a proportional counter filled with argon-isobutane mixtures of different composition and total pressure. The reason of using such mixtures was the fact that the Penning effect in argon-isobutane mixtures is possible since the ionization potential of isobutane (10.67 eV) is lower than the excitation energies of metastable argon states (11.54 eV and 11.72 eV). The measurement should check the applicability of using the proportional-counter method for determining W values for soft X-rays in irregular gas mixtures and, vice-versa, to check the applicability of W values for converting measured ionization yields into energy deposited when using proportional counters. This part of the present paper was one aspect of a comprehensive investigation of various properties of argon - isobutane mixtures in a proportional counter, which included the gas gain determination, the study of the variance of the gas amplification (single electron spectra), and the energy resolution [16]. 2. Model of W in irregular mixtures The processes occurring in Ar - molecular gas mixtures after irradiation by electrons (or, in general, by any ionizing radiation) are the following: Ar + e ( Ar+ + e + eNAr(5a)M + e ( M+ + e + eNM(5b)Ar + e ( Ar*N*(5c)Ar* + Ar + Ar ( Ar2* + Ar km(5d)Ar* + M ( (Ar M)(kQ(5e)(ArM)( ( Ar + M(fragments)1 - h(5f)(ArM)( ( Ar + M+ + eh(5g)where M represents the molecule of the admixed gas with an ionization potential below the metastable state of Ar. Other symbols are defined below. The first two processes (5a) and (5b) represent the direct ionization of an Ar atom or a molecule M. The number of Ar ions formed by process (5a) is NAr, and that of molecular ions formed in process (5b) is NM. The total number of ions formed in this first step is given by Eq.(2) and would lead to the W for regular mixtures, if there were no additional processes of electron formation. The process (5c) represents an excitation of argon to a metastable or any other excited state, and the total number of excited states is N*. The ratio N*/NAr of the number of excited states and the number of argon ions is about 0.5 according to Platzman [17]. It is clear that not all the argon atoms are excited to the same excitation level and the distribution of excitations is determined by the distribution of the oscillator strengths. However, higher excited states are quickly deexcited (by emission of radiation) to either the lowest metastable states or the lowest resonant states. Due to the trapping of the resonant radiation, the resonant states, usually very short-living, are effectively long-living states [18]. In further discussion it will therefore be assumed that (i) all the excited levels come from the first excited configuration of argon (resonant states 1P1, 3P1, metastable states 3P0, 3P2), (ii) they are all considered to be long-living ("metastable"), and (iii) no difference among them (in ionization efficiency h, rate constants for various processes, etc.) will be taken into account. Practically, all four excited states from the first excited configuration are replaced by a single representative level. This assumption is justified by other investigations, see for example [19,20]. Argon excited/metastable states Ar* may be destructed by several processes [21]. Under conditions of relatively high pressure the diffusion and the radiative decay in two-body collisions may be neglected, and the two most important destruction processes are the formation of diatomic molecules in three-body collisions (5d) and collisions of the second kind with admixture molecules (5e). In previous studies of proportional counters filled with Penning mixtures no attention has been paid to reaction (5d). However, studies of VUV emission of rare gases and gas mixtures showed the importance of formation of excited rare gas molecules [22] and the effects of some quenching reactions other than the Penning ionization on the proportional counter operation [20]. The process (5d) is a three-body destruction of argon metastables in which argon excited molecules (eximers) are formed with a rate constant km. The reaction rate constant was measured by [18,20,22,23]. The Ar2* molecule decays within 3.5ms emitting a radiation energy of 10eV, which is not sufficient to ionize most of the admixed molecules. The formation of eximers, thus, leads to the loss of the energy in non-ionizing processes. Since it is a three-body