# Fermi/Coulomb correction factor for beta decay

• rrg92
In summary, Fermi introduced a multiplicative correction factor to account for the Coulomb field's effect on the energy distribution of ejected beta particles in a beta decay reaction. This is necessary because the energy loss or gain is directly related to the particle's momentum, and simply subtracting the energy would not take this into account. The correction factor can be derived using the energy-momentum relation and accounts for the momentum-dependent energy changes.
rrg92
Hi all,

Fermi introduced a multiplicative correction factor in order to correct for the effect of the Coulomb field on the resulting energy distribution of ejected beta particles (i.e., either electrons or positrons) following a beta decay reaction. The result is that positrons are accelerated as they exit the nucleus, while electrons are slowed down. My question is, why does this correction factor have to be a multiplicative term, as opposed to simply subtracting the energy lost or gained for the electron or positron respectively? Is there a way that I can derive the momentum-dependent energy loss/gain, and arrive at the final corrected energy distribution?

Kind regards

Last edited:
,Hello,

Thank you for your question. The reason why the correction factor introduced by Fermi is a multiplicative term is because the energy loss or gain for beta particles is directly related to their momentum. This means that the amount of energy lost or gained will vary depending on the initial momentum of the particle.

To understand this further, we need to look at the concept of momentum conservation. In a beta decay reaction, a neutron is transformed into a proton and a beta particle (either an electron or a positron). This means that the total momentum of the system must be conserved before and after the decay. The Coulomb field within the nucleus affects the momentum of the beta particle as it exits, resulting in a change in its energy.

Now, if we were to simply subtract the energy lost or gained by the beta particle, we would not be taking into account its change in momentum. This is why the correction factor is a multiplicative term, as it accounts for the momentum-dependent energy loss or gain.

To derive this correction factor, you can use the concept of energy-momentum relation, which states that the energy of a particle is equal to its momentum times the speed of light. By considering the change in momentum of the beta particle, you can arrive at the final corrected energy distribution.

I hope this helps to answer your question. Please let me know if you have any further inquiries.

## What is the Fermi/Coulomb correction factor for beta decay?

The Fermi/Coulomb correction factor is a mathematical expression used to correct for the effects of the strong nuclear force and the Coulomb force on beta decay. These forces can affect the energy and angular distribution of beta particles emitted during nuclear decay.

## Why is the Fermi/Coulomb correction factor needed in beta decay calculations?

The strong nuclear force and Coulomb force are both very powerful and can significantly alter the energy and direction of beta particles emitted during nuclear decay. Without the Fermi/Coulomb correction factor, the calculated values for these particles may be inaccurate.

## How is the Fermi/Coulomb correction factor calculated?

The Fermi/Coulomb correction factor is calculated using a complex mathematical equation that takes into account the energy and angular momentum of the beta particle, the mass of the parent and daughter nuclei, and the strength of the strong nuclear force and Coulomb force.

## Does the Fermi/Coulomb correction factor affect all types of beta decay?

Yes, the Fermi/Coulomb correction factor affects all types of beta decay, including beta-minus, beta-plus, and electron capture. This is because all of these types of decay involve the emission of beta particles, which are affected by the strong nuclear force and Coulomb force.

## Can the Fermi/Coulomb correction factor be experimentally measured?

No, the Fermi/Coulomb correction factor is a theoretical concept and cannot be directly measured. However, its effects can be observed in experiments and compared to theoretical predictions, providing evidence for its existence and accuracy.

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