Fluctuations of ionization losses in proportional chambers

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INSTRUMENTS

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(I974) 365-368;

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NORTH-HOLLAND

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F L U C T U A T I O N S OF I O N I Z A T I O N L O S S E S I N P R O P O R T I O N A L C H A M B E R S A. P. O N U C H I N and V . I . T E L N O V

Institute of Nuclear Physics, Siberian Division of the USSR Academy of Sciences, Novosibirsk, U.S.S.R. Received 15 July 1974 There is no theory describing the fluctuation o f the ionization losses at very small absorber thicknesses. Experimental widths o f ionization-loss distributions measured with proportional chambers are presented.

In some experiments proportional chambers are used for measurements of ionization losses. The pulseheight resolution of the proportional chamber itself is connected with the fluctuations of the ion-pair number at a constant absorbed energy and with the statistical character of the gas amplification process. It has been investigated well enough. The full width at halfmaximum is 1) 6 = 2.36 [(F + ~b)/fi]{ , where fi is the mean number of ions produced, F, Fano's factor, is equal to 0.05-0.4, cp is the relative variance of gas amplification which is nearly constant and usually equals 0.7. The pulse-height resolution from fast charged particles is due mainly to the fluctuations of the energy loss in a chamber. The problem of the fluctuations of the ionization energy losses in thin absorbers was treated by Landau2). It is not solved completely so far because the probability per cm, w(e), to transfer an energy e is unknown for e comparable to the atomic binding energy. Landau has found the solution for absorber thicknesses satisfying the following conditions:

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where ~=O.154 zopx/(Af12); fl=v/c; Zo, A, p, x are respectively the atomic number, the atomic weight, the density and the thickness of the substance; eo is the binding energy of an electron in an atom, era,, is the maximum transferable energy in one collision; ~ is expressed in MeV, p in g/cm 3, x in cm. The first condition means that the probability to create a f-electron with an energy about era,, is small. Vavilov 3) has found the solution without this restriction. The second condition means that many electrons are created with an energy of the order of the binding 365

energy. Their contribution to the fluctuation of ionization losses is negligible in this case and therefore the knowledge of w(e) in the region of small energy transfers is not necessary. If we assume that So is equal to the binding energy of the K-shell ( ~ 13.6Zo2) the condition (2) for monoatomic gases at N.T.P. may be rewritten in the form

x >>2fl 2 Zo.

(3)

F r o m eq. (3) it is clear that the condition (2) of Landau's theory is far from being satisfied when a charged relativistic particle passes through the usual proportional chamber with a thickness of about 1 cm. However, K-shell electrons constitute only a fraction of all atomic electrons, and the requirement (3) is somewhat exaggerated. Blunck and Leisegang have taken into account the "resonance" addition to the second moment of the expansion in Landau's theory. This correction leads to a broadening of the ionization-loss distribution, which is the greater with smaller thickness of an absorber. Blunck-Leisegang's corrections were calcul-

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A. P. O N U C H I N

ated in several works4-6). Shulek et al. 7) have found the analogous correction of Vavilov's distributiona). We would like to emphasize that Blunk-Leisegang's and Shulek's corrections do not shift the lower bound defined by the condition (2) to the region of smaller absorber thicknesses. This restriction was not pointed out in the above works4'7). At small absorber thicknesses w(e) must be known in the region of small e. Some information about w (e) can be obtained from the experimental data on photoabsorption 8). Fluctuations of ionization losses in thin absorbers were investigated experimentally by means of magnetic spectrometers 9-15) and proportional counters16-2°). In the latest works 12,14) from a series 9-1 s) it is concluded that the agreement between the experiments and

A N D V. I. T E L N O V

Landau's theory with Blunck-Leisegang's corrections is rather good. In refs. 16-20 disagreement between the experiments and calculations according to Landau's theory was pointed out. The comparison of the experiments and calculations taking the BlunckLeisegang corrections into account was performed for large thicknesses where the corrections were small. There is no conclusion concerning the non-validity of B.L.'s corrections for very thin absorbers. In the present work the pulse-height distributions from minimum ionizing electrons in different gases have been measured and comparison between the experimental results and the calculations according to Landau's and Blunk-Leisegang's theories have been made.

