1
Ines Krajcar Bronić
Rudjer Bošković Institute, P.O.Box 1016, 10001 Zagreb, CROATIA
RBI Internal Report No. IRB-ZEF-13
ABSTRACT
The present status of both experimental and theoretical values of the mean energy required to form an ion pair ( W value) and the Fano factor ( F ) for electrons and photons in pure rare gases (He, Ne, Ar, Kr, Xe) and their mixtures is reviewed. A good correlation between the F and the W/I ratio ( I is the ionization potential) is found for rare gases except xenon. Xenon has exceptionally low F value for relatively high W/I ratio. Also, a good correlation between the Fano factor and the ratio of the total inelastic to total ionization cross section is obtained for all rare gases. The electron W and F values are also compared with the corresponding values measured for
 particles. Binary mixtures of rare gases with the metastable and with the non-metastable Penning effects are discussed.

2
1. INTRODUCTION
In collisions of energetic electrons with rare gas atoms excited states of rare gas atoms and electron-ion pairs are produced. When studying pure rare gases, we are interested in the distribution of the number of ion pairs only. The excited states, however, play an important role when gas mixtures are concerned. The distribution of the number of electron-ion pairs produced as a result of many incident electrons having identical initial energy can be described by its mean value N i
(the ionization yield) and its variance V
N
=

2
N
= ( N i
N i
)
2
.
Instead of these two quantities, a mean energy required to produce an electron-ion pair ( W ) and the Fano factor ( F ) are used. The W value is defined as
W ( T
0
)

T
0
N i
( T
0
)
(1) where T
0
is the initial electron energy, and N i
(T
0
) is the average number of electron-ion pairs produced after complete dissipation of initial energy T
0
. The Fano factor (Fano 1947) is defined as the ratio of the variance of the distribution of the number of electron-ion pairs to its mean value:
F ( T
0
)

V
N
( T
0
N i
( T
0
)
)
W ( E )

1
W a
 U
E
(2)
The Fano factor represents the relative variance of the distribution, and its value ranges between 0 and 1. Higher values of the Fano factor thus indicate a broader distribution of the number of electron-ion pairs than that described by lower values of F . A theoretically limiting case of F = 0 would describe the electron degradation process in which only ionization processes occur (i.e., energy is not dissipated to any non-ionizing process). However, even in this case, the number of electron-ion pairs is not fixed, because the energy losses of the secondary electrons near the end of their ranges fluctuate. As a consequence, F is close to, but not equal to zero, as shown later.
The general characteristics of both W value and the Fano factor may be summarized as follows: the W and F values are characteristics of a gas, they only slightly depend on the kind of the incident particle; and both increase ( W towards infinity, F towards 1) as the initial electron energy decreases approaching the ionization potential of a gas. For high-energy electrons they attain almost constant values.
Energy dependence of W value for electrons is well established: W value approaches a constant value W a
at high energies ( T
0
greater than a few keV), and at lower energies the energy dependent W(E) can be described as (Inokuti 1975)
(3)

3 where U is the mean energy of subionization electrons (their energy is too low to cause further ionizations).

The asymptotic W and F values for photons as incident ionizing particles are reached for photon energies much larger than the nearest atomic shell that can be ionized. In a lower energy range, electronic energy levels may cause some irregularities or discontinuities in energy dependence at photon energies where sudden changes in available energy dissipation channels occur. Detailed discussions on energy dependence of W and F for X-rays in xenon is given in Dias et al (1997).
It is instructive to look at the W/I value, i.e., the ratio of the W value to the ionization potential I of the gas. Namely, the ratio W/I estimates the partition of energy spent in a gas to ionizing and non-ionizing processes: The higher the W/I , the greater the non-ionizing “losses” of energy. According to the energy balance equation (Platzman 1961), the W/I ratio can be obtained as
W
I

E i
I

N ex
N i
E ex
I


I
(4) where E i
and E ex
are the mean energy spent in an ionizing collision and in an excitation collision, respectively, N ex
is the mean number of excited atoms produced, and

is the mean energy of subexcitation electrons. For rare gases, the average value of W/I is about 1.7, while for molecular gases the ratio ranges from 2.2 to 2.6, or even higher. The main reasons for the difference are higher values of the ratios
E i
I
and
N ex
N i
E ex
I
in molecular gases. For the same reasons, the Fano factor for molecular gases (0.24 - 0.37) is also significantly larger than that for rare gases (≤0.2).
From a physical point of view, higher F values should be related with higher W/I values.
Both higher W/I and a higher Fano factor generally mean a greater fraction of energy spent into non-ionizing collisions. Recent analysis of both experimental and theoretical W, W/I and
F values in gases and gas mixtures (Krajcar Bronić 1992) has shown that the F and the dimensionless ratio W/I are linearly correlated for electron energies T
0
> 100 eV
F
 a
W
I
 b (5) where a = (0.188 ± 0.006) and b = (-0.15 ± 0.02) are coefficients obtained by a linear fit to the available data. This relation has been recently confirmed by measurements of W and F for low energy photons in various gases and gas mixtures (Pansky et al 1997).