process, it is proportional to the square of the number of argon atoms, and therefore also to the square of pressure. Experiments showed that the intensity of the light emitted after a radiative decay of rare gas eximers increases with increasing gas pressure [20]. In a collision of Ar* with an admixture (quenching) molecule M, which occurs with a rate constant kQ, the intermediate neutral superexcited molecular state (ArM)( is formed (process 5e). Superexcited states were first introduced by Platzman [24], and they represent highly excited electronic states (above the ionization threshold). Superexcited states have an important role as reaction intermediates in a variety of collision processes [25], among which is also the Penning process. As the destruction processes of Ar* states, (5d) and (5e), occur in competition, the total lifetime t of Ar* is given by:  EMBED Equation.2  (6) where p and n represent the partial pressure and the number density of atoms which are given as subscripts. Which of these two equivalent equations will be used depends on the units in which the rate constants are given. It is important to note that the amount of argon atoms in Eq.(6) is squared. The probability Ps of formation of a superexcited state is given as the ratio of the rate of the process (5e) and the total destruction rate 1/t:  EMBED Equation.2  (7) This probability was discussed in terms of two competitive processes for the first time in an early study of Ne-Ar mixtures, by Penning and Kruithoff [7,8]. The decay of the superexcited quazimolecule (ArM)( may go through dissociation into neutral fragments (process 5f), with the probability 1-h, or through Penning ionization (process 5g) with the probability h, the ionization efficiency of the molecular admixture. Electrons formed in this process could represent additional electrons formed by incident electrons in Penning gas mixtures. For mixtures well-suited for application in proportional counters it is desirable to have a probability of Penning ionization (5g) as high as possible and at the same time a low probability of eximer formation (5d). Under these conditions, the highest number of electrons is formed in the gas mixture by an incident ionizing particle. We are interested to determine the total number of electrons formed at the end of the chain of various processes given in (5). The probability of formation of an additional electron in (5g), Padd, can be calculated as the product of the probability (N*/NAr) for formation of an excited argon atom, the probability Ps for a formation of a superexcited molecule (Ar M)(, and the ionization efficiency h:  EMBED Equation.2  (8) The first term (the ionization efficiency) and the last term (the ratio of the number of argon excited atoms to the number of argon ions) are not pressure dependent. The second term (representing the formation of eximers) introduces an absolute number density of atoms, i.e., the absolute pressure. This relation shows that at higher pressures the number of additional ion pairs will be lower because of the larger frequency of eximer formation. Finally, the total number of ion pairs produced in a sequence of reactions (5) is a sum of the ion pairs produced in a mixture assuming it is a regular one, and an additional number of ions determined by Padd:  EMBED Equation.2  (9) The W value for an irregular mixture is thus given by Eq.(10).  EMBED Equation.2  (10) Comparison of Eq.(10) and Eq.(4) shows that Eq.(10), because of the factor Ps, takes explicitly into account the pressure dependence of destruction of metastable rare gas states: the higher the pressure, the lower the Ps, and the lower the Ps, the higher the Wirr, even for the same concentration fraction of the admixture. 2.1. Results of the model calculations The following values may be inserted in Eq.(10): h=0.4 [12], N*/NAr=0.5 [16], kQ=9(10-10cm3s-1 = 2.4(107mbar-1s-1 [average value from 18-20, 22, 23, 26-28] and km= 10mbar-2s-1 [29]. Fig. 1 shows calculated values of Wirr as a function of isobutane concentration fraction and the total pressure as a parameter. For pressures below 1bar the value of Padd only slightly depends on the pressure because of the great difference in magnitudes of the rate constants kQ and km. The differences for various total pressures of 1bar or lower are seen at low concentration fractions of isobutane, <10%. As the total pressure increases, the minimum in W becomes shallower and moves to a higher concentration fraction of the admixture. For comparison, the W values in Ar-isobutane regular mixture (i.e., neglecting the Penning effect) are also shown. Here, the model of Inokuti and Eggarter [5] has been applied, with the following input values: W(Ar)= 26.3eV [30], W(i-C4H10)=23.4eV [15,30], si(C4H10)/si(Ar) = 5.2 [5,31]. 