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Fig. 2. Pulse-height resolution of the proportional chambers as a function of gas thickness. Ordinates: the ratio of fwhm to the position of maximum. Experimental data: A - ref. 17, x - ref. 18, © - ref. 20, • - present work. C u r v e s - the results o f calculations according to L a n d a u ' s theory: (1) without account of inherent resolution of the chambers; (2) with account of inherent resolution; (3) with account of Blunck-Leisegang corrections and inherent resolution.

FLUCTUATIONS OF IONIZATION LOSSES The measurements were made using eight proportional chambers. All the chambers were placed in a stainless steel box as shown in fig. 1. The effective area of each chamber was 230 × 230 mm 2. Sense wires of 28 p m copper-plated tungsten were wound with 4 mm spacing. Hv planes were made of 50 #m bronzed wires with a spacing of 1 mm. The gap between sense and hv planes was 6 ram. The gap between neighbouring chambers was 20 ram. The box was pumped out by a high-pressure vacuum pump and was filled with the investigated gas to the pressure 1 or 2 atm. We have used a 9°Sr fl-source (Ema x = 2.2 MeV) collimated by steel plates. Minimum ionizing electrons were selected by a 2.5 mm plexiglass absorber in front of a plastic scintillation counter. The signal from the counter was used to trigger a pulse-height analyzer. All sense wires of each chamber were soldered together and connected with an emitter follower. The integration constant of the input circuit was 2.5 ps. Pulses from the necessary number of chambers were added by a linear summator and then the pulse-height analysis was carried out. Performance of the chambers and absence of the electronegative admixtures were controlled by pulseheight spectra of 5.9 keV X-rays from a 55Fe source. For all the gases used the fwhm was 20%. Measurements of ionization losses were carried out in the linear region of gas amplification. A high voltage on the chambers corresponding to the linear region of operation was found from the measurements of the pulse-height ratio from electrons incident perpendicularly and obliquely to the plane of the chamber and by the pulse-height ratio from 55Fe and 9 ° S r s o u r c e s . In fig. 2 we present the results of measurements of the pulse-height distribution width for the following gases: H e + 5 % CO2, N e + 5 % CO2, A r + 1 0 % CO2, X e + 1 0 % CO2, CO2. Data for a thickness greater than 9 cm are obtained at a pressure of 2 atm. The results obtained at 1 atm do not differ from those obtained at 2 atm. Data for Xe and CO2 have been obtained only for a pressure of 1 atm. The experimental results include the following systematic errors: l) Non-monochromaticity of electrons leads to a spread of the average energy loss of _+ 1%. 2) An angular divergence of the beam which is connected with the finite size of the collimator and multiple scattering on wires and gas leads to a spread of electron paths in the chambers. The estimations show that in our case this effect is negligible. This is confirmed by the fact that the widths of spectra were the same in all the chambers, In fig. 2 are also presented the experimental data

367

of other authors and results of calculations according to Landau's theory extrapolated to the region of small thicknesses. The parameter b 2 of the Blunck-Leisegang theory was calculated in accordance with refs. 5 and 6 by the formula b 2 = q A 2 a i z ~ i / ~ 2 , w h e r e q = 20 eV, z~ is the mean energy loss per 1 cm, al the fraction of electrons belonging to atoms with an atomic number zl. In the case of He the value 10z~ was replaced by 39.5 eV, the exact average binding energy in the He atom. The corrections of an inherent resolution of the chambers were calculated proceeding from the width of the pulse-height distribution from a 5SFe source (20 % for the energy 5.9 keV) and from the dependence of the resolution on the absorbed energy in a form 1/x/z1. The relative widths of the distributions by Blunck-Leisegang at 6 ~> 100% are presented formally since a part of the distribution passes into the region of negative losses. It should be noted that the theoretical calculation concerns the energy lost in a chosen layer while the experiment measures the energy absorbed in the same layer. Knock-on electrons produced in the walls or in the gas in front of the chamber may enter the chamber, or secondary electrons produced in the chamber may leave it without dissipation of all their energy. Our

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Fig. 3. Pulse-height resolution of the proportional chambers of 1.2 cm thickness as a function of gas atomic number. The results of measurements: A - ref. 17, • - present work. Curves calculations according to Landau's theory: (1) without account of inherent resolution of the chambers; (2) with account of inherent resolution; (3) with Blunck-Leisegang's corrections and without account of inherent resolution of the chambers; (4) with BlunckLeisegang's corrections and with account of inherent resolution of the chambers.

