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.  

BETA DECAY

There are 3 models of beta radioactivity

i) Negatron (β^-) Emission

ii) Orbital Electron Capture

iii) Positron (β⁺) Emission

BETA SPECTROSCOPY

Beta ray spectra is of two types:

i) Continuous Spectrum

ii) Sharp Line Spectrum

The continuous spectrum is due to Negatrons and Positrons.

There is a possibility of the daughter nucleus being created in an excited state, which may decay by gamma emission.

Rutherford suggested that part of gamma radiation is absorbed by outer electrons of same atom and as a result the secondary beta ray electrons are ejected.  The process is called “Internal Conversion”.

The sharp Line Spectrum is due to secondary beta rays emitted due to internal conversion.

The process of Beta disintegration differs from alpha disintegration in following two respects:

i) The alpha particles are already present in the initial nucleus while beta particles are not present in the initial nucleus. Beta particles are created at the time of emission.

ii) The energy spectrum of alpha particles is discrete while energy spectrum of beta particles is continuous.

iii) Beta decay is a three body problem while alpha decay is a two body problem.

In the Neutrino, the spin and angular momentum vector are oppositely directed and in anti neutrino these vectors are aligned together.

Since a matter-antimatter pair is formed whenever energy is converted into mass, in a conversion of a nuclear Neutron to a Proton, the negative electron (matter) should accompany anti neutrino (anti matter). Similarly Neutrino is emitted with positron emission and orbital electron capture.

FERMI THEORY OF BETA DECAY

In 1934, Fermi made a successful theory of beta decay. The theory is based on following assumptions:

1) The light particles, the electron and neutrino ar created by transformation of a neutron into a proton in a nucleus or vice versa.

Note:- Neutron or Proton that are transformed to beta particles are not free particles but are bound to Nucleus by Nuclear Forces.

2) The energy remains conserved in decay process, the available energy being shared among the electron and the neutrino.

3) The beta decay process is analogous to the emission of electromagnetic radiation by an atom, with electron-neutrino field acting in place of Electromagnetic field.

4) “Electron-Neutrino” field is weak in contrast to short range strong interactions which exist between Nucleons bound in the nucleus.

5) Time   Dependent Perturbation theory is a very good approximation because of smallness of coupling constants.

6) As Nucleons move with velocities of only nearly c/10 in nuclei calculations can be made with non relativistic nuclear wave functions.

Nuclear Changes