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Use of sum signals of ionization and scintillation in liquid rare gases and the Fano factor for the sum signals
Nuclear Instruments and Methods in Physics Research B 234 (2005) 203–209 www.elsevier.com/locate/nimb
Use of sum signals of ionization and scintillation in liquid rare gases and the Fano factor for the sum signals Tadayoshi Doke
*
Kikuicho-Branch, Advanced Research Institute for Science and Engineering, Waseda University, Kikuicho-17, Shinjuku-ku, Tokyo 162-0044, Japan Received 8 November 2004; received in revised form 17 January 2005 Available online 31 March 2005
Abstract Scintillation signals and ionization signals produced in liquid rare gases by ionizing radiation can be simultaneously observed with high efficiencies. The fluctuation of the sum of scintillation and ionization signals is smaller than that of either of the individual signals. The present paper discusses the theoretical limit of energy resolution of the sum signals, compares it with the experimental results obtained in liquid rare gases, and presents comments recent papers treating related topics. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Sum signals; Ionization; Scintillation; Liquid rare gases; Recombination; Fano factor
1. Introduction It is generally difficult to observe an ionization signal produced in a scintillator by high energy radiation. In contrast, it is easy to observe an ionization signal produced in a semiconductor detector (e.g. a Si detector), but it is impossible to observe a scintillation signal produced in it. There are thus no detector media from which both ionization and scintillation signals can be observed,
*
Tel.: +81 3 3203 9434; fax: +81 3 3203 3231. E-mail address: [email protected]
except for rare gases in the liquid or solid phase. In the gaseous phase of rare gases, the scintillation yield is minute because the probability of recombination between electrons and ions is extremely low. Their full recombination is realized only in the liquid or solid phase. However, it is very difficult to acquire stable charge signals in the solid phase. At present, therefore, it is possible to obtain stable sum signals of ionization and scintillation only in a liquid phase. The present paper will clarify certain problems of energy loss fluctuation in such sum signals, as presented in recent papers [1,2], and will attempt at interpreting the experimental results we have obtained so far [3–7].
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.01.118
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Simultaneously measuring both ionization and scintillation signals in liquid rare gases improves the energy resolution. This was first shown in a measurement of energy loss for relativistic La ions in liquid argon [3]. Fig. 1 shows the variations of the scintillation intensity S and the collected charge Q simultaneously measured as a function of the electric field between the cathode and the anode in a liquid argon chamber subjected to La ions as well as for Ne, Fe, and Au ions [3–6]. The scintillation intensity is normalized to the intensity S0 at zero field, and the collected charge is normalized to the charge Q1 produced by incident ions, in the chamber. Fig. 2 illustrates a correlation pattern between S/S0 and Q/Q1 [7]. The data points, except for those for Au, are clearly on a straight line, which demonstrates that the quantities are complementary. The deviation of the data points for of Au from the straight line is caused by the so-called quenching effect, as shown later. Fig. 3 presents the energy resolutions of the scintillation S, the ionization Q and their sum, Q + aS, as a function of the electric field in liquid argon [3], where a is described later. Because the I and aS are complementary, the energy resolution of Q + aS is much better than those of S and Q, and is nearly independent of the electric field. Recently, Conti et al. [1] applied the same method for relativistic electrons using a liquid xenon gridded chamber and found that the use of the sum signals improved energy resolution. With this
Fig. 2. Relation between scintillation intensity and collected charge in liquid argon for relativistic Ne, Fe, La, Au ions. The solid line shows the theoretical relation [7].
Fig. 3. The pulse height resolution in fwhm for scintillation S, charge I, and sum signal I + aS of the scintillation and the charge as a function of electric field.
Fig. 1. A set of the saturation curves of ionization (open symbols) and scintillation (solid symbols) for relativistic Ne, Fe, La, and Au in liquid argon as a function of the electric field. These data are taken from the Bevalac experiments [3–5].
