Alpha-Particle Ionization in Mixtures of the Noble Gases

Abstract

However, expressions for secondary yields and energy losses based upon this cross section actually vanish since, in this approximation, o-q is zero, a fact not recognized in previous theories. This is an immediate consequence of the orthogonality relation between the lattice eigenfunctions belonging to k and k+2-n-q/a, J tktk+2irqfa*dT = Q.Substitution of Eq. (3) into Eq. (7) yields 7FS m , n a n (k)d m *(k+27rq/a)J > exp[(27r^)(n-q-m)'r]rfr = 2 m a m+q (k)a m *(k+27rq/a)-0. (8) Substitution of Eq. (8) into Eq. (6) yields a zero cross section. In order to obtain a finite result, it is necessary to take into account the variation of a m (k') with K'. This can be accomplished by a Taylor series expansion of a m (W) about the point k , = k+27rq/a. This results in a cross section which for sufficiently high energies has the same form as that obtained by Be the 3 for the ionization of atoms, namely, <r q =U/£)ln(£/£'),where E is the energy of the primary electron and A and E r are parameters characteristic of the medium. A similar expression is obtained for the rate of energy loss by electrons passing through solids. These results are entirely different from those obtained on the basis of Eq. (4) ; which have previously been interpreted 1 ' 2 to mean that both the rate of production of secondaries and the rate of energy loss should be practically independent of the energy of the primary. Actually, these quantities are zero in the approximation leading to Eq. (4), and as indicated by Eq. (9) and the equivalent expression for the energy loss, they decrease rapidly with energy. It should be pointed out that the above considerations do not apply to the case of free electrons (q=0), which has been treated by Baroody 4 and by Dekker and van der Ziel 2 , since values of S in the neighborhood of S m i n are forbidden because they correspond to transitions to occupied states.The questions outlined here will be treated in more detail in a forthcoming paper. * Supported by the ONR. i D. E. Wooldridge, Phys. Rev. 56, 562 (1939). 2 A. J. Dekker and A. van der Ziel, Phys. Rev. 86, 755 (1952). 3 H. Bethe, Ann. phys. 5, 325 (1930). 4 E. M. Baroody, Phys. Rev. 78, 780 (1950).ARGON CONCENTRATION-PTS PER 10,000 BY VOLUME FIG. 1. Ion pairs collected per alpha-particle as a function of argon concentration in helium. Runs A and O represent commercial "spectroscopically pure" He. Run X represents this He after further purification.average energy W to produce an ion pair is, of course, the energy of the polonium alpha-particle (5.298 Mev) divided by this number.The ionization chamber was pumped and baked for twelve hours at a temperature above 200°C at the beginning of the measurements, and extreme care was taken to minimize gaseous impurities from the system.The graph in Fig. 1 shows the effect on the ionization produced per alpha-particle of adding extremely small quantities of argon to pure helium. The ionization per alpha-particle at first increases rapidly with increasing argon concentration and then more slowly, apparently approaching ...

First Results of Using a UVTron Flame Sensor to Detect Alpha-Induced Air Fluorescence in the UVC Wavelength Range

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Gaseous and dual-phase time projection chambers for imaging rare processes

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Penning transfer in argon-based gas mixtures

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