3. Experimental The proportional counter method of ionization yield measurement follows that developed by Srdoc [32,33] and Srdoc and Clark [34] for determining W values. It consists of the measurement of pulse height distributions (spectra) produced by single electrons, and by low-energy X rays under the same experimental conditions. The experimental setup, schematically presented in Fig. 2, consists of a proportional counter with the charge sensitive preamplifier mounted directly to the anode wire, an amplifier, a multichannel analyzer connected with an on-line VAX computer, and a high voltage supply. The inner diameter of the stainless steel counter is 5cm, the length is 15cm, and it is placed in a copper shield, 8cm in diameter. The anode is a stainless steel wire of 25mm in diameter. The 5.89 keV X rays from the 55Fe source passed through a collimator and entered the active volume of the counter through the Be window 5mm thick. Single electrons were released by UV radiation from a 28nm thick semitransparent Al film deposited on the quartz rod. The Al film was aligned with the cathode. As the source of UV radiation, a lamp emitting mostly the line 253.7nm (equivalent to 4.9eV) was used. The photoelectrons thus produced had initial energies below 1eV and were incapable of producing immediate ionization. Gas mixtures of argon and isobutane were prepared by mixing the gases in the proportional counter. Several total pressures in the range from 100 to 900mbar were chosen. At each pressure several mixtures of various concentration ratios (between 2.2% and 30% of isobutane) were prepared. To give an impression of the measured data, Figures 3a and 3b show pulse-height distributions of 5.89 keV photons (Fe) and of single electrons (SE) in argon-isobutane mixtures. Each single electron (SE) spectrum was fitted with a Polya distribution of the form P(X) = aXbexp(-cX) [33], where X represents the channel number of a measured pulse-height distribution. The mean pulse height XSE can be determined from the parameters of P(X) according to XSE = (1+b)/c. The ionization yield, defined as the mean number Nion of ionizations indicated by the proportional counter per 5.89 keV photon, can now be calculated from the mean pulse height XSE of the SE spectrum and of the pulse height XFe of the peak of 55Fe spectrum using Eq.(11).  EMBED Equation.2  (11) Here GSE and GFe are the electronic gains applied for measuring the SE and Fe spectra. Nion of Eq.(11) can be used to determine the W value according to Eq.(1) provided (i) that the proportional counter is operated in its strict proportional region, (ii) because of the definition of W values, that the total energy of the primary radiation is completely dissipated in the sensitive volume of the counter, and (iii) that there are no other processes producing additional electrons at walls or in the filling gas. If these requirements are not fulfilled, a gain dependence of Nion can be expected. In this case Nion can not be interpreted as the mean number of ionizations produced upon the complete particle slow down but only as a fictitious one which depends on the counter construction and on the operating conditions. Nevertheless, the measurement of Nion requires a high stability of the gas gain during independent recording of SE and Fe spectra. The uncertainty in Nion is given by the errors in the determination of the mean values of Fe and SE spectra. The position of the Fe peak could be determined very precisely, with uncertainty <0.3%. Special attention was paid to the calculation of the mean value of the single electron spectra, XSE, because the error in this mean value directly propagates into the error of Nion. The low-energy (left-hand side) of the SE spectrum is covered by the noise of the preamplifier and the amplifier system, and thus the lower bound of the region which is to be fitted has to be carefully chosen. This is specially important in mixtures containing low isobutane partial pressure with resulting single electron