Discovery of the Positron

Michela Filaoro

March 17, 2014

Abstract

This paper presents with a study of cosmic-ray tracks the evidence of the existence of light

positive particles, the positrons, confirming the Dirac’s theorical prediction. Below it presents

a historical background and the Anderoson’s experiment which gave a esperimental evidence

of the positrons existence.

1 Historical introduction

In 1928 Dirac pubblisched his relativistic equation which combined quantum theory and special

relativity to describe the behaviour of an electron moving at a relativistic speed. The equation

would allow whole atoms to be treated in a manner consistent with Einstein’s relativity theory.

Dirac’s equation appeared in his paper The quantum theory of the electron, received by the

journal Proceedings of the Royal Society A on 2 January 1928. It won Dirac the Nobel prize

in physics in 1933. In this equation emerged the propriety of the electron that we describe as

’spin’. However, it was soon found that the equation provided for the existence of four differnt

states of the electron and not the observed two (spin up and down). The two additional

states described an electron with negative energy. These states correspond to a particle with

a positive electric charge.

2 January 1928 Dirac interpreted the equation to mean that for every particle there exists

a corresponding antiparticle, exactly matching the particle but with opposite charge. For

the electron there should be an ”antielectron” identical in every way but with a positive

electric charge. In his 1933 Nobel lecture, Dirac explained how he arrived at this conclusion

and speculated on the existence of a completely new universe made out of antimatter: If we

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accept the view of complete symmetry between positive and negative electric charge so far

as concerns the fundamental laws of Nature, we must regard it rather as an accident that

the Earth (and presumably the whole solar system), contains a preponderance of negative

electrons and positive protons. It is quite possible that for some of the stars it is the other

way about, these stars being built up mainly of positrons and negative protons. In fact, there

may be half the stars of each kind. The two kinds of stars would both show exactly the same

spectra, and there would be no way of distinguishing them by present astronomical methods.

1 September 1931 Paul Dirac published a paper mathematically predicting the existence

of an antielectron that would have the same mass as an electron but the opposite charge. The

two particles would mutually annihilate upon interaction. He wrote:

This new development requires no change whatever in the formalism when expressed in terms

of abstract symbols denoting states and observables, but is merely a generalization of the pos-

sibilities of representation of these abstract symbols by wave functions and matrices. Under

these circumstances one would be surprised if Nature had made no use of it.

2 Experiment setup

The experiment setup is made of a cloud chamber whith a lead plate in the presence of a

magnetic field. The cloud chamber, also known as the Wilson chamber, is a particle detector

used for detecting ionizing radiation. The lead plate is used to slow dawn the particles and

the magnetic field to curve the particle path.

When an ait mass satured with water vapor is borne upwards by convection currents it

expands adiabaticcaly temperature falls.The excess amount of water vapor separates out in

the form of liquid drops which appear as cloud of fog. The Wilson cloud chamber operates on

a similar principie. In this istrument a definite volume of non condensable gas satured with

a vapor is suddently expanded. The result is that the gas, now at the lower temperature ,

conteins more vapor than it can hold in the satured state, it is supersatured. When ionizing

particle passes trought the supersatured the supersatured vapor in the chamber,it leaves a trail

of charged particles (ions) tha served as condensation centre fot the vapor which condenses

around them. The path of radiation is thereby indicated by tracks of tiny liquid droplets in

the supersatured vapor.

When any uniform magnetic field is applied across the cloud chamber, positively and negatively

charged particles will curve in opposite directions, according to the Lorentz force law with two

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Figure 1: cloud chamber

particles of opposite charge.

3 Experiment

The figure 3 is a picture of one of the first positron tracks observed by Anderson in 1933.

The band across the middle is the lead plate, which slows down the particles. The radius

of curvature of the track above the plate is smaller than that below. This means that the

particle is travelling more slowly above the plate than below it, and hence it must be travelling

upwards. From the direction in which the path curves one can deduce that the particle is

positively charged. Since the particle lost same of its kinetic energy in the plate, its speed

decreased and the curvarture of the path increased after the plate had been traversed.

That it is a positron and not a proton can be deduced from the long range of the upper

track - a proton would have come to rest in a much shorter distance. The reason that this

interpretation seemed so inevitable is that the track appearing on the upper half of the figure

cannot possibly have a mass as large as the proton for as soon as the mass is fixed the energy is

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Figure 2: Cloud Chamber of Carl Anderson

at once fixed by the curvature. Infact, the equation of a charged particle moving in a magnetic

field is:mv2

r= qvB

The energy of a proton of that curvature comes out out 300,00o volts, but a proton of that

energy according to well establisched and universally accepted determinationshas a total range

of 5mm in air while that portion of the range actually visible in this case exceeds 5cm without

a noticeable change in curvature.

4 Other evidence of positrons existence

It was later found that certain artificial radioactive isotopes emit positrons, for example an

isotope of phosphorus:

15P30 →14 Si

30 + e+

In this process, which is called (β+emission, a proton in the nucleus transforms into a neutron

and a positron (and another particle, as we shall soon see). According to Dirac’s theory, a

photon of energy greater than 1.022 MeV (double the rest mass of the electron) could turn

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Figure 3: A 63 million volt positron (Hρ = 2.1 ∗ 105 gauss-cm) passing through a 6 mm lead plate

and emerging as a 23 million volt positron (Hρ = 7.5∗104 gauss-cm). The length of this latter path

is at least ten times greater than the possible length of a proton path of this curvature.

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Figure 4: A positron of 20 million volts energy (Hρ = 7.1104 gauss-cm) and a negatron of 30 million

volts energy (Hρ = 10.2104 gauss-cm) projected from a plate of lead. The range of the positive

particle precludes the possibility of ascribing it to a proton of the observed curvature.

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into an electron-positron pair, and the phenomenon was indeed observed in cosmic rays. This

process cannot occur in a vacuum, since it cannot then obey both the conservation of energy

and momentum. (For example, suppose that the photon energy is exactly 1.022 MeV. If it

turns into an electron-positron pair the particles would have to be at rest, since all the photon

energy would be converted to mass, leaving nothing for kinetic energy. Thus, the particles

would have zero momentum, meaning that all the original momentum of the photon had

vanished - which is contrary to the law of conservation of momentum.*) Thus the process -

called ’pair production’ - can only take place in matter in the vicinity of a nucleus which can

take up the excess momentum of the photon. This is one of the processes by which energetic

gamma rays lose energy in passing through matter. The positron formed in this way does not

survive long. When it collides with an electron a process known as ’annihilation’ occurs, the

two particles disappearing and transforming into a number of photons:

e+ + e− → nγ

Pair production and annihilation are impressive illustrations of the equivalence of mass and

energy, and of the fact that the difference between a particle with mass and one without mass

is not so crucial after all.

5 References

Carl D. Anderson The Positive Electron, Phys. Rev. 43, 491, 1933

Yuval Ne’eman, The particles hunters, Cambridge University Press, 1996

Wikipedia, claud chamber

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