method, generally, the collection efficiency for photo-electrons in the photo-cathode is extremely small, because the solid angle for light collection is small and the quantum efficiency of the photocathode is also small. Furthermore, how to treat ‘‘ionization’’ Q and ‘‘scintillation’’ S on the same footing is a main problem in this case. In other
T. Doke / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 203–209
words, if we express the sum by Q + aS, the resolution of the sum signals depends on how we select a value of a. In the liquid argon experiment with La ions, the value of a was carefully determined [3], but, the choice of a was not so clear in the work by Conti et al. [1]. In a recent review paper on calorimeters for particle physics [2], Fabjan and Gianotti also pointed out that the best energy resolution would be achieved by taking the sum signals of ionization and scintillation as shown above for heavy ions [3] and, derived the theoretical limit of the fluctuation in the ionization signals alone in a homogeneous argon calorimeter by using the following formula: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rðN ion Þ ¼ N ðN ion =N ÞðN scint =N Þ; N ¼ N ion þ N scint ; if Nion/N = 0.8 and Nscint/N = 0.2, pffiffiffiffi rðN ion Þ 0:4 N ; where Nion is the number of electron–ion pairs and Nscint the number of photons produced by an ionizing radiation with a fixed energy. However, derivation of the above formula remains obscure. Later I will show you the correct formula derived by Fano. Last, I will show another method using the sum signals, which we discovered about 20 years ago [8–11]. By doping photo-sensitive organic materials into liquid argon or xenon, we observed a large increase in collected electronic charge. We can obtain signals near the ideal sum signals, because the quantum efficiencies of triethylamine (TEA) and trimethylamine (TMA) doped in liquid xenon for photo-ionization are very high (80%) [12]. In these cases, however, we cannot determine the correct value of a and, as a result, some ambiguities remain, so long as the quantum efficiency for photo-ionization is not 100%. Apart from such ambiguities, a method for deriving the correct a value will be described, and a correct expression for the Fano factor for ionization calorimeter will be shown. In addition, the correct Fano factor for the sum signals or for scintillation signals in a zero electric field will be derived.
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2. Fundamental processes of ionization and scintillation in liquid rare gases In order to understand the correlation between ionization and scintillation, we must know their mechanisms in liquid rare gases. The ionization process in liquid rare gas produced by ionizing radiation is simply shown as follows: R ! Rþ þ e
ð1Þ
However, the mechanism of scintillation in liquid rare gas is not so simple. Generally, the scintillation from a liquid rare gas is produced by the following two processes of excitons R* and ions R+ produced by ionizing radiation [13]: R þ R þ R ! R2 þ R;
ð2Þ
R2 ! 2R þ hm; Rþ þ R ! Rþ 2;
ð3Þ
Rþ 2 þ e ! R þ R;
R ! R þ heat; R þ R þ R ! R2 þ R; R2 ! 2R þ hm; where hm denotes the ultraviolet photon and the process R** ! R* + heat corresponds to a nonradiative transition.
Fig. 4. LET dependence of scintillation yield, Y, in argon. Solid circles show the yields for relativistic particles [3–5]. The yields for non-relativistic particles are represented by open circles. Open squares and triangles show the yields for non-relativistic protons, whereas small open circles show those for nonrelativistic helium ions [13–17,19].
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To clarify the scintillation mechanism in liquid rare gas, here, consider the relation between the scintillation yield and the linear energy transfer (LET) for different kinds of ionizing radiation. Fig. 4 shows the LET dependence of scintillation yields in liquid argon obtained under excitation by relativistic heavy charged particle such as He, He, Ne, Fe, Kr, La, and Au [3–5] as well as those by non-relativistic particles [14–19]. These results were obtained without an electric field. We will explain this LET dependence in the following section.
3. Estimation of the number of excited atoms and ionized atoms produced by ionizing radiation In the case of liquid argon excited by relativistic heavy ions, the number of scintillation photons under zero electric field for the energy E0 deposited by an ionizing particle, Nsci is [20] N sci ¼ N i N ex ¼ N i ð1 þ N ex =N i Þ ¼ E0 =W ð1 þ N ex =N i Þ; where Ni and Nex are the numbers of ions and excited atoms produced by an ionizing particle and W is the average energy required to form an ion– electron pair. From the above equation, we can obtain Wsci = W/(1 + Nex/Ni) as the average energy required to produce a scintillation photon by an ionizing particle. Here, the sum signal Q + aS is normalized by Ni + Nex Fig. 5 presents [6] the var-
Fig. 5. LET dependence of the ratio, (Q/e + aSr)/(Nex + Ni), in liquid argon. Data points for non-relativistic particles are given in parentheses.