pulse-height distributions of shapes approaching that of an exponential distribution (Fig. 3b, curve SE-1092) [16]. A very good reproducibility, and thus lower errors, of single electron spectra taken under the same conditions were obtained if a SE spectrum had a peak (Fig. 3b, curves SE-831 and SE-1069). The uncertainty in determination of XSE ranged from (1.5% for pure isobutane and mixtures with partial pressure of isobutane >100 mbar, to (10% for mixtures with the lowest isobutane partial pressure. The overall estimated uncertainty of the measured ionization yield, taking into account possible small changes in gas pressure and mean gas amplification factor, is better than 2% for mixtures with sufficient amount of isobutane (>100mbar). The uncertainty increases as the amount of isobutane decreases, reaching (10% in mixtures containing the lowest amount of isobutane (10mbar). 4. Experimental results 4.1. Ionization yield as a function of gas gain Ionization yields were measured at various mean gas amplification factors (gas gains) in the range 900 - 2(104. At lower gains it was not possible to obtain single electron spectra significantly above the electronic noise to ensure satisfying fitting. The typical dependence of the yield Nion on the gas gain is shown in Figures 4a to 4c for pressures 100, 300 and 900mbar for several mixture compositions (concentration fraction of isobutane). In pure isobutane (Fig. 4b) and in mixtures of 20% and 30% of isobutane at 900mbar (Fig. 4c) Nion is constant (within experimental uncertainty) for gas gains up to about 8(103, indicating that charge collection in relatively low fields was complete. All other gas mixtures showed an increase of the yield at low gas gains, 900 - 2000, followed by relatively constant values up to gains between 7000 and 9000. At even higher gains in all gas mixtures a decrease of Nion is observed. 4.2. Ionization yield as a function of isobutane concentration fraction When comparing ionization yields in mixtures of the same isobutane concentration fraction at various total pressures, it is observed that Nion increases faster with the gas gain increase and attains higher values at intermediate gains for lower total pressure. As an example, Fig. 5 shows the dependence of Nion on the gas gain for 30% mixtures at three total pressures. The decrease of Nion with increasing gas gain starts at somewhat lower gains at higher pressure than at low pressures (gain (7(103 at 900 mbar, compared to gain (9(103 at 100 mbar). Since the yield is a function of gas gain for each mixture, its comparison in various mixtures should be performed at the same gain. Therefore, Figure 6 shows Nion at low gains (app. 103) and at intermediate gas gain ((5(103) as a function of isobutane concentration fraction. At low gas gain no significant difference of the measured values for different pressures is obtained, and Nion increases as the concentration fraction of isobutane decreases. At intermediate gains Nion also increases as the concentration fraction of isobutane decreases, but the rate of the increase depends on the total pressure. 4.3. Ionization yield as a function of isobutane partial pressure When mixtures of the same isobutane partial pressure are compared, it is observed for intermediate gas gains that the ionization yields at the same isobutane partial pressure (90, 60, 30, 20, 10 mbar) are almost independent of the total pressure. To demonstrate this fact, Figure 7 shows Nion as a function of the partial pressure at a low and in addition also at an intermediate gas gain; the data for different total pressures are characterized by different symbols. A more or less unambiguous linear correlation between yield values and the logarithm of the partial pressure of isobutane at intermediate gain is obtained. (The exception is 10% at 300 mbar mixture, which gave systematically lower values of Nion.) In mixtures with less than 100 mbar of isobutane the yields at a gas gain of (5(103 are significantly higher than those at a gain of (103. 