Positrons*

Jean Thibaud, Paris

The positron was discovered by Anderson in studying the paths of ionizing particles of cosmic rays, photographed in a Wilson chamber. This discovery was confirmed by the experiments of Blackett and Occhialini. Later it became clear that these particles are also emitted from matter under the action of $\gamma$-rays[^1]. However, positrons are encountered by the experimenter comparatively rarely, and all our information about them has been obtained only from experiments with the Wilson chamber. Measurements of the curvature of positron tracks in a magnetic field and investigation of their length and ionization density have shown that these particles, in mass and charge (apart from the sign), are considerably closer to the electron than to the proton or to any other known positive particle.

Below I describe a method of investigation that makes it possible to obtain concentrated beams of charged particles emitted in large numbers by a small source, and some results obtained with the aid of this method in the study of positrons emitted from lead irradiated by $\gamma$-rays.

“The trochoid method”

Fig. 1 shows a longitudinal section, and Fig. 2 a transverse section, of my apparatus. The pole pieces of the electromagnet, facing one another, are separated by a gap, in the center of which the field strength reaches $10^4$ gauss; at the edges of the gap the field strength has a considerable radial gradient. In this peripheral region is placed the source $S$ (see below); charged particles emitted from $S$ in directions lying in a plane close to the plane of Fig. 2, under the action of the field, describe “trochoidal” trajectories shown in Fig. 2; in this process the particles emitted in almost all directions in the indicated plane or in planes close to it (with a scattering angle almost equal to $2\pi$!) are all collected in a small region $F$, diametrically opposite $S$, also in the peripheral part of the interpolar gap. This method makes it possible to obtain particles in quantities 100 or 1,000 times greater than any device in which deflection is produced by a homogeneous magnetic field.

* Physical Review 45, 781, June 1, 1934. Translated by V. L. Pulver.

The source of positrons (and electrons) consists of a narrow tube containing some powerful source of $\gamma$-rays (radon, a radium salt, or better a RaTh salt), enclosed in a lead “emitter” (rolled lead foil of thickness from

Fig. 1. Longitudinal section of the apparatus.

0.15 to 0.3 mm). The “receiver” $F$ (shielded from the $\gamma$-rays of the source $S$ by a lead screen of thickness from 10 to 15 cm, Fig. 1) may be a Geiger–Müller counter, an ionization chamber, or a photographic plate; I used chiefly the latter. It is enough to change the direction of the magnetic field, and electrons instead of positrons, or conversely, begin to fall on the plate (Fig. 6). Both produce on the plate the appearance of a very narrow line (Fig. 6), whose edge facing $S$ is bounded especially sharply, as is seen in the microphotogram of Fig. 3. The lines appearing under the action of electro-

Fig. 2. Cross-section of the apparatus and shape of the trochoidal trajectory.

Fig. 3. Microphotogram of a positron track.

rons and positrons are obtained as identical if the first particles are exposed 100 or 200 times less than the second. In order to verify whether the cause of the blackening of the film is particles flying along trochoidal trajectories, the following tests were carried out: a) displacement of \(S\) in the plane of Fig. 2 caused a symmetrical displacement of the line on the film; b) the position of the line (to a first approximation) did not depend on the strength of the magnetic field; c) the line became weaker when \(S\) was shifted in the direction toward the axis of the apparatus, where the magnetic field is uniform; d) on a film placed perpendicular to \(H\), curves of the expected shape are obtained; e) all particles passed through a narrow slit in a screen placed across the trochoidal trajectory of Fig. 2. Let us note that the direction of motion of the particles along the trochoid in the given magnetic field and the complete similarity of the tracks left by negative electrons and the new particles made it possible for us, from the very beginning, to conclude that the ratio of the charge of these particles to their mass is a positive quantity and of the same order as for negative electrons.