iation of (Q + aS)/(Ni + Nex) as a function of LET for various particles shown in Fig. 4. Here we measured the collected charge Q in absolute number of electrons, and therefore we should determine the value a so that aS may be the absolute number of scintillation photons emitted. The scintillation yields for low LET particles are smaller than unity in Fig. 4. However, we know from Fig. 5 that the ratio of (Q + aS)/(Ni + Nex) is unity for relativistic particles lighter than Au, whereas the ratios of Au, alpha particles and fission fragments are smaller than unity. From these facts, we concluded that the ratios of the latter are smaller than unity, because of the quenching process of scintillation, and the scintillation yield in the low LET region is reduced because of the escape of electrons from recombination [20]. We also concluded that the scintillation yield in the flat region in Fig. 4 is 100%. The values of Ni/Nex, W-value, and Wsci for liquid argon were experimentally derived as N ex =N i ¼ 0:21 [21,22];
W ¼ 23:6 eV [21];
W sci ¼ 19:5 eV [23]: In a zero-electric field, Nsci is given as Nsci = E0/ Wsci = (E0/W)(1 + Nex/Ni); the scintillation signal is 100%. Under an infinite electric field, E0/ W = Ni can be completely measured as a charge signal and (E0/W)(Nex/Ni) can also be determined from the number of scintillation photons; the scintillation signal is 17.4% and the ionization signal is 82.6%. However, the size of the sum signal is just equal to that obtained in a zero-electric field. Of course, both quantities obtained by measurement depend on the strength of the electric field, but the sum of ionization and scintillation gives a constant value in all fields. Thus, the anti-correlation between ionization and scintillation signals is obtained in liquid rare gases. Fig. 2 shows a typical anti-correlation pattern between I/I1 and S/S0 for relativistic heavy particles [7]. For liquid xenon, Nex/Ni = 0.06 [21,24], W = 15.6 eV [24], and Wsci = 14.7 eV [23]. Here Nex/Ni was obtained by a theoretical calculation but the W values were obtained experimentally. For consistency with experimental results, Nex/Ni = 0.06
T. Doke / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 203–209
is too small. Recently, therefore, we proposed have a new value of Nex/Ni = 0.13 [6], which changes the theoretical Wsci value slightly, i.e. to 13.8 eV [6]. The anti-correlation pattern for 1 MeV electrons differs from those for relativistic heavy particles although the dependence of Q/Q1 or S/ S0 on the electric field is similar to that for relativistic heavy particles. Fig. 6(a) and (b) illustrate the correlation pattern between ionization Q/Q1 and scintillation S/S0 for 1 MeV electrons in liquid argon and xenon. The data points for low electric fields are not on the anti-correlation line, because of the electron attachment to the electronegative gases and a modest recombination rate; data points in the high electric fields are on the anti-correlation line [6]. In other words, the complete compensation between ionization and scintillation occurs only for high electric fields. This shows that using the sum signals for low electric fields is ineffective for good energy resolution.
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4. Determination of a From the above arguments, the observed scintillation intensity at zero field S0 is given as [3] S 0 ¼ ð1=aÞDE=W sci ; where a includes all efficiencies for photon detection so that aS0 is the number of photons emitted under zero electric field, DE is the energy absorbed in the sensitive region of the detector and Wsci is the W-value for scintillation at the maximum level as defined above. Therefore, Wsci should never be used for 1 MeV electrons or gamma-rays because it is very difficult to completely collect photons emitted from recombination of ions and escaped electrons in a zero electric field; doing so requires a very long time (order of ms). In this case, the Wsci-value (=Wb) for 1 MeV electrons as shown in [6] should be used.
5. Fano factor for the sum signals The Fano factor, Fi, for ionization can be rewritten as follows [25]: Fi ¼F1 þF2 þF3 ¼ ðN ex =N i Þ½1 þ N ex =N i ðW 2ex =W 2 Þ þ ½hðei W i Þ2 i=W 2 þ ðN ex =N i Þ½hðeex W i Þ2 i=W 2 :
The first term F1 is due to the redistribution of the numbers of excited and ionized atoms. The second term F2 and third term F3 are due to energy loss fluctuations in ionization and excitation. The contribution of the first term is large compared to that of the others. If we can use the sum signals, the first term should be zero and Fi is reduced to the sum of the second and the third terms, which are usually very low compared with the first term. The contribution from the terms due to energy loss fluctuation is estimated to be about 0.04 for liquid Ar and Xe [25]. Accordingly, the fluctuation of the sum signals, rsum, expressed in rms is approximately pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi rsum ffi ri 0:04N i 0:2 N i Fig. 6. (a) Relation between Sr/Sr0 and Q/Q0 in liquid argon. (b) Relation between Sr/Sr0 and Q/Q0 in liquid xenon.
for liquid Ar or Xe.
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The energy loss fluctuation in a homogenous liquid argon calorimeter is given as F = F1 + F2 + F3 = 0.076 + 0.036 + 0.004 = 0.116 [25]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ri ¼ 0:116N i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:116ðN i þ N ex Þ½N i =ðN i þ N ex Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi ¼ 0:0959N sum ¼ 0:31 N sum because F = F1 + F2 + F3 = 0.076 + 0.036 + 0.004 = 0.116 [25]. This is slightly smaller than that ðri ¼ pffiffiffiffiffiffiffiffiffivalue ffi 0:4 N sum Þ given by Fabjan. Also, the Fano factor Fsci for scintillation in a zero electric field should be equal to Fsum for relativistic heavy ions such as relativistic Ne, Fe, Kr, and La ions, because, in this case, the scintillation without an electric field corresponds to a kind of the sum signals. In contrast, the Fano factor for scintillation when the electric field is infinite should be equal to Fi When an electric field is applied, Fsci should be between the above two limiting cases, since it depends on the electric field. However, the energy resolution of sum signals obtained so far is not as good as the best value obtained by a gridded ionization chamber [26]. As I have recently learned, the best energy resolution for sum signals was achieved by AprileÕs group [27] but it was slightly better than the best value obtained with a gridded ionization chamber. In order to show a large discrepancy in energy resolution between experimental results and theoretical estimation, finally, we show the best energy resolutions in liquid argon and xenon obtained so far with usual gridded ionization chambers in Table 1 Comparison between the best energy resolutions for 976 keV electrons and 570 keV gamma rays obtained experimentally and their theoretical limits
Ionizing radiation Fano factor Nex/Ni W (eV) Wsci (eV) Rtheor (keV) Rexper (keV)
Liquid Ar
Liquid Xe
976 keV electrons 0.11 0.21 23.8 19.5 3.7 28 [26]
570 keV gamma-rays 0.08 0.13 15.6 (15.8) 13.8 2.0 28 [26]
Rtheor: the theoretical limit of energy resolution, Rexper: the best energy resolution experimentally obtained so far.