5. Discussion The signals measured in our proportional-counter experiments can be assumed to be caused by a two-stage process. At first stage, the photons emitted by the 55Fe source transfer their total energy to the molecules of the counter gas mainly via photoelectric absorption thus producing photoelectrons and Auger electrons which are, because of their short ranges, completely slowed down in the filling gas by a series of excitation and ionization interactions. The resulting number of ion pairs per primary photon represents the ionization yield Nion to be measured. It can be unambiguously expressed by the W value of the filling gas, if the primary photon energy is completely dissipated in the sensitive volume of the proportional counter. At second stage, it can be assumed that the photon-induced primary electrons and all of their secondaries, after slowing down to low energies, are accelerated in the electric field of the proportional counter. They can therefore produce further ions and electrons the latter of which can also be accelerated in the electric field and cause a next generation of ion pairs as long as they reach the anode wire of the counter. The electron avalanche formed in this way determines the measured pulse height, which is proportional to the ionization yield produced in the counter gas at first stage, provided that the counter is operated in its strictly proportional region. This restriction means that the mean gas amplification factor (gas gain) is an exponential function of the applied high voltage. If this requirement is fulfilled and in addition also that of a complete dissipation of the primary photon energy in the counter gas (see above), the pulse height at the peak of the measured 55Fe spectra should be directly proportional to the reciprocal of the W value for the counter gas used. Assuming these requirements to be fulfilled and having in mind the results of our theoretical model concerning the dependence of W in argon-isobutane mixtures on isobutane partial pressure (see Figure 1), it could be expected (i) that the mean ionization yields Nion measured with our proportional counter as a function of isobutane concentration fraction should continuously decrease from about 264 at the lowest concentration fraction (2.2% of isobutane at 900mbar) to about 252 for pure isobutane, and (ii) that Nion should be almost independent of the total pressure apart from mixtures with a very low isobutane content. Comparing now these findings with our experimental results, severe discrepancies in both the absolute value and pressure dependence of Nion can be recognized. The absolute values of Nion (Figure 6) is equal to about 290 at low isobutane concentration fractions (2.2% isobutane at 900 mbar) at intermediate gas gains, and is therefore almost 10% higher than expected from the model calculations. In addition, a dependence of Nion on the total gas pressure is much stronger than expected from the model calculations. Reasons for these discrepancies can be found by taking into account rather strong dependence of the measured ionization yields on gas gain (see Figures 4 and 5). It is therefore necessary to understand two important aspects of the measured dependence of Nion as a function of gas gain, the first being its increase with increasing gain in the low-gain region and the second, its decrease in the high-energy region. Studies of gas amplification [16] (both of the mean value and the relative variance) in argon - isobutane mixtures have shown that the amount of isobutane (i.e., its partial pressure) determines the dependence of the gain on the applied voltage, as well as the dependence of the relative variance of the single electron spectra on the gas gain. In mixtures containing less than about 100 mbar of isobutane an exponential increase of the gas gain with the applied high voltage is found up to gas gains of about 800 for 20 mbar, and about 2(103 for 60 mbar (Figure 8.). Above the upper limiting high voltage of exponential gas gain increase, the gas gain curves are "over-exponential", i.e., they are increasing faster than exponentially. This over-exponential increase of the gas gain in mixtures of a rare gas and a molecular gas is explained by insufficient quenching [35]. In the process of avalanche formation additional electrons are formed in some other processes, not mentioned in Eq.