4
Knowledge of accurate W values is important from both theoretical and practical point of view. For example, both W and F values limit the energy resolution of gas-filled chambers.
Therefore, a continuous interest in W and F values for various ionizing particles and in various materials exists. Several comprehensive analyses can be found in literature. W values and
Fano factors for different particles and in various materials have been reviewed by Doke
(1969, 1981), by International Commission for Radiation Units and Measurements (ICRU
1979), and by the International Atomic Energy Agency group (Srdoč et al 1995).
Christophorou (1972) lists W values for

and

particles in rare gases and many molecular gases.
ICRU Report 31 (1979) gives energy dependence and recommends high-energy W values for electrons, protons,

particles and heavy ions in various gases including rare gases.
The results obtained until 1979 and discussed in ICRU 31 are not discussed in detail in the present paper. Srdoč et al (1995) in IAEA TECDOC 799 gave W values and Fano factors for gases of interest for radiotherapy, and only Ar of all rare gases is included. W values and Fano factors in mixtures, as well as the relation between F and W/I were discussed. In the present paper, an updated analysis of W and F values for rare gases and mixtures of rare gases is presented. The main emphasis is given to electrons and photons as incident particles, but some results for other ionizing particles (protons,

and

particles) are also mentioned for comparison.

2 . METHODS
2.1. Experimental determination of W and F in gases
Measurement of W value and the Fano factor in gas is performed by using gas-filled ionization detectors. The particle energy and the number of electron-ion pairs formed in a gas by each particle have to be determined. When the Fano factor is to be measured, the distribution of the number of primary ion pairs and its width (i.e., the energy resolution) have to be determined. Various methods of measurements have been developed: a) ionization chamber method, b) proportional counter method, c) gas proportional scintillation method, d) single electron counting method.
The ionization chamber method is used for

particles and can be applied for all rare gases. W values in all rare gases have been determined by this method, as shown later.
However, only F in He (Ishida et al 1992a), Ar (Kase et al 1984) and Xe (Ishida et al 1992b) have been reported.
In the gas proportional counter method the dominant contribution to the line width is fluctuation f in the number of electrons in electron avalanches formed during the electron multiplication process in strong electric fields. The value of f is sometimes taken as 0.7, but recent studies of various pure molecular gases and some gas mixtures (tissue-equivalent mixtures, argon-based mixtures) have shown that f depends on the gas gain. More importantly, in mixtures of argon with a molecular gas f additionally depends on the mixture composition

5 and its pressure (Krajcar Bronić 1995, Krajcar Bronić and Grosswendt 1997). Unfortunately, the method cannot be applied for pure rare gases without a quenching gas.
The gas proportional scintillation method (GSPC) avoids electron multiplication in a strong electric field. In a region of high electric field, electrons gain enough energy to excite gas molecules, but the energy is not enough to ionize them. The de-excitation of excited atoms/molecules leads to the production of scintillation, i.e., to the large number of photons, which are then detected by a photomultiplier tube. The energy resolution is determined by the fluctuations in the number of primary ion pairs only (i.e., by the Fano factor) and is therefore better than in a proportional counter. The Fano factor can be directly determined from the measured pulse width (Dias 1994). The method can be applied for heavy rare gases (Kr, Xe) by using X rays in the keV energy range.
In the first three methods one basically determines the limit of energy resolution of the detector, and then infers the Fano factor. For this purpose, all possible contributions to the pulse width have to be known. In all cases the measured Fano factor presents an upper limit of its real value and any further refinement of the experimental methods may result in lower experimental F values.
The single electron counting method (Pansky et al 1996, 1997) can be used for measurements of W and F and their energy dependence in various gases and gas mixtures. The method is based on individual counting of single ionization electrons induced in a lowpressure gas by ultra-soft (~100 eV) to soft X-ray (<2 keV) photons. The method combines an experimental measurement of the distribution of the number of electron-ion pairs formed by an X-ray photon in a gas, and a Monte Carlo simulation of the detection process. An efficient counting of the small number of primary electrons should provide the ultimate energy resolution, limited only by the Fano factor. However, up to now no measurement with pure rare gases have been performed.
2.2. Calculation of W and F
The calculation of the yield of ion pairs, and therefore of the W value, as well as of the
Fano factor, requires two steps: ( i ) determination of the cross sections for all major collision processes of the incident particle and of electrons with molecules in irradiated matter, and ( ii ) determination of the consequences of the collision processes to both the particle and the material (Inokuti 1975, Kimura et al 1993). A theoretical calculation of W and the Fano factor is possible and meaningful for gases for which the complete set of cross sections is available.
Basically, two complementary approaches are used in the analysis of the consequences of collision processes: analytic transport theories and a Monte Carlo (MC) method. In the MC method, one simulates histories of collisions for many particles and draws conclusions from statistics of those histories. The method can be applied to a wide range of problems. By applying Monte Carlo calculations, Unnikrishnan and Prasad (1979) and Parikh (1980) calculated W and F in argon, Grosswendt (1984) in He, Ne and Ar, Dayashankar et al (1982) and Dayashankar and Unnikrishnan (1983) in Kr, Dias et al (1993, 1997) simulated energy dependence of W and F in Xe.