Deflection of Positrons in an Electric Field

In front of the photographic film \(F\), perpendicular to the axis of the trochoid, two grids were installed (Figs. 2 and 4); between them a potential difference \(V\) was applied, corresponding to which an electric field of strength \(E\) acted in the space between the grids, directed parallel to the axis of the trochoid and perpendicular to the magnetic field \(H\); this field caused a radial displacement \(x\) of the particle trajectories and, consequently, of the track on the film. The displacement \(x\) is proportional to \(\frac{E}{H}\) and to the time \(t\) during which the particles are in the space between the grids. The time interval \(t\) depends on the distance \(\theta\) between two neighboring turns of the trochoidal trajectory; the latter quantity can be controlled by changing the gradient of the magnetic-field strength in the space where the source and the trajectories are located, by shifting the source \(S\) in the radial direction. To a first approximation the formulas for \(\theta\) and \(x\) are as follows:

Fig. 4. Displacement of the trochoid under the influence of an electric field.

\[ \theta=\frac{\pi r\Delta H}{2H} \tag{1} \]

\[ x=\frac{4V}{300\beta\Delta H}, \tag{2} \]

where \(r\) is the radius of a turn of the trochoid, \(\Delta H\) is the difference in the strengths of the magnetic field on opposite sides of the turn, and \(\beta c\) is the velo-

...velocity of the particles \((0 < \beta < 1,\ c\) is the velocity of light). In formulas (1) and (2) the units are the centimeter, the volt, and the gauss*.

In the experiment the electromagnet had cylindrical pole pieces of diameter \(2\ \mathrm{cm}\); the width of the gap between them was \(3.5\ \mathrm{cm}\); the particles moved in a curved tube made of Pyrex glass (Fig. 5); in the figure the source \(S\) is visible on the right, and the film \(F\) on the left; the two grids \(G\) were placed parallel to the film and were at a distance of \(1\ \mathrm{cm}\) from one another. When a voltage was applied between the grids, the trace obtained when the film was bombarded by particles was displaced by approximately \(1\ \mathrm{mm}\) for every \(5{,}000\ \mathrm{V}\); Fig. 6, which shows the trace of positrons, shows a displacement of \(2.3\ \mathrm{mm}\) obtained as a result of changing the voltage from \(+5{,}000\) to \(-7{,}500\ \mathrm{V}\). When the direction of the magnetic field was changed, when electrons instead of positrons fell on the film, the trace was displaced by the electric field in the opposite direction.

Fig. 5. Photograph of the apparatus for obtaining positrons.

Measurement of the ratio \(\dfrac{e}{m}\) of positrons

Considering equation (2) together with

\[ Hr = \frac{\left(m_{0}c\,\dfrac{2}{e}\right)\beta}{(1-\beta^{2})^{1/2}}, \tag{3} \]

it is evident that \(\dfrac{e}{m}\) and \(\beta\) can be found if at all points of the trochoidal orbit \(r\) and the intensity of the magnetic field are known. The latter quantity was determined with the aid of a nickel plate of known magnetic susceptibility, suspended at various places in the interpolar gap; the radius \(r\) was measured by photographing the traces of positrons. Unfortunately, the velocities of the positrons for different particles were very different; the most probable value of their energy lies between 800 and 900 thousand electron-volts; the measured value of \(r\) is only an average value; the most that can be obtained from such an “absolute” measurement of the ratio \(\dfrac{e}{m_{0}}\) of the positron is that it lies between

* L. Cartan² showed that these formulas remain valid also for relativistic mechanics.

half and twice the value of the charge-to-mass ratio of the electron. A more accurate “relative” measurement was made by comparing the magnitudes of the displacement \(x\) of the positron and electron tracks. Plotting these values of \(x\) as a function of the voltage, we obtained straight lines shown in Fig. 7; their slopes, within the accuracy of the experiment, are the same, and consequently the quantities*

\[ \frac{\left(\dfrac{m_0}{e}\right)\beta^2}{(1-\beta^2)^{1/2}} \]

are also the same; comparing the mean values of the radii of the coils of the trochoids described by electrons and positrons, I came to the conclusion that the charge-to-mass ratio of the positron cannot differ by more than 15% from the same ratio for the electron.

Fig. 6.

\[ -7500\ \mathrm{V} \qquad\qquad +5000\ \mathrm{V} \]

Fig. 7. Determination of \(\dfrac{e}{m}\).