Table 1 as well as the theoretical limits given by the above theory [25]. The energy resolutions shown in the table with electronic noise subtracted are the best values obtained by our group in liquid argon [10] and xenon [11]. They are about 10 times worse than the theoretically estimated resolutions. Here, we used the values of W and Wsci in liquid xenon which are obtained by using the new value of Nex/Ni = 0.13. The causes of this large discrepancy were discussed in [26], but remain incompletely understood. 6. Summary Questionable points on the energy resolution appeared in two recent papers [1,2] are clarified. Concerning [1], the constant value a, which shows a correct relation between Q and S, was given and, concerning [2], the Fano factor for a homogeneous liquid argon ionization calorimeter was directly derived. In addition, the use of the sum signals of ionization and scintillation is investigated and its advantage is suggested. The theoretical limits of the energy resolution for the sum signals and for scintillation signals are also given. References [1] E. Conti, R. DeVoe, G. Gratta, T. Koffas, S. Waldman, J. Wodin, D. Akimov, G. Bower, M. Bower, M. Breidenbach, R. Conley, M. Danilov, Z. Djurcic, A. Dologenko, C. Hsall, K. Wamba, O. Zeldovich, Phys. Rev. B 68 (2003) 054201. [2] C.W. Fabjan, Fabiola Gianotti, Rev. Mod. Phys. 75 (2003) 1243. [3] H. Crawford, T. Doke, A. Hitachi, J. Kikuchi, P.J. Lindstrom, K. Masuda, S. Nagamiya, E. Shibamura, Nucl. Instr. and Meth. A 256 (1987) 47. [4] T. Doke, H.J. Crawford, C.R. Gruhn, A. Hitachi, J. Kikuchi, K. Masuda, S. Nagamiya, E. Shibamura, S. Tamada, Nucl. Instr. and Meth. A 235 (1985) 136. [5] E. Shibamura, H.J. Crawford, T. Doke, J.M. Engelarge, I. Flores, A. Hitachi, J. Kikuchi, P.J. Lindstrom, K. Masuda, K. Ogura, Nucl. Instr. and Meth. A 260 (1987) 437. [6] T. Doke, A. Hitachi, J. Kikuchi, K. Masuda, H. Okada, E. Shibamura, Jpn. J. Appl. Phys. 41 (2002) 1538. [7] K. Masuda, E. Shibamura, T. Doke, A. Hitachi, J. Kikuchi, Phys. Rev. A 39 (1989) 4732. [8] S. Suzuki, T. Doke, A. Hitachi, A. Yunoki, Nucl. Instr. and Meth. A 245 (1986) 78.
T. Doke / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 203–209 [9] S. Suzuki, T. Doke, A. Hitachi, J. Kikuchi, A. Yunoki, Nucl. Instr. and Meth. A 245 (1986) 366. [10] H. Ichinose, T. Doke, A. Hitachi, J. Kikuchi, K. Masuda, H. Matsui, E. Otobe, E. Shibamura, T. Takahashi, Nucl. Instr. and Meth. A 295 (1990) 354. [11] H. Ichinose, T. Doke, A. Hitachi, J. Kikuchi, K. Masuda, E. Shibamura, Nucl. Instr. and Meth. A 322 (1992) 216. [12] A. Hitachi, H. Ichinose, J. Kikuchi, T. Doke, K. Masuda, K. Masuda, E. Shibamura, Phys. Rev. B 55 (1997) 5742. [13] T. Doke, Portugal Phys. 12 (1981) 9. [14] A. Yunoki, K. Masuda, J. Kikuchi, T. Takahashi, T. Doke, Bull. Sci. Eng. Res. Lab., Waseda Univ. 113 (1986) 54. [15] A. Hitachi, A. Yunoki, T. Doke, T. Tamada, Phys. Rev. A 35 (1987) 3956. [16] T. Doke, S. Tamada, A. Hitachi, K. Masuda, J. Kikuchi, T. Takahashi, M. Sekiguchi, INS-Annu. Rep. (1983) 43. [17] A. Hitachi, T. Takahashi, T. Hamada, E. Shibamura, N. Funayama, K. Masuda, J. Kikuchi, T. Doke, Nucl. Instr. and Meth. 196 (1982) 97. [18] T. Kato, T. Doke, J. Kikuchi, K. Masuda, K. Ozaki, E. Shibamura, M. Tanaka, Nucl. Instr. and Meth. A 433 (1999) 619.