6
In the analytic transport theory one writes an equation for a quantity of interest. The equations are numerically solvable only in simpler cases. The most often used analytical approaches are solving the Fowler equation (e.g., for neon Dayashankar (1979), for argon
Eggarter (1975), for Kr Dayashankar (1981)), or solving the Spencer-Fano (SF) equation. By solving the SF equation, one obtains the so-called electron degradation spectrum (or the tracklength distribution), which is fundamental for calculating a variety of quantities describing the electron slowing-down process, including the mean ionization yield and the Fano factor
(Kowari et al 1989, Kimura et al 1992, 1993). Another analytical approach, not often used, is the solution of the integral Knipp equation for the probability distribution of the number of ion pairs (Prasad and Unnikrishnan 1981). Sato et al (1974) calculated the W values for pure rare gases irradiated by 100 keV electrons by combining the binary encounter-collision theory with the theory of degradation spectrum. Later, the method was improved by taking into account double-collision processes (Okazaki et al 1975). In both cases, the agreement with the experimental values was good only for helium. Although the improved method yielded W values closer to the experimental ones, especially for neon, the deviations from the experimental values were large and increased from Ne (~10%) to Xe (~24%).
3. W AND F VALUES FOR PURE RARE GASES
Table 1. shows the ionization potential I , energy of metastable excited states and their lifetimes for all rare gases (from Siska 1993). Both experimental and theoretical W and F values for electrons and photons are shown in Table 2. W and F values for

particles are also presented, and in the last column of Table 2 some W and F values for high-energy protons are also shown. (Note that the values measured by Parks et al (1972) are differential
 values for high-energy protons). In the following section, W and F values are separately discussed for each pure rare gas, and then all the rare gases are compared in the summarizing section.
3.1. Helium
Calculated W values for electrons in He (Miller 1956, Alkhazov and Vorob´ev 1969,
Grosswendt 1984, Biagi 1998) closely agree (46.5, 46, 45.5 and 46.0 eV, respectively), but are in discrepancy with most experimental results obtained by measurements with

particles.
Okazaki et al (1974) calculated W = 43.9 eV. Platzman (1961) pointed out the possibility of ionization of excited He atoms with n >3 ( n is the main quantum number) in thermal collisions. This process called collateral ionization, He
*
+ He

H
2
+
+ e
-
, would decrease W for high-pressure He to values around 42 - 43.5 eV (Inokuti 1975). By applying the Spencer-
Fano method, Douthat (1975) showed that the W value decreased by 8% when the collateral ionization was taken into account.
The recommended ICRU value (1979) for photons and electrons is based on two experimental values, 42.3 eV for tritium

particles (Jesse and Sadauskis 1955a) and 40.3 eV for 2 MeV X-rays (Weiss and Bernstein 1956). The later lower value might be a consequence

7 of a very small amount of a contaminating gas, as explained in the next section. Therefore, there exist no accurate experimental data for photons of any energy and electrons of a fixed energy. New measurements exist for W and F for

particles (Ishida et al 1992a), but no new experimental results for W for electrons or X-rays are available. The experimental W value in helium can be determined only from the measurements by using

particles. The average experimental W is (43.2 ± 0.4) eV without the highest value measured by Bortner and Hurst
(1954), and (43.7 ± 0.5) eV when all the experimental data for 
and

particles and protons are taken into account.
The ratio W/I in helium has a value ~1.87 if the theoretical (non-corrected for collateral ionization) W values are considered, but when the corrected or experimental W value is taken,
W/I reaches lower values, about 1.76.
Alkhazov et al (1967) estimated F in He by using available experimental cross section data of 0.17. (The same value was obtained also for Ne and Ar). However, more detailed calculations that followed (Alkhazov and Vorob´ev 1969, Alkhazov 1972, Grosswendt 1984,
Biagi 1998) have shown that F for He is close to 0.2.
3.2. Neon
Among rare gases, neon is the least studied gas. Calculated W values (Alkhazov 1972,
Soong 1976, Dayashankar 1979, Grosswendt 1984) group around 35.8 eV, while only the recent calculation by Biagi (1998) gives higher value, 37.5 eV. The ICRU average (35.4 eV), which is comparable to the theoretical value, is based on three experimental values: 36.6 eV for

particles (Jesse and Sadauskis 1955a), 36.3 eV for 2-MeV X-rays (Weiss and Bernstein
1956), and 34.3 for

rays (Cooper and Mooring 1968). No new experimental result exists for electrons. Averaged experimental W value for

particles is 36.6 eV, the same as that measured for tritium

particles. As in the case of He (and Ar, see below) there should be a contribution of the collateral ionization to the experimental W value. The contribution in Ne can be roughly estimated by taking the average of the higher contribution in He and the lower in Ar, giving the contribution in Ne to be 1-2 eV. It brings now the recent calculations of
Biagi (1989) into a better agreement with the experimental results. As mentioned above, deviation of the W value calculated by Okazaki et al (1975) from the experimental and other theoretical values is large. Further on, their W values will not be discussed although shown in
Table 2.

All calculated F for electrons (Alkhazov 1972, Grosswendt 1984, Biagi 1998) indicate that F for Ne (0.13) is lower than F for He. In fact, the F for Ne is the lowest among the Fano factors for rare gases. The ratio W/I for neon approaches also the lowest value among rare gases, ~1.64, as it was predicted by Alkhazov (1972).