Passage of positrons through matter: scattering and absorption

The trochoid method and photometric measurements of tracks on photographic film (we used a self-recording microphotometer

* In expression (2), for \(x\), \(\Delta H\) is proportional to the gradient of the magnetic field and to the radius \(r\) of the trajectory. Thus \(x\) is inversely proportional to \(\beta r\), whence, according to (3), \(x\) is also inversely proportional to the quantity

\[ \frac{\left(\dfrac{m_0}{e}\right)\beta^2}{(1-\beta^2)^{1/2}} \]

(Shalonka and Lambert) are very convenient for studying the “absorption” of particles of matter. The law of blackening for positrons and electrons is the same,^3 and it has been verified that the density \(S\) of the track is proportional to the number of incident positrons over the entire range of the blackening curve up to \(S = 1\). In Fig. 7a are shown microphotograms taken from tracks obtained with three thicknesses of the absorbing substance (the absorbing screens were placed flush against the film):

Fig. 7a. Microphotogram of tracks of one and the same beam of positrons that passed through three layers of absorbing substance of different thickness.

it is clearly visible that the general character of the tracks (especially their asymmetry) remains unchanged.

For each element investigated, we plotted a graph in which along the ordinate axis we laid off the logarithm of the intensity of the beam of particles that had passed through the substance (or the photographic density of the track on the film), and along the abscissa axis—the mass of substance falling on \(1 \text{ cm}^2\) of the absorbing screen (in Fig. 9 a graph constructed for platinum is given). Usually the curves constructed in this way, within the limits from \(x = 0\) to \(x = 50 \text{ mg}/\text{cm}^2\), are concave toward the abscissa axis; subsequently they proceed rectilinearly over a considerable (but finite!) interval of \(x\), which allowed us to find in the usual way the absorption coefficient per unit mass \(\frac{\mu}{\rho}\).

Fig. 8. Absorption curve of positrons in air.

For a large number of the elements investigated (C, Al, S, Ca, Mn,

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Ni, Cu, Zn, As, Se, Mo, Pd, Ag, Cd, Sn, Ce, Ta, Pt, Au, Pb) the values found for \(\frac{\mu}{\rho}\) for particles whose velocity distribution was determined by the source RaTh selected by us fluctuated within the limits from 8 to 10; individual deviations are probably explained partly by errors of measurement, and partly by periodic changes of \(\frac{\mu}{\rho}\) as a function of the atomic number \(Z\). Negative electrons emitted from the same source (knocked out by the \(\gamma\)-rays of thorium from the atoms of the radioactive substances and from the surrounding lead foil) have an analogous absorption curve which, when plotted on a semilogarithmic scale, possesses a long rectilinear section*; in the example shown in Fig. 9 (lower curve), the value of \(\frac{\mu}{\rho}\) was obtained equal to 13.7.

Fig. 9. Absorption curves of positrons and electrons in platinum. The curved parts should be attributed to the action of photons.

The absorption of positrons in air was investigated by introducing air into the apparatus at various pressures and measuring the density of the tracks obtained on the film. In this case the total length \(L\) of the trajec-

* It has long been known that a nonuniform electron beam, like ours, can be absorbed according to an exponential law (to which a rectilinear curve corresponds on a semilogarithmic scale).

of the farther trajectory was calculated by the formula \(L=\dfrac{4\pi RH}{\Delta H}\), where \(R\) is the distance of the source \(S\) from the axis of the apparatus (Fig. 2). The semilogarithmic curve corresponding to this case is shown in Fig. 8; it is concave* downward for small values of \(x\) and soon becomes rectilinear; in good agreement with the results of absorption measurements in solid substances, the value of \(\dfrac{\mu}{\rho}\) for air was found to be 8.5.

Our conclusions amount to the following: when positrons pass through matter, so long as the thickness of the layer of the latter does not exceed \(500\ \mathrm{mg/cm^2}\), these particles behave in the same way as negative electrons, undergoing the same scattering and slowing down as a result of their interaction with atomic electrons and nuclei**. At the same time, with a further increase in the thickness of the screens, the behavior of positrons differs sharply from the behavior of negative electrons.