(5), at the cathode or in the gas by the UV photons emitted by rare gas atoms. Thus, the number of detected avalanches is too high, and consequently also the measured ionization yield. In other words, the yield Nion measured in a proportional counter, filled with a gas of incomplete quenching properties, cannot be correlated unambiguously to the W value of the gas. When using proportional counters at high gas gains, additional electrons produced in the process of an avalanche formation prevent the direct application of W for energy-deposited calculations and also the accurate determination of W values in mixtures containing low amount of a quenching admixture by a proportional counter. The effect of additional electron production may explain the measured increase of ionization yield with increasing gas gain in the range 900 - 2(103. Isobutane partial pressures of more than 100 mbar seem to be necessary to ensure complete quenching, and, in consequence, to provide (i) gas-gain curves which are exponential over the whole range of gas gains, (ii) relative variances of single electron spectra less than 1 [16], and (iii) ionization yields Nion independent of gas gain, at least for gas gains of up to several thousands. To prove the proposed explanation for the increase of Nion at low gas gains it would be necessary to measure simultaneously the number of electrons and the photon emission. Jarvinen [20] showed that both the light gain and the charge gain increase if the applied high voltage increases. Similar measurements would be needed for a wide range of mixture compositions and total pressures, as described in this paper, to prove that the intensity of unquenched UV photons increases if the absolute amount of the quenching admixture decreases. A different process is responsible for the observed decrease of Nion at high gas gains, which was observed in all investigated mixtures independent of their isobutane content. It can be understood by the decrease of gas gain caused by a screening of the electric field strength due to positively charged ions moving slowly towards the cathode. This screening effect occurs if the total number of charges of an avalanche exceeds a certain high number [35]; in this case a proportional counter does not work any longer in its strictly proportional region and the gas amplification depends on preceding signals. In our case this means that avalanches started by single electrons will experience higher gas amplification than avalanches started by the approximately 250 electrons produced by one 5.89keV photon when applying the same high voltage. The difference in gas gain for these two kinds of primary signal is clearly seen in Figure 9, if the gas gain curves obtained by both sources are compared. As a consequence of different gas amplification for SE and Fe spectra for the same applied high voltage, the ionization yield starts to decrease at gas gains higher than (8(103. 6. Conclusions The model of W values in irregular gas mixtures presented in this paper showed that the pressure dependence of the W value in argon-based Penning mixtures at low concentration fraction of a polyatomic admixture may be explained by the pressure dependence of argon metastable state destruction. At higher total pressure of the mixture the rate of eximer formation is higher, and thus the energy cannot be used for ionization of isobutane gas through the Penning effect. Argon eximers deexcite by emitting photons of insufficient energy to ionize an isobutane molecule. The same pressure dependence of the W value may be expected also in some other Penning mixtures of argon with propane, ethane or acetylene. However, it should be pointed out that the pressure dependence of W value as presented here is not expected in irregular mixtures in which the ionization energy of the admixture is lower than the energy of photons emitted by eximers. These photons may ionize the admixture, and thus the energy used for production of metastable states that form eximers is not "lost" or "wasted" energy, as in argon-isobutane mixtures. Admixtures with ionization energies lower than the energy of argon molecular emission lines are propylene (I=9.73eV) or trans-2-butene (I= 9.24eV), the quenching properties of which were investigated by Agrawal and Ramsey [36]. Unfortunately, it was not possible to compare the W values predicted by the proposed model with W values measured by the proportional counter technique. This technique requires gas gains >103, and Penning mixtures of low partial pressure of isobutane do not ensure a stable, strictly proportional regime of proportional counter operation at these gas gains. Additional electrons are formed during the process of avalanche formation, which cause an increase of the ionization yield with gas gain. This increase is