3.3. Argon
Argon is theoretically the most studied rare gas. Variations among calculated W values are not large, and give a mean value of (26.87 ± 0.30) eV, resulting in the average W/I for

8 argon of ~1.70. Eggarter (1975) estimated the contribution of collateral ionization at higher pressures and found the corrected W value to be 25.9 eV, as compared with 26.86 eV without the collateral ionization. The corrected value was higher than the experimental W value measured at that time (26.4 eV, for

particles). The only recent experimental W value for 5.9 keV photons at pressure 128 kPa by Borges and Conde (1996), ( W = 25.8 + 0.6 eV), however, seems to be in very good agreement with the Eggarter´s estimation. W values for

particles
(Table 2) give an average of 26.35 ± 0.05 eV, while the only W value measured for protons having energy 3 MeV (Thomas and Burke 1987) is very close to the recent experimental value for photons (Borges and Conde 1996).

The values of the Fano factor for high-energy electrons in Ar seem to be grouped around
0.15 - 0.16. Such a low F value has not yet been confirmed by measurements (compare de
Lima et al 1982, Hashiba et al 1984). Similar F value has been calculated also for protons
(Inokuti et al 1992), while F for

particles is somewhat higher (~0.2, Alkhazov et al 1967,
Kase et al 1984).

Combecher (1980) measured W for low-energy electrons in the energy range from the ionization threshold to 500 eV in Ar, to 300 eV in Kr, and to 1000 eV in xenon. In these energy ranges the W value does not reach the constant high-energy value and therefore his data cannot be directly compared with other high-energy data. Low-energy W values measured by
Combecher (1980) in all three gases show similar energy dependence with shoulders at electron energies a few eV below twice the ionization potential. The shoulders are superposed to the energy dependence that can be described by Eq.(3). Energy dependence of W for electrons in Ar is shown in Fig. 1. The experimental data (Combecher 1980) are compared with the Monte Carlo calculations (Grosswendt 1984) and the results of the SF theory (Kowari et al 1989). A shoulder at T
0
~ 25 eV, observed in the experiment, has recently been confirmed by the new Monte Carlo calculation of energy dependence of W (Biagi 1998).
Figure 2 presents energy dependence of the Fano factor in Ar. Here, only the theoretical values can be compared. A shoulder at T
0
~ 40 eV in the Monte Carlo calculations
(Grosswendt 1984) has been confirmed in the calculations by Biagi (1998) as a peak at around
T
0
~ 40 eV. Similar peaks in F have been obtained also in He and Ne at T
0
~ 60 eV and ~50 eV, respectively (Biagi 1998).
3.4. Krypton
The only experimental W value for 5.9 keV photons of Borges and Conde (1996) is slightly lower (but within given experimental uncertainties) than the average ICRU W value.
Again, the ICRU value is an average of W for

particles (24.2 eV, Jesse and Sadauskis
1955a) and for 2-MeV X-rays (24.7 eV, Weiss and Bernstein 1956). The two W values calculated by Dayashankar (1981) and Dayashankar et al (1982) by two different methods, the
Fowler equation and Monte Carlo calculations, respectively, are lower and higher, respectively, than the experimental value (Borges and Conde 1996). The average of all existing data for electrons or photons in Kr is (24.16 ± 0.40) eV.
W for

particles (Jesse and
Sadauskis 1953, Hurst et al 1965, Kubota 1970) and

particles from tritium (Jesse and

9
Sadauskis 1955) are not much different from those for electrons. The W value as a function of electron energy calculated by Dayashankar (1981) shows similar energy dependence as the measured W value for low energy electrons (Combecher 1980), but is consistently ~3 eV
(15%) lower than the experimental one in the overlapping energy region ( T
0 above 30 eV).
The Fano factor in Kr probably approaches the value below 0.19. No data for F in Kr for particles other than electrons or photons exist. The W/I for krypton is about ~1.73 ± 0.03, higher than that for neon, and comparable with that for argon.
3.5. Xenon
When compared to other rare gases, xenon is one of the best experimentally studied gases (Table 2). One of the reasons is that xenon is suitable for gas scintillation proportional counters (GSPC). The ICRU high-energy value (22.1 eV, ICRU 1979) is again based on two measurements for

particles and X-rays (Jesse and Sadauskis 1955a, Weiss and Bernstein
1956). W value for very low-energy electrons (up to 60 eV) was measured by Samson and
Haddad (1976) and for electron energies up to 1 keV by Combecher (1980). A W value of
(21.5 ± 0.4) eV for low-energy (1.7 - 10.5 keV) X-rays in Xe was obtained by applying a xenon gas total absorption ionization chamber (Lyons et al 1971). The recently measured W value for 5.9 keV photons at pressure of around 1 bar (21.7 ± 0.5 eV, Borges and Conde 1996) is not significantly different from the previous values. The W/I ratio based on the ICRU value is then ~1.82, while the two above mentioned experimental W values result in W/I of about
1.78. However, recent experiments with low-energy X-rays are very much dependent on the photon energy used, and it is therefore difficult to recommend an accurate "high-energy" W value. Calculated W for electrons in xenon are 22.4 eV (for electron energies >300 eV,
Dayashankar 1981), W = 22.38 eV for 6-keV, and 22.0 eV for 10-keV photons (Dias et al
1993). The Fano factor at sufficiently high energies may be even lower than 0.15, as measured by Anderson et al (1979), and Kowalski et al (1989).
Discontinuities in both W and F for X-rays in Xe were observed experimentally
(Kowalski et al 1989, Tsunemi et al 1993, Budtz-Jorgensen et al 1995) and by Monte Carlo calculations (Dias 1994, Dias et al 1993, 1997). The discontinuities in both quantities are located near the xenon K (34.5 keV) and L (4.7, 5.1 and 5.4 keV) absorption edges. It was shown that the discontinuities in the W and F values reflect the discontinuities of the Xe photoionization cross sections at the photoabsorption edges (Dias et al 1997). When the increasing X-ray energy reaches a value just high enough to allow for the photoionization of a new inner atomic subshell, the Fano factor shows a sudden increase, followed by a gradual decrease and it eventually stabilizes when the energy becomes much higher than the highest absorption edge. For example, W for photon energies just below and just above the L edges are 22.0 eV and 22.5 eV, respectively, and the Fano factor is 0.18 and 0.32, respectively. The discontinuity at the K edge is evident (Figs. 4 and 5 in Dias et al 1997), but not so pronounced, W is 21.7 eV and 21.9 eV, and the Fano factor 0.18 and 0.23, for energies just below and just above the K edge, respectively.

