Pair Production - Conversion of Radiation into Matter

The cloud chamber experiments revealed that a Photon can give up its energy to materialize as two electrons of opposite charge. Certainly the Photon must have an energy of atleast 2mₑc² in order to produce a pair.

No photon, regardless of its energy, can produce a pair in a perfect vacuum.

Pair Production is strictly an Electromagnetic Process. It seems to occur mostly in the intense electric field near the nucleus rather than inside the nucleus.

At higher energies or with heavy targets it is typically reasonable to ignore the energy transferred to target, so that nearly all energy from Photon goes to electron-positron pair.

Energy equation

h𝜈 → 2mₑc²+E1+E2

holds approximately.

 mₑc²→ rest energy of each electron

 E1, E2 → Kinetic Energies of particles

 The heavier the target, the more nearly the equation is satisfied. 

Pair Production can occur in the vicinity of an electron.

Pair Annihilation

Positron and Electron coalesce to produce atleast two photons

e⁺ + e⁻→2𝛾

Annihilation into three or more Photons is possible but less likely. Each extra photon tends to supress the rate of annihilation by a factor of order of magnitude of fine structure constant 1/137.

A Positron moves thru matter and forms ion pairs giving up energy in the process. There is about 2% chance that a Positron will hit an electron and annihilate.

But more likely output is that Positron will stop and become attracted to an electron. The atom formed by these two particles is called Positronium.

The Positron-Electron system drops into successively lower energy states, emitting (low energy) photons, until it arrives in ground state.

Properties of Positronium

The lowest Bohr orbit of Positronium is one for which n=1 and l=0, so that the lowest is an S-state.

The S state has fine structure due to the spins of particles; when the two spins are oppositely directed, the atom is in a ¹S state. When the two spins are parallel, it is in a ³S state, and has higher energy.

The triplet state is a meta stable state and has longer life time than singlet state.

The life time of singlet state was revealed by J.Pirenne, J A wheeler and is of order 10⁻¹º Sec.

The life time of Triplet state was revealed by Ore & Powell and is about 1.4x10⁻⁷ Sec.

Annihilation radiation emitted by combination of electron-Positron pair in ¹S state should consist of two gamma ray photons emitted simultaneously.

Radiation from ³S state of this system should consist of 3 𝛾 ray Photons emitted simultaneously.

The first experimental evidence for formation of Positronium was obtained by M. Deutsch, who observed time delay between emission of Positron from ²²Na and appearance of annihilation photon from substance in which Positrons are observed. Several gases N₂, O₂ etc are used as absorbers of Positrons. The time delay is due to formation of Positronium.

Properties of Pions

• Pions are Mesons
• There are 3 kinds of Pions: π⁺, π⁻, π⁰
• Either charged Pion possess a mass of 139.6 MeV and neutral Pion is 135.0 MeV.
• Pions have spin zero.
• P+P → π⁺ + n + P
• P+P → π⁰ + P + P
• P+n → π⁻ + P + P

• Charged Pions decay into Muons (Weak Process in Decay):

π⁺ → 𝜇⁺ + 𝜈

π⁻ → 𝜇⁻ + 𝜈

• The mean life is 2.6 x 10⁻⁸ Sec. 

• The neutral Pion decays in different way; process is 

π⁰ → 𝛾 + 𝛾 ; This decay is Electromagnetic in nature.

The presence of photons in final state leads us to expect the process is electromagnetic in nature.

The Photons from the decay always seem to come from the spot at which π⁰was produced in some bombardment process. The measurement of life time of such a short lived object is not easy but emulsion techniques provide enough spatial resolution so that in case of rare decay modes

 π⁰ → 𝛾 + 𝛾

π⁰ → 𝛾 + 𝛾 

it is barely possible to measure separation of electrons from place at which  π⁰ was produced.

•  The mean life of  π⁰ is about 0.89 x 10⁻¹⁶ Sec.

 

CLASSIFICATION OF ELEMENTARY PARTICLES

How to calculate Electric Field from a Uniform Plane Sheet of Charge?

Assume that the sheet is infinite in extent and that the charge per unit area is 𝛔.

Considerations of symmetry lead us to believe that a field direction is every where Normal to Plane and if we have no field from any other charges in the world, the fields must be same in magnitude on each side.

Let us choose a Gaussian surface - a rectangular box that cuts thru the sheet as shown in figure below.

The field is Normal to these two faces. The two faces parallel to sheet will have equal areas say A.

As the electric field 'E' is parallel to area element dS;

∫E.dS = E∫dS = EA

The total flux from two faces is given by

∫E.dS1 + ∫E.dS2 = EA+EA

The total charge enclosed in the box is  𝛔A.

So according to Gauss Law, EA+EA = 𝛔A.

E=𝛔/2𝛆₀