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

What is Internal Conversion?

It is a process which enables an excited Nuclear state to come down to some lower state with out emission of a Gamma Photon. The energy ∆E involved in this Nuclear transition gets transferred directly to bound electron of atom. Such a electron gets knocked out of atom. Electrons like this are called conversion electrons and the process is called internal conversion.

It is interesting to note that wave mechanically, an atom electron spends part of its time inside a nucleus. This probability is highest for K-shell electrons which are closest to Nucleus. For such a case, Nucleus may de excite not by Ɣ- emission but by giving excitation energy ∆E directly to a K-shell electron.

Internal conversion is also possible for higher atomic levels L,M etc.

The kinetic energy of converted electron 'Ke' is Ke=∆E-Bₑ

  Bₑ - atomic binding energy of electron

∆E = Ei-Ef ; Nuclear Excitation energy

Usually continuous 𝜷-spectra are super imposed by discrete lines due to conversion.

It was wrongly believed that internal conversion process is like Photoelectric effect; a Ɣ-photon emitted by a nucleus is absorbed by orbital electron which is emitted as in photoelectric effect.

The simplest situation which disproves this is a transition between two states having spin equal to zero.

A 0→0 transition (∆I=0) is forbidden for all multipole orders and so Ɣ-emission by nucleus is completely forbidden.

However 0→0 transition is readily found to proceed by internal conversion. The experiment was performed on 0.7MeV level of ⁷²Ge. This is a 0→0 transition and it was found that conversion electrons can be detected, but there is a complete absence of Ɣ- ray emission.

In 1932, Taylor and Mott suggested that transition probability 'λ' from a Nuclear state 'a' to a Nuclear state 'b' is sum of two terms

λ=λₑ+λᵧ

λₑ & λᵧ are partial decay constants for conversion electron emission  and for gamma emission respectively.

Ratio between two decay constants is called conversion coefficeint and is measured as ratio between total number of conversion electrons emitted  (N) and total no. of gamma rays (N) emitted in same transition over the same time.

Conversion Coeff(α) = Nₑ/Nᵧ=  λₑ/λᵧ

 value of 'α' is found to depend on transition energy, multipole character of transition and atomic number Z.  

Born-Haber Cycle