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[19] S. Kubota, A. Nakamoto, T. Takahashi, T. Hamada, E. Shibamura, M. Miyajima, K. Masuda, T. Doke, Phys. Rev. B 17 (1978) 2762. [20] T. Doke, H.J. Crawford, A. Hitachi, J. Kikuchi, P.J. Lindstrom, K. Masuda, E. Shibamura, T. Takahashi, Nucl. Instr. and Meth. A 269 (1988) 291. [21] M. Miyajima, T. Takahashi, S. Konno, T. Hamada, S. Kubita, E. Shibamura, T. Doke, Phys. Rev. A 9 (1974) 1438. [22] S. Kubota, A. Kuge, A. Nakamoto, T. Takahashi, S. Konno, T. Hamada, M. Miyajima, A. Hitachi, E. Shibamura, T. Doke, Phys. Rev. B 13 (1976) 1649. [23] T. Doke, K. Masuda, E. Shibamura, Nucl. Instr. and Meth. A 291 (1990) 617. [24] T. Takahashi, S. Konno, T. Hamada, M. Miyajima, S. Kubota, A. Nakamoto, A. Hitachi, E. Shibamura, T. Doke, Phys. Rev. A 12 (1975) 1771. [25] T. Doke, A. Hitachi, S. Kubota, A. Nakamoto, T. Takahashi, Nucl. Instr. and Meth. 134 (1976) 353. [26] E. Shibamura, K. Masuda, T. Doke, A. Hitachi, Jpn. J. Appl. Phys. 34 (1995) 1897. [27] E. Aprile, private communication.
Use of sum signals of ionization and scintillation in liquid rare gases and the Fano factor for the sum signals Tadayoshi Doke
*
Kikuicho-Branch, Advanced Research Institute for Science and Engineering, Waseda University, Kikuicho-17, Shinjuku-ku, Tokyo 162-0044, Japan Received 8 November 2004; received in revised form 17 January 2005 Available online 31 March 2005
Abstract Scintillation signals and ionization signals produced in liquid rare gases by ionizing radiation can be simultaneously observed with high efficiencies. The fluctuation of the sum of scintillation and ionization signals is smaller than that of either of the individual signals. The present paper discusses the theoretical limit of energy resolution of the sum signals, compares it with the experimental results obtained in liquid rare gases, and presents comments recent papers treating related topics. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Sum signals; Ionization; Scintillation; Liquid rare gases; Recombination; Fano factor
1. Introduction It is generally difficult to observe an ionization signal produced in a scintillator by high energy radiation. In contrast, it is easy to observe an ionization signal produced in a semiconductor detector (e.g. a Si detector), but it is impossible to observe a scintillation signal produced in it. There are thus no detector media from which both ionization and scintillation signals can be observed,
*
Tel.: +81 3 3203 9434; fax: +81 3 3203 3231. E-mail address: [email protected]
except for rare gases in the liquid or solid phase. In the gaseous phase of rare gases, the scintillation yield is minute because the probability of recombination between electrons and ions is extremely low. Their full recombination is realized only in the liquid or solid phase. However, it is very difficult to acquire stable charge signals in the solid phase. At present, therefore, it is possible to obtain stable sum signals of ionization and scintillation only in a liquid phase. The present paper will clarify certain problems of energy loss fluctuation in such sum signals, as presented in recent papers [1,2], and will attempt at interpreting the experimental results we have obtained so far [3–7].
0168-583X/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.01.118
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T. Doke / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 203–209
Simultaneously measuring both ionization and scintillation signals in liquid rare gases improves the energy resolution. This was first shown in a measurement of energy loss for relativistic La ions in liquid argon [3]. Fig. 1 shows the variations of the scintillation intensity S and the collected charge Q simultaneously measured as a function of the electric field between the cathode and the anode in a liquid argon chamber subjected to La ions as well as for Ne, Fe, and Au ions [3–6]. The scintillation intensity is normalized to the intensity S0 at zero field, and the collected charge is normalized to the charge Q1 produced by incident ions, in the chamber. Fig. 2 illustrates a correlation pattern between S/S0 and Q/Q1 [7]. The data points, except for those for Au, are clearly on a straight line, which demonstrates that the quantities are complementary. The deviation of the data points for of Au from the straight line is caused by the so-called quenching effect, as shown later. Fig. 3 presents the energy resolutions of the scintillation S, the ionization Q and their sum, Q + aS, as a function of the electric field in liquid argon [3], where a is described later. Because the I and aS are complementary, the energy resolution of Q + aS is much better than those of S and Q, and is nearly independent of the electric field. Recently, Conti et al. [1] applied the same method for relativistic electrons using a liquid xenon gridded chamber and found that the use of the sum signals improved energy resolution. With this
Fig. 2. Relation between scintillation intensity and collected charge in liquid argon for relativistic Ne, Fe, La, Au ions. The solid line shows the theoretical relation [7].