10
W values measured for

particles (Jesse and Sadauskis 1953, 1955a, Klots 1966, Ishida et al 1992b), except the one measured by Kubota (1970), as well as that for

particles from tritium (Jesse and Sadauskis 1955a), agree well with the W for electrons and photons.
However, the Fano factor for

particles is much higher than that for electrons (Ishida et al
1992b).

3.6. Summary for pure rare gases
The present analysis of W and F values in pure rare gases shows that although the interaction of ionizing particles with rare gases has been extensively studied both experimentally and theoretically, there are still some open questions when accurate numerical data are needed. From the presented data one can see that more experimental values are available for

particles than for electrons, while calculations are performed for electrons (and photons, in the case of Xe) as incident particles. Generally, a good agreement between theoretical and experimental W values for different particles is obtained, except in the case of helium. For He, the experimental W values are grouped about 3 eV below the theoretical value. No new (after ICRU Report in 1979) experimental data exist for electrons or photons in
He and Ne, and the only new experimental W in Ar and Kr is that for 6-keV photons (Burges and Conde 1996). More experimental data exist for xenon, due to the fact that xenon is a good medium for gas scintillation proportional counters. However, a strong energy dependence of both W and F prevents accurate determination of their high-energy values.

W values for high-energy electrons in rare gases decrease from He to Xe as the ionization potential decreases, and the ratio W/I remains practically constant, being on the average 1.7. Rare gases make a rather homogeneous group as compared to molecular gases when the ratio W/I is discussed. However, within this limited group one can see some variations. The W/I for He is the largest (1.88 theoretical, 1.76 experimental value), accompanied by the largest Fano factor, and W/I is the smallest for Ne, accompanied by the smallest Fano factor. When F is plotted vs . the W/I ratio (Krajcar Bronić 1992), shown in
Figure 3, a relatively good correlation (see Eq. (5)) is obtained for He, Ne, Ar and Kr, while the data for Xe deviate from the regression line, because of relatively high W/I (~1.82) accompanied by small F (~0.13).
A dissipation of ionizing particle energy to excitations and ion-pair formations of the gas is determined by the magnitudes of the cross sections for excitation (
 ex
) and that for ionization (
 i
). The total energy loss in inelastic collisions is therefore determined by the total inelastic cross section,
 tot
=
 i
+
 ex
. The W value should be proportional to the total inelastic cross section, and the relative magnitudes of
 ex
and
 i
would determine a partition of the ionizing particle energy to the two kinds of inelastic processes. Therefore, it may be interesting to compare both W/I and F with the ratio of the total inelastic cross section to the total ionization cross section,
 tot
/
 i
. Data for total excitation and total ionization cross sections were taken from de Heer and Jansen (1977) for He, and for other rare gases from de
Heer et al (1979). Ratio
 tot
/
 i
is the largest for He (~1.43), and smallest for Ne and Xe
(~1.12). In Figure 4 we show the relations W/I vs.
 tot
/
 i
, and F vs.
 tot
/
 i
.
A correlation between the cross section ratio and the W/I ratio (Figure 4a) is good for 4 rare gases excluding

11
Xe: the higher the ratio of cross sections, the higher the W/ I ratio. Xe is an exception, having small cross-section ratio, and relatively high W/I . Better correlation is obtained between the cross section ratios and the Fano factor (Figure 4b): the higher the cross section ratio, the higher the Fano factor. The largest deviation from the linear relation is seen for Kr (too high
F ), probably because the limiting low F has not yet been measured.
The Fano factor for

particles may contain the contribution of elastic nuclear collisions, and is therefore larger than the Fano factor for X-rays or electrons (Kase et al 1984, Doke et al
1992, Inokuti et al 1992). A contribution of low-energy electrons produced by

particles may also result in an increase of the Fano factor for

particles (Ishida et al 1992a,b). The only
Fano factor for protons in argon is that calculated by Inokuti et al (1992). Their calculated energy-dependent Fano factors are almost the same as those for electrons of the same speed, but smaller than the Fano factors for

particles of the same speed. This result indicates that the main contribution to higher F for

particles comes from elastic nuclear collisions.
4. RARE GAS MIXTURES
Binary gas mixtures consisting of two gas components have been studied for a long time because of their importance for both theoretical studies and practical applications. Two groups of gas mixtures can be generally distinguished when one considers possible interaction between the two components: regular gas mixtures and mixtures with irregular effect (or irregular mixtures). In regular gas mixtures, the two gases do not interact, i.e., the energy of ionizing radiation is dissipated to each of the components in a certain proportion. The aim of many studies was to determine in which proportions is the energy dissipated (see the complete reference list in Krajcar Bronić and Srdoč 1994). It was recently shown that the total ionization cross sections determine the energy dissipation (Inokuti and Eggarter 1987,
Swallow and Inokuti 1988, Krajcar Bronić and Srdoč 1994). In such mixtures, one can calculate the total ionization yield if one knows the yield in each of the components.
Therefore, W value in a regular mixture is given by
W reg


