Method for the measurement of the mean ionizing cross-section of fast particles and of the corresponding charge produced

2014 A method using a capacitive microphone as an ionization chamber enables the ionizing collision of a fast particle with a gas atom to be observed. The probability of this collision and the corresponding number of electrons removed were measured in air, for 4 MeV alpha particles leaving a radioactive source. Tome 39 N° 15 ler AOL1T 1978 LE JOURNAL DE PHYSIQUE LETTRES Classification Physics Abstracts 52.20H 35.80 Introduction. It has been shown in a previous paper [1] that a capacitive microphone can be used as an ionization chamber to investigate the ionizing action of fast particles in a gas. In fact, a particle reaching the outer plate of the microphone passes through it and creates a number of electron-ion pairs in the interelectrode space, which are carried off by the polarization electrical field to the external circuit. Actually, since the interelectrode distance is small, the effect of a particle is itself very weak and cannot be observed by itself : the method is therefore based on the measurement of a mean effect in the presence of a high flux of incident particles. It is summarized briefly here. Let x(t) be the effect, in the external circuit, associated with the arrival at random of an ionizing particle at the microphone. If all the effects are identical and if their frequency, p, is such that they are independent, the external circuit detects a total effect, X(t), whose mean values in time are given by Campbell’s theorems : Under these conditions, it is clear that the simultaneous measurement of the average value of X(t) and the mean square value of the fluctuation about this average allows the frequency of elementary effects and the amplitude of each to be determined. The frequency, p, is the product of the frequency of arrival of the particles, pi, and the probability that they ionize the gas located between the electrodes of the microphone. By varying the pressure until this probability is low, hence comparable to the probability of a single ionizing collision P( 1 ), it is then easy to conceive that the proposed method enables P(l) as well as the corresponding number of removed electrons to be measured. Experimental. The foregoing principle is applied by means of an experimental setup shown schematically in figure 1. A monoenergetic unidirectional beam of ionizing particles arrives at normal incidence, striking the active part of a capacitive microphone, located in a chamber filled with a gas of variable type and pressure. Through vacuum tight electrical passages, the polarization of the microphone is achieved by a power supply unit mounted in series with a picoammeter. The analog output of the picoammeter supplies a voltage, V(t), which is analysed in two separate circuits : one measures the d.c. compoArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019780039015025300 L-254 JOURNAL DE PHYSIQUE LETTRES FIG. 1. Experimental apparatus. A. Detailed diagram of the basic set up : a) diaphragm, b) back plate, c) hole for pressure equalization, d) housing, e) insulator, f ) Ti foil, g) 244 cm. B. Electronic block diagram. nent, Vo, of V(t) by means of a voltmeter; the second filters the a.c. component of V(t) in a frequency range Af centred on the value f, with gain 1/-~/A/, and measures its r.m.s. value, Vf averaged with an adjustable time constant. An analog system provides the ratios V021V f 2 and V f 2/ Vo at the input Y of a dual recorder for which the variable X consists of a signal proportional to the pressure. From equations (1) and (2) and the electrical block diagram, one can easily show that the signals Vo and V f are simply associated with the average charge, Q, deposited on the microphone plates after the passage of a particle, by equations : where h( f ) is the Fourier transform, at frequency f, of signal x(t) which, as f approaches zero, itself approaches the value h(O) given by the equation : where T is the transfer impedance of the picoammeter in the d.c. mode, CM designates the capacitance of the microphone, and Cin the input capacitance of the picoammeter. The ratio I h(f)/h(O) I depends exclusively on the electrical characteristics of the experimental setup, independent of the pressure and polarization voltage of the microphone. By means of prior calibration making it possible to determine this ratio and the values of Cin, CM and T, the recorded curves of Vo J V f and V]/Vo thus show respectively the relationship of p and Q with pressure. Let pi be the number of ionizing particles arriving per second at the microphone, and P(k) the probability that each of these particles makes k ionizing collisions between the electrodes, thus : where Z is the average number of electrons with charge e stripped during a collision. Equation (7) implies that the charge collected is strictly equal to the charge created, i.e. that there is neither avalanche nor recombination effect between the plates. As shown in reference [1], this condition can be satisfied with a careful choice of the polarization voltage of the microphone, for pressure values ranging in a ratio of 1 to 10. If one assumes that this range of pressures includes a value, Pc, at which the mean free path of the ionizing particles approaches the interelectrode distance, d, two alternatives occur. When p >> Pc, ~(0) -~ 0, p -~ pi, and the main contribution in equation (7) derives from the terms of high k values. If I,, denotes the specific ionization the charge created is : Curve ~(/?) is hence a line passing through the origin, if 7~ varies only slightly in the energy range of the incident particles corresponding to the assumed range of variations in p. On the other hand, when p Pc, P(O) is no longer negligible. When p ~ 0, it even happens that P(0) ~> P(1) > P(2),sothatp ~ pi P(l)/ ° Q Qo = Ze. In this pressure range, the measurement of p, compared to its saturation value, pi, gives the probability of an ionizing collision, related to the corresponding effective cross-section a(l) by the equation : where no denotes the neutral density and d the interelectrode distance. Note that, in relation to the usual measurements of total effective cross-section of elec-