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A. P. O N U C H I N AND V. I. TELNOV

estimation shows that the contribution of this effect to the distribution widths is negligible. In fig. 2 one can see that the experimental values lie between Landau's and Blunck-Leisegang's curves. A difference between the experimental data and the calculations is large for small gas thicknesses and large Zo; with increasing absorber thickness the calculated curves approach the experimental points. Fig. 3 shows the dependence of the pulse-height resolution on the mean atomic number for one chamber of 1.2 cm thickness. Chambers with such a thickness are often used in experiments. Curves 3 and 4 are shown by the dotted line in the region of He since a considerable contribution to the resolution is given by the CO 2 admixture. Experimental values of 6 decrease with increasing atomic number up to Zo ~ 20 and then stay almost constant. This effect is surprising per se. It follows from this that for improvement cf the resolution polyatomic gases must be used rather than monoatomic with large z o. This is demonstrated by our results with CO2 shown in fig. 2. The discrepancy between the experiment and the theory exists also in the value of the most probable energy loss. For example in the A r + 10% CO2 mixture at 1.2 cm thickness the most probable pulse height is 10% smaller than that calculated according to Landau's theory. Blunck-Leisegang's corrections only increase this discrepancy. We would like to emphasize in conclusion that no theory exists which describes the fluctuations of the ionization energy losses for relativistic particles at gas thicknesses of the order of 1 cm under normal conditions, which are usually employed in proportional chambers. Extrapolation of Landau's theory together

with the Blunck-Leisegang corrections into the region of such small absorber thicknesses gives a considerable difference from the experimental results. With reference to the wide usage of gas instruments for the detection of particles we would like to urge theoreticians to consider ionization losses in very thin absorbers.

References 1) G. P. Alchazov, Nucl. Instr. and Meth. 89 (1970) 155. 2) L. Landau, J. Exp. Phys. (USSR) 8 (1944) 201. 3) p. Vavilov, Zh. Eksp. Teor. Fiz. 32 (1957) 920 [JETP 5 (1957) 749]. 4) O. Blunck and S. Leisegang, Z. Physik 128 (1950) 500. 5) O. Blunck and R. Westphal, Z. Physik 130 (195t) 641. 6) L. Spencer and U. Fano, Phys. Rev. 93 (1954) 1172. 7) p. Shulek, B. Golovin, L. Kulukina, S. Medved and P. Pavlovich, Yad. Fiz. 4 (1966) 564. 8) V.K. Ermilova, A . P . Kotenko, T.I. Merson and V.A. Chechin, Zh. Eksp. Teor. Fiz. 56 (1969) 1608. 9) p. White and G. Millington, Proc. Roy. Soc. (London) 120 (1928) 701. a0) W. Paul and H. Reich, Z. Physik 127 (1950) 429. 11) S. Kageyama and K. Nishimura, J. Phys. Soc. Japan 7 (1952) 292. i% S. Kageyama and K. Nishimura, J. Phys. Soc. Japan 9 (1953) 682. 13) F. Kalil and R. Birkhoff, Phys. Rev. 91 (1953) 505. 14) E. Hungerford and R. Birkhoff, Phys. Rev. 95 (1954) 6. 15) B. Shpinel, Zh. Eksp. Teor. Fiz. 22 (1952) 421. a6) P. Rothwell. Proc. Phys. Soc. (London) 64 (1951) 911. 17) D. West, Proc. Phys. Soc. (London) 66 (1953) 306. 18) P. Ramana Murthy and G. Demeester, Nucl. Instr. and Meth. 56 (1967) 93. 19) Z. Dimcovski, J. Favier, G. Charpak and G. Amato, Nucl. Instr. and Meth. 94 (1971) 151. 2o) S. Parker, R. Jones, J. Kadyk, M. L. Stevenson, T. Katsura, V.Z. Peterson and D. Yount, Nucl. Instr. and Meth. 97 (1971) 181.