Radiation Arising in Braking and Annihilation

Returning to Fig. 9, we see that the rectilinear portions of both absorption curves pass, at large thicknesses, into curves turned with their convexity downward and tending toward not quite horizontal asymptotes. This can be explained by the fact that the action on the film of photons arising under the influence of particles flying inside the metal becomes noticeable in comparison with the action of the particles themselves, which, before reaching the film, traverse the entire thickness of the metal. In the case of negative electrons these photons should be identified with the well-known x-radiation (both characteristic and continuous), arising in collisions of fast electrons with atoms of matter. The blackening of the film under the action of these photons is very weak; it amounts to only \(\dfrac{1}{7500}\) of the blackening density of the primary beam when the absorbing substance is absent. This is not surprising if one recalls the small “yield” (a few percent) of the x-radiation of platinum bombarded by electrons of such velocities. Comparing the two curves of Fig. 9, it is evident that the photons appearing under the influence of positrons have a considerably greater effect.

* Curves of this kind were obtained with negative electrons by Crouser[^1].

** We note that the trochoidal trajectory enters the solid absorbing screen almost parallel to the surface of the latter; however, from the scattering of positrons, which begins immediately after the particles enter the matter, it may be assumed that the thickness of the screens corresponds to the path which the positrons traverse in the metal. This assumption is confirmed by the agreement of the values obtained from measurements with solid bodies and with air.

When the platinum thickness exceeds \(500\ \mathrm{mg/cm^2}\) (when even more than \(1\%\) of the incident positrons pass through), the presence of intense and highly penetrating radiation is evident. At its maximum it produces on the film a blackening amounting to \(\dfrac{1}{180}\) of the blackening density due to the primary beam, i.e., almost fifty times stronger than that caused by the photons arising under the action of negative electrons (this difference is clearly seen from the fact that, with an absorbing layer of \(100\ \mathrm{mg/cm^2}\), equal blackening from positrons and electrons is obtained when the exposure of the former is 200 times greater than that of the latter, whereas at \(1000\ \mathrm{mg/cm^2}\) the exposure ratio is only 4). At the same time the appearance of the trace on the film changes: the initially narrow “line” (Fig. 3) broadens greatly and loses the sharp outline of its edges and of the central maximum of blackening. From this we concluded that the trace of the directly transmitted part of the positron beam is masked by secondary radiation (photons) proceeding in all directions.

The mean value of the frequency of this new radiation could be found from the slope of the above-mentioned not quite horizontal asymptote (Fig. 9). Most of the photons apparently arise near the front surface of the absorbing metal,* whereas a large part of their photographic action is probably due in origin to secondary electrons knocked out near the rear surface and flying from the metal onto the film. We arranged the screens in such a way that the rear surface of the metal was pressed against the film, but so that at the same time the front surface was always at the same distance from the film; these apparently contradictory requirements were fulfilled by using several screens placed at appropriate distances from one another and playing the role of an absorbing substance of varying thickness. Using King’s functions, one can calculate what fraction of the energy emitted (in the form of photons in all directions), after absorption in screens arranged in the above-described manner, causes the appearance of secondary electrons reaching the film; this remaining fraction proves to be close to 0.05.

Experiments carried out in this way with thicknesses of absorbing substances reaching \(1700\ \mathrm{mg/cm^2}\) gave, for the photon absorption coefficient, the value 0.2. This result was confirmed

* This follows from the very strong scattering of particles that occurs shortly after they enter the metal; therefore, at a very small distance \(s\) from the front surface of the metal, one can find particles already traveling in the metal at distances \(L\) considerably exceeding \(s\) and approaching the end of the free path and final annihilation. Our measurements show that in platinum half of the positrons are scattered sideways already at a depth of \(0.0035\ \mathrm{cm}\). At a thickness of \(0.05\ \mathrm{cm}\) or more, corresponding to a density of \(1000\ \mathrm{mg/cm^2}\), only very few positrons pass through the metal unscattered. The center of photon emission, therefore, proves to be very close to the front surface.

by direct counting of the photons passing through the absorbing substance, using a Geiger counter placed in place of the film (in this case much trouble was caused by the γ-rays emitted by the radioactive substances of the positron source). The value of the absorption coefficient 0.2 leads to the conclusion that the photon energy is close to 0.5 MEV (1 MEV = \(10^6\) electron-volts). The energy of the X-ray photons arising under the action of negative electrons is sufficiently close to the indicated value to justify our assumption of the identical photographic action of individual photons both of the radiation appearing under the action of electrons and of positrons. It follows from this that positrons cause the appearance of photons in a quantity 50 times greater than electrons.