W i
 
 i i
C i
C i
(6) where W i
,
 i
and C i
are the W value, the total ionization cross section evaluated at electron energies much higher than the ionization threshold energy, and the concentration of the i-th component, respectively. The Fano factor in regular mixtures can be estimated in a similar way (Krajcar Bronić et al 1992) if one knows the Fano factors F i
for each gas component:
F reg



F i

 i i
C i
C i
W i
W i
(7)

12
In irregular mixtures the two gas components can interact, and intermolecular energy transfer is possible. Energy is transferred from an excited species of the parent gas to a second gas (an admixture) having a lower ionization potential. In such collisions, ionization of the admixture molecules is possible through the Penning effect. When we speak about the
Penning processes, we distinguish a metastable Penning effect (MPE) and a non-metastable
Penning effect (NMPE). In the MPE, the energy stored in excitation of a metastable excited state of a rare gas atom is transferred to an admixture. Not only the metastable states contribute to the energy transfer, but also higher dipole accessible states (usually called resonant states), and then we talk about the non-metastable Penning effect (Melton et al
1954). Metastable states have long lifetime (Table 1), and very low concentration of an admixture is required for an efficient energy transfer. This concentration is much lower than in the case of the NMPE. However, due to the trapping of resonance radiation, resonance levels have also relatively long effective lifetime and play an important role in the interpretation of the Jesse effect (Hurts et al 1965).
The total ionization yield in irregular mixtures in therefore due to the direct ionization of each component plus the ionization of the admixture through the Penning processes.
Metastable and other excited states of a rare gas prevent the application of the additivity rule for the ionization yield calculation in mixtures where the Penning effects are possible. The total ionization yield is higher than it would be without the energy transfer, and consequently the W and the F are smaller than calculated from Eqs. 6 and 7. In a mixture with the MPE, the concentration fractions of admixtures are usually in the order of 0.1 - 1%, and the W value is lowered by up to 20% compared with the W in regular mixtures. In mixtures with the NMPE, the changes in W value are much smaller (not more than 5%) and the required concentration fraction of the admixture is higher (≥5%). If both processes are possible in a binary mixture, the NMPE has a dominant role in additional ionization yield at relatively high admixture concentrations, >5% (Kubota 1970).
Increase in ionization yield in a Penning mixture has been observed in experiments by
Jesse and Sadauskis (1952, 1953, 1955b), Bertolini et al (1954), Bortner and Hurst (1954),
Melton et al (1954), Moe et al (1957), Hurst et al (1965), Klots (1967), Kubota (1970), and later in many other experiments with gas mixtures (ICRU 1979, Srdoč et al 1995, Krajcar
Bronić and Grosswendt 1996). The effect of lowering
W values for small concentrations of an admixture is afterwards usually called the Jesse effect . Therefore, the Jesse effect is a macroscopic manifestation of the Penning effect that takes place on a microscopic level.
The first who mentioned a possibility of obtaining low F values in Penning mixtures were Vorob´ev et al (1961) who recognized that the magnitude of the ionization fluctuations
(described by the Fano factor) is mainly determined by the redistribution of the number of ionized and excited atoms, while their total number appears to fluctuate considerably less. If the total number of ionized and excited atoms can be determined, the fluctuations should be very small. They proposed to make use of the Penning effect, i.e., to add a small amount of an admixture that would efficiently de-excite metastable rare gas atoms and thus enable detecting the total number of excited and ionized atoms. They estimated the value of the Fano factor in a mixture with effective additional ionization to be reduced to about 0.02 to 0.04. Later

13 calculations and experiments with various Penning mixtures (Table 3) showed that their estimate was very close but slightly lower than the actually obtained values. The difference arises probably because of less efficient additional ionization than supposed in Vorob´ev´s calculations. Alkhazov and Vorob´ev (1969) showed that both W and F values in Penning mixtures strongly depend on the probability

of de-excitation of a metastable atom followed by an additional ionization of the admixture. Both values decrease when

increases, and F reaches the value of 0.05 if

= 1.

Because of relatively high metastable states of rare gases and of relatively low ionization potential of molecular gases (10 - 12 eV), mixtures with very pronounced Penning effects are mixtures of a parent rare gas (He, Ne, Ar) and a very small concentration of a molecular gas
(acetylene, propane, butane, etc.). Here we discuss only the mixtures of two rare gases.
Klots (1967) studied ionization yield in various rare gas - based mixtures (He-Ar, He-
Kr, He-Xe; Ne-Kr), but he was not interested in the Penning effect occurring at low admixture concentrations. He was interested in the mixing formula for W over the whole range of mixing ratios. An interesting behavior was observed in Ne-Kr mixtures when Kr (and similarly Ar) was added to Ne: the ionization yield was increasing symptomatically to the Jesse effect, but then for concentrations of more than several percent started to decrease reaching a minimum for ~12% Kr, and then increasing again towards the yield for pure Kr. The effect was called the negative Jesse effect.
Kubota (1970) measured ionization yield by

-particles in binary rare gas mixtures (He-
Ne, Ar-Kr, Ar-Xe, Kr-Xe) over the whole range of mixing ratios to clarify the contribution of
NMPE to the total ionization yield. He estimated the relative contribution of the NMPE and
MPE processes to the total yield in He-Ar mixture. The NMPE had a dominant role over the
MPE in the region of large Ar concentrations, while the MPE was dominant at very small concentrations of Ar. In all mixtures where NMPE was possible, an increase in ionization yield was observed. The contribution of the NMPE to ionization yield was observed also by
Tawara et al (1987) in Ar-Kr and Ar-CH
4
mixtures.
Some W and F values in rare gas mixtures are presented in Table 3.