more pronounced in mixtures containing a lower amount of the polyatomic admixture. The real pressure dependence of W value in an irregular mixture might be studied in another kind of experiment that do not require gas amplification, or by using high-pressure (pressure of several bar) proportional counters filled with "thin" (low concentration fraction of an admixture) Penning mixtures. High-pressure counters, studied and successfully applied by Jarvinen [20], will assure a sufficient absolute amount (>100 mbar) of isobutane even at low concentration fractions. The properties of Penning mixtures, such as lower W value and lower Fano factor F, (and consequently better energy resolution), higher first ionization Townsend coefficient and low anode voltage made such mixtures very promising for application in high-resolution X-ray spectroscopy. However, spectroscopy of low-energy (sub-keV) X-rays requires high gas gains. High gas amplification causes a large number of argon UV photons in the gas mixtures, and the amount of the quenching admixture is not longer high enough to ensure complete quenching. The results obtained here imply that Penning mixtures (at relatively low total pressures) should not be used in applications that require high gas gains. A mixture with low admixture concentration resulting in lower W value is not a good proportional counter gas. It was believed that the Penning mixtures will provide better energy resolution than do pure gases or regular mixtures, but as a consequence of non-sufficient quenching in mixtures with low isobutane content, the relative variance of the single electron spectra that determines energy resolution together with W and F values, is higher, and becomes the dominating factor in energy resolution degradation. It is shown in refs. [16,37] that the energy resolution is better in Penning mixtures with a low amount of a quenching admixture only at very low gas gains (50 - 200), and that it is worsened faster with increasing gas gain in mixtures with lower isobutane partial pressure. The fast degradation of energy resolution with gas gain in mixtures with low isobutane partial pressures is caused by fast increase of the relative variance of the single electron spectra due to additional electron formed in the process of avalanche formation [37]. In order to improve energy resolution, mixtures with either higher isobutane concentration fraction at the same pressure, or the same concentration fraction at higher total pressure should be used. Such an increase of the partial pressure of isobutane causes better quenching and more stable proportional counter operation, but the W value of the gas is higher. The present study and that in ref. [37] show that the utilization of Penning mixtures in high-resolution proportional counters is rather complicated and that our knowledge of all processes of importance in Penning gas mixtures is far from being complete. Acknowledgments: Experimental part of the work was performed at the Physikalisch-Technische Bundesanstalt, Braunschweig. The financial support of the PTB to IKB is greatly appreciated. Research performed under the Grant 1-07-064 from the Ministry of Science, Republic of Croatia. Figure captions: Fig. 1. W value for several total pressures of argon-isobutane mixtures as calculated by the simple model presented in the text. For comparison, Wreg is also shown. Fig. 2. Experimental setup. HV - high voltage supply, PC - proportional counter with Al and Be windows for SE and 55Fe sources, respectively, PA - preamplifier, MCA - multichannel analyzer, VAX - on-line computer. Fig. 3. Experimental pulse height distributions: (a) 55Fe spectrum in the mixture of argon and 20% isobutane at total pressure of 300 mbar and gas gain of 1850; the energy resolution of the measured spectrum, defined as FWHM (full width at half maximum), is 15%. (b) SE spectra are presented on a semi-logarithmic plot: ( 30% isobutane, total pressure 300 mbar, gas gain 2800, relative variance f=0.75; ( 20% isobutane, total pressure 300 mbar, gas gain 1850, f=0.67; lines (-..