We know the yield of X-rays when antikathodes consisting of different substances are bombarded by electrons of various velocities. From this one can roughly find the expected number of X-ray photons appearing as a result of the bombardment of the various absorbing substances, appearing in these experiments, by negative electrons whose velocities have some distribution near a mean value close to 0.4.*

In the case of platinum, approximately one photon corresponds to every 25 electrons. Multiplying this number by 50, we obtain about two photons for each positron. Such is the “yield” of this additional process characteristic of positrons. To obtain more accurate figures it is necessary to know more precisely the energy distribution of the negative electrons.

Our two principal conclusions—that the photon energy is close to 0.5 MEV, and that their number exceeds the number of positrons by a factor of 2—are evidently entirely compatible with the theory according to which these photons arise in the annihilation of positrons with negative electrons (the latter, apparently, are taken from among those present in the metal), with each such process producing two photons, between which is divided the energy equivalent to the rest mass of both particles. Because if two particles of opposite sign, moving with negligibly small velocities, collide and, being annihilated, are converted into radiation—

* These electrons have a continuous spectrum of velocities extending up to 2 MEV, and, in addition, separate “lines” of photoelectric origin. The “practical mean velocity” possessed by the electrons that have overcome the thin surface layer of platinum was found from the absorption coefficient indicated above (\(\mu/\rho = 13.7\)). We determined this coefficient for Al, after which, taking the corresponding velocity of the electrons from Lenard’s tables, it turned out that the value of \(\beta\) is somewhat less than 0.85, which corresponds to an energy of about 0.4 MEV. We calculated the yield of radiation of this energy from the formula \(C \cdot Z \cdot U\), taking \(Z = 78\) (atomic number of Pt), \(U = 0.4\) MEV (energy of the electrons), taking the constant \(C = 10^{-6}\), and dividing the quantity \(C \cdot Z \cdot U\) by the average photon energy found. Such a calculation is justified by the results of measurements\(^7\) of the X-radiation arising under the action of β-rays of radioactive substances. We neglected the influence of the \(K_\alpha\) line, weakened by absorption tens of times.

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then, in this case, two identical photons must fly off in opposite directions, in order that conservation of momenta take place. Each quantum must possess half the energy concentrated before the collision in the rest masses of the two particles, equal to 1.2. In the preceding discussion, by “negligibly small velocities” one should understand those to which there corresponds a kinetic energy very small in comparison with 0.5 MEV; it is natural to suppose that positrons and electrons are especially “inclined” to merge when their velocities are small precisely in this sense.

All that has been said permits us to conclude that we now have the most evident proof of all that have existed up to now of the transformation of electric charges, or, in other words, of the transformation of matter into radiation—a process that has often been assumed in recent years and that is an extraordinarily fruitful hypothesis in many cosmogonic theories. This process is directly opposite to the process of transformation of radiation into electric charges, first postulated by Dirac, who assumed that it occurs in many cases when positrons are observed. For example, when these particles are emitted during the bombardment of heavy metals by γ-rays. However, this commonly assumed process, in the latter case, is not the direct opposite required to explain the experiments described in the present paper. In these experiments, when two particles merge, apparently two identical photons arise, whereas in the case mentioned above one photon causes the appearance of two particles. The transformation of one photon into two particles violates conservation of momenta unless this process, taking place in the immediate vicinity of a nucleus, imparts some momentum to the latter; generally speaking, one may suppose that this occurs. At the same time it seems (from the experiments described in the literature) that the transformation of photons into charged particles occurs chiefly under conditions in which atomic nuclei take part in the phenomenon, whereas the transformation of particles into a photon is a predominantly closed process, occurring without the participation of nuclei**.