4.1. He-based mixtures
Any gas (except Ne) may be considered as an impurity to helium because of the high energy of the metastable He states (Table 1.). The "Jesse" effect (Jesse and Sadauskis 1952) was indeed observed for the first time during studies of the ionization yield by charged particles in helium with addition of a very small (~0.01%) quantity of almost any gas except neon. Jesse and Sadauskis (1955b) measured an increase of up to 50% relative to pure He when small amounts of Ar, Kr or Xe were added to He, or when Ar and Kr were added to Ne.
When about 20-30% of Ne was added to He, an increase of ~15% in ionization yield was observed relative to pure helium (Kubota 1970).
Parks et al (1972) studied W value for protons in mixtures of He with Ne, Ar, Kr and Xe as a function of pressure and concentration. In mixtures of Ar, Kr and Xe a pronounced Jesse

14 effect was observed, which was also very much dependent on pressure when only a few parts per million of impurity were introduced. Neon in helium did not produce an increase in the ionization yields, but a very small amount of Ne added to He slightly increased the W of He (a negative Jesse effect).
Alkhazov (1972) calculated W value and the Fano factor for electrons in He-Ar, He-Xe,
Ne-Ar and some other mixtures. The ratio W/I in a mixture of helium with a very small argon and xenon concentration was 1.12 and 1.10, respectively, in contrast to ~1.8 in pure helium.
The Fano factor was in both mixtures ~0.06, in contrast to 0.2 in pure He.
Measurements of W (Bortner and Hurst 1954, Jesse and Sadauskis 1952, 1955b, Kubota
1970, Ishida et al 1992a) for

particles in He-Ar mixtures show W similar to that for electrons, but the Fano factor (Ishida et al 1992a) is considerably higher, 0.11±0.02, compared with ~0.06 for electrons.
4.2. Ne-based mixtures
Ne + Ar (0.1%) is the best known Penning mixture. The effect of energy transfer from the metastable state to the ionization of the admixture was originally discovered in Ne-Ar mixtures (Penning 1934, Kruithoff and Penning 1937). Ne - Ar mixture is suitable for soft Xray counting, while for harder X-rays mixtures containing heavier rare gases (Ar-Kr, Ar-Xe,
Kr-Xe) are more interesting (Sipila 1977). Mixtures of neon with typically 0.1% argon have been used to lower the operating voltage in monochrome plasma display panels (Boeuf et al
1997). However, Ne-Ar mixture is of little practical use in proportional counters. At low gas gains, ≤10, energy resolution is better than that in pure Ne, but it rapidly degrades at higher gains due to the development of avalanche chains in the process of electron multiplication
(Agrawal and Ramsey 1988, Krajcar Bronić 1995).
According to Alkhazov (1972), a ratio of the number of excited Ne atoms to the number of neon ions is 0.44. By assuming that each excited Ne atom in collisional ionization produces an Ar ion, i.e
.,

= 1, the minimal W value in Ne doped with a small amount of an admixture
(e.g., Ar) is expected to be W min
= W
Ne
/(1 +

N ex
/N i
) = W
Ne
/1.44 = 25.1 eV. Experimental W value for 55 Fe 5.9 keV photons (Jarvinen and Sipila 1983) of 25.4 - 25.7 eV is very close to that theoretical value, proving that the ionization efficiency in Ne-Ar mixture is close to unity.

The Penning effect is most pronounced when the concentration of an admixture (Ar or
Xe in Ne) is less than 1%. Most of the electron energy is then deposited in excitation and ionization of neon, and the ionization of the admixture atom by an excited neon atom occurs with high probability. In mixtures of neon with more than a few percent of Ar or Xe, the
Penning effect does not play a significant role because most of the electron energy is spent into xenon excitation and ionization (Boeuf et al , 1997).
4.3. Ar-based mixtures
In argon-based mixtures, both MPE and NMPE are possible, depending on the ionization potential of the admixture. Melton et al (1954) noticed that the ionization yield