Fig. 3. The pulse height resolution in fwhm for scintillation S, charge I, and sum signal I + aS of the scintillation and the charge as a function of electric field.
Fig. 1. A set of the saturation curves of ionization (open symbols) and scintillation (solid symbols) for relativistic Ne, Fe, La, and Au in liquid argon as a function of the electric field. These data are taken from the Bevalac experiments [3–5].
method, generally, the collection efficiency for photo-electrons in the photo-cathode is extremely small, because the solid angle for light collection is small and the quantum efficiency of the photocathode is also small. Furthermore, how to treat ‘‘ionization’’ Q and ‘‘scintillation’’ S on the same footing is a main problem in this case. In other
T. Doke / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 203–209
words, if we express the sum by Q + aS, the resolution of the sum signals depends on how we select a value of a. In the liquid argon experiment with La ions, the value of a was carefully determined [3], but, the choice of a was not so clear in the work by Conti et al. [1]. In a recent review paper on calorimeters for particle physics [2], Fabjan and Gianotti also pointed out that the best energy resolution would be achieved by taking the sum signals of ionization and scintillation as shown above for heavy ions [3] and, derived the theoretical limit of the fluctuation in the ionization signals alone in a homogeneous argon calorimeter by using the following formula: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rðN ion Þ ¼ N ðN ion =N ÞðN scint =N Þ; N ¼ N ion þ N scint ; if Nion/N = 0.8 and Nscint/N = 0.2, pffiffiffiffi rðN ion Þ 0:4 N ; where Nion is the number of electron–ion pairs and Nscint the number of photons produced by an ionizing radiation with a fixed energy. However, derivation of the above formula remains obscure. Later I will show you the correct formula derived by Fano. Last, I will show another method using the sum signals, which we discovered about 20 years ago [8–11]. By doping photo-sensitive organic materials into liquid argon or xenon, we observed a large increase in collected electronic charge. We can obtain signals near the ideal sum signals, because the quantum efficiencies of triethylamine (TEA) and trimethylamine (TMA) doped in liquid xenon for photo-ionization are very high (80%) [12]. In these cases, however, we cannot determine the correct value of a and, as a result, some ambiguities remain, so long as the quantum efficiency for photo-ionization is not 100%. Apart from such ambiguities, a method for deriving the correct a value will be described, and a correct expression for the Fano factor for ionization calorimeter will be shown. In addition, the correct Fano factor for the sum signals or for scintillation signals in a zero electric field will be derived.
205
2. Fundamental processes of ionization and scintillation in liquid rare gases In order to understand the correlation between ionization and scintillation, we must know their mechanisms in liquid rare gases. The ionization process in liquid rare gas produced by ionizing radiation is simply shown as follows: R ! Rþ þ e
ð1Þ
However, the mechanism of scintillation in liquid rare gas is not so simple. Generally, the scintillation from a liquid rare gas is produced by the following two processes of excitons R* and ions R+ produced by ionizing radiation [13]: R þ R þ R ! R2 þ R;
ð2Þ
R2 ! 2R þ hm; Rþ þ R ! Rþ 2;
ð3Þ
Rþ 2 þ e ! R þ R;
R ! R þ heat; R þ R þ R ! R2 þ R; R2 ! 2R þ hm; where hm denotes the ultraviolet photon and the process R** ! R* + heat corresponds to a nonradiative transition.
Fig. 4. LET dependence of scintillation yield, Y, in argon. Solid circles show the yields for relativistic particles [3–5]. The yields for non-relativistic particles are represented by open circles. Open squares and triangles show the yields for non-relativistic protons, whereas small open circles show those for nonrelativistic helium ions [13–17,19].
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To clarify the scintillation mechanism in liquid rare gas, here, consider the relation between the scintillation yield and the linear energy transfer (LET) for different kinds of ionizing radiation. Fig. 4 shows the LET dependence of scintillation yields in liquid argon obtained under excitation by relativistic heavy charged particle such as He, He, Ne, Fe, Kr, La, and Au [3–5] as well as those by non-relativistic particles [14–19]. These results were obtained without an electric field. We will explain this LET dependence in the following section.