* Gray and Tarrant, as well as other authors, observed radiation emitted by metals irradiated with γ-rays, which they attributed to this process. It was assumed that the positrons involved in this phenomenon are created by photons of γ-rays (together with electrons) inside the metals. Joliot⁸ likewise observed, by the absorption method, radiation of the same nature emitted by metals when bombarded with positrons. He used a Geiger counter for observation, and a considerable part (86%) of the observed radiation apparently was produced as a result of parasitic phenomena, possibly from contamination of the laboratory charge (see my critical remarks⁹); the photographic method eliminates these sources of error.

** See the references at the end of note 1; see also the papers of Oppenheimer and Plesset¹⁰.

*** This view is confirmed by the observations of Gray and Tarrant, who, on the basis of their experiments, came to the conclusion that photons with an energy of 0.5 MEV appeared in considerably greater quantity than photons with an energy of 1 MEV.

Range of Positrons Before Transformation

The positron differs from its negative “twin” by a very short “mean duration of existence,” ending with its transformation into radiation. We are entitled to maintain that, generally speaking, this difference may not be essential, but has simply resulted from the considerable predominance of electrons in the universe that we know. If the orbital electrons of atoms were positive instead of negative, then it would probably be the former that had the short duration of existence.

From the curves of Fig. 9 we conclude that the free path of positrons before transformation is, in platinum, at least \(0.03\ \text{cm}\); it corresponds to a layer of metal with a total density of \(600\ \text{mg}/\text{cm}^{2}\); at the same time our measurements in air give for the range the value \(640\ \text{mg}/\text{cm}^{2}\) (at least \(500\ \text{cm}\) of air at normal temperature and pressure). The very close agreement of these two numbers leads to the conclusion that the interaction of positrons with electrons consists both in slowing down and in their final transformation into radiation.

Positrons of Radioactive Substances

We found that a thin-walled glass ampoule containing radon emits more positrons than our source, which consisted of the same ampoule enclosed in lead[^1]; an analogous result is obtained with a RaTh ampoule. It is hardly the thin glass walls, consisting of light elements, that are the cause of this radiation. We see its cause in phenomena occurring in the radioactive substance itself; possibly—in the transformation of \(\gamma\)-rays into positrons, and perhaps in collisions of \(\alpha\)-particles with nuclei.

Several years ago I observed[^2] photons of \(\gamma\)-rays with energy \(0.507\ \text{MeV}\), emitted by RaC- and ThC\('\)-substances, in whose \(\gamma\)-spectra radiation with energy considerably exceeding \(1\ \text{MeV}\) is present. It is quite plausible to suppose that these \(\gamma\)-rays may arise during the transformation into radiation of “natural” positrons emitted by the radioactive substance itself and transformed into radiation before they emerge outside.

Literature

1. Anderson, Science 76, 238, 1932; Blackett and Ochialini, Proc. Roy. Soc., A 139, 699, 1933; Anderson and Neddermeyer, Phys. Rev. 43, 1043, 1932; Curie et Joliot, C. R. 196, 1581, 1933; Meitner and Philipp, Naturwiss. 24, 468, 1933; history of the discovery and reviews: Blackett, Natur 132, 917, 1933; Darrow, Rev. Sci. Inst. 4, 263, 427, 1933; M. 5, 115, 1932; Scientific Monthly 38, 1, 1932.

2. L. Cartan, C. R. 197, 1604, 1933.

3. Thibaud et Dupré la Tour, C. R. 198, 805, 1934.

4. See, for example, K. W. F. Kohlrausch, Radioaktivität, p. 367, Handb. d. Physik.

5. Thibaud, C. R. 198, 562, 1934.

6. Crowther, Proc. Roy. Soc., A 80, 186, 1908.

7. J. A. Gray, Phys. Rec. 25, 237, 1925.

8. Joliot, C. R. 197, 1622, 1933.

9. Thibaud, C. R. 198, 562, 1934.

10. See also Oppenheimer and Plesset, Phys. Rev. 44, 53–55, 1933.

11. Thibaud, C. R. 197, 915, 1933.

12. J. Thibaud, Thesis, Paris, 1925; see C. R. 198, 562, 1933.