15 increased also when a mixture having I higher than the energy of Ar metastable state is added to Ar, but to make the effect measurable, much higher admixture concentrations (of several percent) were required than for the Jesse effect previously observed. When MPE possible, energy defect plays an important role. (Energy defect is the difference between the energy of the metastable Ar state and the ionization energy of the admixture).
Mixtures of argon and a polyatomic gas (Ar + CH
4
, CO
2
and others) are widely used in high-energy physics, nuclear physics, astronomy. Considerable improvement in energy resolution has been achieved by using additives with lower ionization potential I (propane, ethane, butane; propane being the best additive because of the smallest energy defect).
Experimental studies of various molecular gases mixed with argon were performed by
Bertolini et al (1954), Hurst et al (1965), Melton et al (1954), Moe at el (1957), Agrawal and
Ramsey (1988), Krajcar Bronić (1995).
Among rare gases, only Kr and Xe can be mixed to Ar. The ionization potential of Kr and Xe is higher than the metastable levels of Ar, so only the contribution of the NMPE to the ionization yield is possible (Kubota 1970, Tawara et al 1987). The largest increase in the ionization yield was observed for ~20% of either Kr or Xe added to Ar. The Fano factor measured by de Lima et al (1982) supports the hypothesis of occurrence of NMPE in both mixtures.
Ar - Xe mixture is an especially interesting mixture because Xe acts as a quenching gas
(the same role as a polyatomic admixture) for Ar as a main gas (Fusezy et al 1972, Sipila
1977, Agrawal et al 1989, Budtz-Joergensen et al 1991). In Ar - Xe mixture useful high gas gains can be reached at much lower voltages than in pure gases or common mixtures with polyatomic gases. The absence of organic gases makes this mixture useful in chambers exposed to large amount of radiation, and in applications that require long lifetimes of the chambers. Ar - Xe mixture provides high gas gain, good energy resolution, and detection of high-energy X-rays (10-30 keV) with better efficiency than any other argon-based mixture, including the "best-matched" Penning mixture of Ar and acetylene (Agrawal et al 1989).
Inoue et al (1978) showed that the best energy resolution was obtained with Ar + 20% Xe mixture, confirming thus observation of the maximal increase in the ionization yield.
4.4. Kr-based mixtures
As an additive to Kr, only Xe among the rare gases can be considered. However, the I of
Xe is rather high compared with the lowest excited or metastable Kr states, and thus only relatively high excited states of Kr may be involved in NMPE. W value measured by Kubota
(1970) for

particles resulted in deviation from the expected regular behavior. The largest increase of 11% in ionization yield was observed for ~20% Xe added to Kr. From the measurements of the Fano factor (Ribeirete et al 1983) no conclusions about the occurrence of the NMPE effect were obtained, because of relatively large experimental errors and a small expected effect. Among polyatomic gases propylene ( I = 9.7 eV) seems to be well matched to the first metastable state of Kr, because of the small energy defect (Ramsey and Agrawal
1988).


16
4.5. Xe-based mixtures
Counters filled with xenon-based mixtures at high pressure are often used for medium energy (<100 keV) X-ray astronomy due to a high absorption efficiency of Xe for hard X-rays.
The energy limit can be even extended to ~1 MeV when ultra-high-pressures (>2 MPa) are used (Manchanda et al 1990). However, to provide a stable counter operation a small percentage of a quenching gas is needed. Only polyatomic admixtures can be considered, since Xe has the lowest-lying ionization potential and the lowest metastable states among rare gases.
It is difficult to find an admixture with lower I than the energy of Xe metastable state.
Propylene ( I = 9.7 eV) is a very good admixture to Xe, because its ionization potential is very close to a group of very strong metastable Xe states centered on 9.5 eV, and very good energy resolution and high gas gain are obtained (Ramsey and Agrawal 1988). However, the best quench gas for xenon is TMA (trimethylamine), having ionization potential of ~8.3 eV that lies just below the 8.32 eV metastable state of Xe. The energy defect is very small, the
Penning effect occurs, and gas gain increases when TMA is added to Xe (Ramsey and
Agrawal 1988).
CONCLUDING REMARKS
More experiments are needed for both W and F in all rare gases. Special attention should be paid to energy dependence of both quantities, especially for low-energy photons as incident particles. Pressure dependence of W should be also studied experimentally in more details. When rare gas mixtures are concerned, a pressure dependence of the Penning effect has not yet been clarified. Experimental data on the Fano factor for various ionizing particles are also needed. More precise measurements of the Fano factor in mixtures with the nonmetastable Penning effect are desirable.
Acknowledgment
The work was financed by the JSPS Fellowship (S-97055) and by the Ministry of
Science, Republic of Croatia (P0207). I thank Prof. T. Doke, Waseda University, for the invitation, his hospitality, and useful comments and discussions. The suggestions for the manuscript improvement by Prof. S. Kubota, Rykkio University, are also aknowledged.

17
Figure captions:
Figure 1. Energy dependence of W value for electrons and photons in Ar. Except experimental W values for low-energy electrons (Combecher 1980),for 5.9keV-photons (Borges and Conde 1996) and for 5-MeV

particles (ICRU
1979), all other values are calculated.

Figure 2.
Figure 3.
Figure 4.
Energy dependence of the Fano factor F for electrons and photons in argon. All values are calculated by various methods, see text.
Relation between the Fano factor and the ratio W/I in rare gases. The line F =
(0.31 ± 0.10) W/I - (0.37 ± 0.18), r
2
= 0.91, presents the linear correlation obtained for 4 data points (He-theory, Ne, Ar, Kr). The experimental values for
He and those for Xe are not included in the regression calculations.
Relation between the a) ratio W/I and b) the Fano factor in rare gases and the ratio of total inelastic cross section to the total ionization cross section,
 tot
/
 i
.
The line in Fig. 4b, F = (0.22 ± 0.05)
 tot
/
 i
. - (0.11 ± 0.06), r
2
= 0.89, shows a linear regression obtained for all 5 datapoints.

18
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