3. Estimation of the number of excited atoms and ionized atoms produced by ionizing radiation In the case of liquid argon excited by relativistic heavy ions, the number of scintillation photons under zero electric field for the energy E0 deposited by an ionizing particle, Nsci is [20] N sci ¼ N i N ex ¼ N i ð1 þ N ex =N i Þ ¼ E0 =W ð1 þ N ex =N i Þ; where Ni and Nex are the numbers of ions and excited atoms produced by an ionizing particle and W is the average energy required to form an ion– electron pair. From the above equation, we can obtain Wsci = W/(1 + Nex/Ni) as the average energy required to produce a scintillation photon by an ionizing particle. Here, the sum signal Q + aS is normalized by Ni + Nex Fig. 5 presents [6] the var-
Fig. 5. LET dependence of the ratio, (Q/e + aSr)/(Nex + Ni), in liquid argon. Data points for non-relativistic particles are given in parentheses.
iation of (Q + aS)/(Ni + Nex) as a function of LET for various particles shown in Fig. 4. Here we measured the collected charge Q in absolute number of electrons, and therefore we should determine the value a so that aS may be the absolute number of scintillation photons emitted. The scintillation yields for low LET particles are smaller than unity in Fig. 4. However, we know from Fig. 5 that the ratio of (Q + aS)/(Ni + Nex) is unity for relativistic particles lighter than Au, whereas the ratios of Au, alpha particles and fission fragments are smaller than unity. From these facts, we concluded that the ratios of the latter are smaller than unity, because of the quenching process of scintillation, and the scintillation yield in the low LET region is reduced because of the escape of electrons from recombination [20]. We also concluded that the scintillation yield in the flat region in Fig. 4 is 100%. The values of Ni/Nex, W-value, and Wsci for liquid argon were experimentally derived as N ex =N i ¼ 0:21 [21,22];
W ¼ 23:6 eV [21];
W sci ¼ 19:5 eV [23]: In a zero-electric field, Nsci is given as Nsci = E0/ Wsci = (E0/W)(1 + Nex/Ni); the scintillation signal is 100%. Under an infinite electric field, E0/ W = Ni can be completely measured as a charge signal and (E0/W)(Nex/Ni) can also be determined from the number of scintillation photons; the scintillation signal is 17.4% and the ionization signal is 82.6%. However, the size of the sum signal is just equal to that obtained in a zero-electric field. Of course, both quantities obtained by measurement depend on the strength of the electric field, but the sum of ionization and scintillation gives a constant value in all fields. Thus, the anti-correlation between ionization and scintillation signals is obtained in liquid rare gases. Fig. 2 shows a typical anti-correlation pattern between I/I1 and S/S0 for relativistic heavy particles [7]. For liquid xenon, Nex/Ni = 0.06 [21,24], W = 15.6 eV [24], and Wsci = 14.7 eV [23]. Here Nex/Ni was obtained by a theoretical calculation but the W values were obtained experimentally. For consistency with experimental results, Nex/Ni = 0.06
T. Doke / Nucl. Instr. and Meth. in Phys. Res. B 234 (2005) 203–209
is too small. Recently, therefore, we proposed have a new value of Nex/Ni = 0.13 [6], which changes the theoretical Wsci value slightly, i.e. to 13.8 eV [6]. The anti-correlation pattern for 1 MeV electrons differs from those for relativistic heavy particles although the dependence of Q/Q1 or S/ S0 on the electric field is similar to that for relativistic heavy particles. Fig. 6(a) and (b) illustrate the correlation pattern between ionization Q/Q1 and scintillation S/S0 for 1 MeV electrons in liquid argon and xenon. The data points for low electric fields are not on the anti-correlation line, because of the electron attachment to the electronegative gases and a modest recombination rate; data points in the high electric fields are on the anti-correlation line [6]. In other words, the complete compensation between ionization and scintillation occurs only for high electric fields. This shows that using the sum signals for low electric fields is ineffective for good energy resolution.
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4. Determination of a From the above arguments, the observed scintillation intensity at zero field S0 is given as [3] S 0 ¼ ð1=aÞDE=W sci ; where a includes all efficiencies for photon detection so that aS0 is the number of photons emitted under zero electric field, DE is the energy absorbed in the sensitive region of the detector and Wsci is the W-value for scintillation at the maximum level as defined above. Therefore, Wsci should never be used for 1 MeV electrons or gamma-rays because it is very difficult to completely collect photons emitted from recombination of ions and escaped electrons in a zero electric field; doing so requires a very long time (order of ms). In this case, the Wsci-value (=Wb) for 1 MeV electrons as shown in [6] should be used.
5. Fano factor for the sum signals The Fano factor, Fi, for ionization can be rewritten as follows [25]: Fi ¼F1 þF2 þF3 ¼ ðN ex =N i Þ½1 þ N ex =N i ðW 2ex =W 2 Þ þ ½hðei W i Þ2 i=W 2 þ ðN ex =N i Þ½hðeex W i Þ2 i=W 2 :
The first term F1 is due to the redistribution of the numbers of excited and ionized atoms. The second term F2 and third term F3 are due to energy loss fluctuations in ionization and excitation. The contribution of the first term is large compared to that of the others. If we can use the sum signals, the first term should be zero and Fi is reduced to the sum of the second and the third terms, which are usually very low compared with the first term. The contribution from the terms due to energy loss fluctuation is estimated to be about 0.04 for liquid Ar and Xe [25]. Accordingly, the fluctuation of the sum signals, rsum, expressed in rms is approximately pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi rsum ffi ri 0:04N i 0:2 N i Fig. 6. (a) Relation between Sr/Sr0 and Q/Q0 in liquid argon. (b) Relation between Sr/Sr0 and Q/Q0 in liquid xenon.
for liquid Ar or Xe.