- and ---, respectively) are apparent linear fits to the high-energy part of the spectra; ( 20% isobutane, total pressure 300 mbar, gas gain 2.6(104, f=0.98; the full line is an apparent linear fit to the whole spectrum. The latter two spectra show how the SE spectra in the same gas mixture change shape with the gas gain increase. Fig. 4. Ionization yield for 5.9keV photons measured by the proportional counter filled with argon-isobutane mixtures of various compositions as a function of gas gain, pressure (a) 100mbar, (b) 300 mbar, and (c) 900 mbar. Lines are obtained as adjacent averages of 3 successive datapoints, and are presented here to guide the eye. Fig. 5. Ionization yield for 5.9keV photons measured by the proportional counter filled with argon-isobutane mixtures of various compositions as a function of gas gain for 30% mixtures at 100, 300, and 900mbar total pressure. Lines are obtained as adjacent averages of 3 successive datapoints, and are presented here to guide the eye. Fig. 6. Ionization yield for 5.9keV photons in argon-isobutane mixtures at low gas gain ((103) and at intermediate gas gain ((5(103) as a function of isobutane concentration fraction. Fig. 7. Ionization yield for 5.9keV photons in argon-isobutane mixtures at low ((103) and at intermediate ((5(103) gas gains as a function of isobutane partial pressure. The line represents a linear relation between Nion and the logarithm of partial pressure. Fig. 8. The mean gas amplification factor M (gas gain) as a function of the applied high voltage for several argon-isobutane mixtures. The relative concentration of isobutane and the total pressure of the mixture are indicated. Fig. 9. Comparison of gas gains obtained by measuring the 55Fe 5.9keV peak (lines) and by measuring single electron spectra (symbols) in several argon-isobutane mixtures. It is seen that at high voltages a higher gain is obtained by the single electron spectra. References T.D.Strickler, J. Phys. Chem. 67 (1963) 825. H.J. Moe, T.E. Bortner, G.S. Hurst, J. Phys. Chem. 61 (1957) 422. P.Huber, E.Baldinger, W.Haeberli, Helv. Phys. Acta. 23 (1949) 85; W.Haeberli, P.Huber, E.Baldinger, Helv. Phys. Acta. 26 (1953) 145. T.E.Bortner, G.S.Hurts, Phys. Rev. 93 (1954) 1236. M. Inokuti, E. Eggarter, J. Chem. Phys. 86 (1987) 3870. I. Krajcar Bronic, D. Srdoc, Radiat. Res. 137 (1994) 18. F.M. Penning, Physica 1 (1934) 1028. A.A. Kruithoff, F.M. Penning, Physica 4 (1937) 430. W.P Jesse, Phys. Rev. 174 (1968) 173. W.P Jesse, J. Sadauskis, Phys. Rev. 88 (1952) 417. W.PJesse, J. Sadauskis, Phys. Rev. 100 (1955) 1755. C.E. Melton, G.S. Hurst, T.E. Bortner, Phys. Rev. 96 (1954) 643. G.D. Alkhazov, Zh. Tekh. Fiz. 41 (1972) 2513-2523; Engl. Transl. Sov. Phys. - Techn. Phys. 16 (1972) 1995. C.E. Klots, J. Chem. Phys. 56 (1972) 124. J.E Parks, G.S. Hurst, T.E. Stewart, H.L. Weidner, J.Chem. Phys. 57 (1972) 5467. M-L. Jarvinen, H. Sipila, Nuclear Instrum. Methods 217 (1983) 282. I. Krajcar Bronic, D. Srdoc, B. Obelic, Radiat. Res. 125 (1991) 1. I. Krajcar Bronic, The mean energy required to form an ion pair and the Fano factor in gas mixtures with an emphasis on argon-isobutane mixtures, PhD Thesis, University of Zagreb and the Rudjer Boskovic Institute, Zagreb, 1993. R.L. Platzmann, Int. J. Appl. Radiat. Isot. 10 (1961) 116. E. Ellis, N.D. Twiddy, J. Phys. B: Atom. Mol. Phys. 2 (1969) 1366. L.G. Piper, J.E. Velazco, D.W. Setser, J. Chem. Phys. 59 (1973) 3323. M-L. Jarvinen, Acta Polytechnica Scandinavica, Appl. Phys. Ser. 142 (1984) 36 pp. A.H. Futch, F.A. Grant, Phys. Rev. 104 (1956) 356. M.H.R. Hutchinson, Appl. Phys. 21 (1980) 95. T. Oka, M. Kogoma, M. Imamura, S. Arai, J. Chem. Phys. 70 (1979) 3384.; T. Oka, K.V.S. Rama Rao, J.L. Redpath, R.F. Firestone, J. Chem. Phys. 61 (1974) 4740. R.L. Platzman, Radiat. Res. 17 (1962) 419. Y. Hatano, Radiochimica Acta 43 (1988) 119. H.J. de Jong, Chem. Phys. Lett. 25 (1974) 129. M. Bourene, J. Le Calve, J. Chem. Phys. 58 (1973) 1452. J.E. Velazco, J.H. Kolts, D.W. Setser, J. Chem. Phys. 69 (1978) 4357. A.V. Phelps, J.P. Molnar, Phys. Rev. 89 (1953) 1202. International Commission on Radiation Units and Measurements, ICRU Report no. 31, Washington, DC (1979). B.L. Schram, M.J. van der Wiel, F.J. de Heer, H.R. Moustafa, J. Chem. Phys. 44 (1966) 49. D. Srdoc, Nuclear Instrum. Methods 108 (1973) 327. D. Srdoc, USDOE Progress Report COO-4733-2, Columbia University, New York (1979) p.65. D. Srdoc, B. Clark, Nuclear Instrum. Methods 78 (1970) 305. G.F. Knoll, Radiation Detection and Measurements, John Wiley & Sons, New York, 1979, pp. 816. P.C. Agrawal, B.D. Ramsey, Nuclear Instrum. Methods A 273 (1988) 331. I. KrajcarBronic, Radiat. Prot. Dosim. 61 (1995) 263. 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