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The energy loss fluctuation in a homogenous liquid argon calorimeter is given as F = F1 + F2 + F3 = 0.076 + 0.036 + 0.004 = 0.116 [25]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ri ¼ 0:116N i pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:116ðN i þ N ex Þ½N i =ðN i þ N ex Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi ¼ 0:0959N sum ¼ 0:31 N sum because F = F1 + F2 + F3 = 0.076 + 0.036 + 0.004 = 0.116 [25]. This is slightly smaller than that ðri ¼ pffiffiffiffiffiffiffiffiffivalue ffi 0:4 N sum Þ given by Fabjan. Also, the Fano factor Fsci for scintillation in a zero electric field should be equal to Fsum for relativistic heavy ions such as relativistic Ne, Fe, Kr, and La ions, because, in this case, the scintillation without an electric field corresponds to a kind of the sum signals. In contrast, the Fano factor for scintillation when the electric field is infinite should be equal to Fi When an electric field is applied, Fsci should be between the above two limiting cases, since it depends on the electric field. However, the energy resolution of sum signals obtained so far is not as good as the best value obtained by a gridded ionization chamber [26]. As I have recently learned, the best energy resolution for sum signals was achieved by AprileÕs group [27] but it was slightly better than the best value obtained with a gridded ionization chamber. In order to show a large discrepancy in energy resolution between experimental results and theoretical estimation, finally, we show the best energy resolutions in liquid argon and xenon obtained so far with usual gridded ionization chambers in Table 1 Comparison between the best energy resolutions for 976 keV electrons and 570 keV gamma rays obtained experimentally and their theoretical limits
Ionizing radiation Fano factor Nex/Ni W (eV) Wsci (eV) Rtheor (keV) Rexper (keV)
Liquid Ar
Liquid Xe
976 keV electrons 0.11 0.21 23.8 19.5 3.7 28 [26]
570 keV gamma-rays 0.08 0.13 15.6 (15.8) 13.8 2.0 28 [26]
Rtheor: the theoretical limit of energy resolution, Rexper: the best energy resolution experimentally obtained so far.
Table 1 as well as the theoretical limits given by the above theory [25]. The energy resolutions shown in the table with electronic noise subtracted are the best values obtained by our group in liquid argon [10] and xenon [11]. They are about 10 times worse than the theoretically estimated resolutions. Here, we used the values of W and Wsci in liquid xenon which are obtained by using the new value of Nex/Ni = 0.13. The causes of this large discrepancy were discussed in [26], but remain incompletely understood. 6. Summary Questionable points on the energy resolution appeared in two recent papers [1,2] are clarified. Concerning [1], the constant value a, which shows a correct relation between Q and S, was given and, concerning [2], the Fano factor for a homogeneous liquid argon ionization calorimeter was directly derived. In addition, the use of the sum signals of ionization and scintillation is investigated and its advantage is suggested. The theoretical limits of the energy resolution for the sum signals and for scintillation signals are also given. References [1] E. Conti, R. DeVoe, G. Gratta, T. Koffas, S. Waldman, J. Wodin, D. Akimov, G. Bower, M. Bower, M. Breidenbach, R. Conley, M. Danilov, Z. Djurcic, A. Dologenko, C. Hsall, K. Wamba, O. Zeldovich, Phys. Rev. B 68 (2003) 054201. [2] C.W. Fabjan, Fabiola Gianotti, Rev. Mod. Phys. 75 (2003) 1243. [3] H. Crawford, T. Doke, A. Hitachi, J. Kikuchi, P.J. Lindstrom, K. Masuda, S. Nagamiya, E. Shibamura, Nucl. Instr. and Meth. A 256 (1987) 47. [4] T. Doke, H.J. Crawford, C.R. Gruhn, A. Hitachi, J. Kikuchi, K. Masuda, S. Nagamiya, E. Shibamura, S. Tamada, Nucl. Instr. and Meth. A 235 (1985) 136. [5] E. Shibamura, H.J. Crawford, T. Doke, J.M. Engelarge, I. Flores, A. Hitachi, J. Kikuchi, P.J. Lindstrom, K. Masuda, K. Ogura, Nucl. Instr. and Meth. A 260 (1987) 437. [6] T. Doke, A. Hitachi, J. Kikuchi, K. Masuda, H. Okada, E. Shibamura, Jpn. J. Appl. Phys. 41 (2002) 1538. [7] K. Masuda, E. Shibamura, T. Doke, A. Hitachi, J. Kikuchi, Phys. Rev. A 39 (1989) 4732. [8] S. Suzuki, T. Doke, A. Hitachi, A. Yunoki, Nucl. Instr. and Meth. A 245 (1986) 78.
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