# Rutherford cross section in CM frame

• jocke_x1
In summary, the appropriate energy to use in the Rutherford cross section formula depends on the specific scenario being studied. Options include the projectile energy converted to CM, the kinetic energy of the CM frame, and the total kinetic energy in the CM frame. The choice of energy will depend on the research question and perspective of the analysis. It is recommended to discuss with an advisor or colleagues for the most suitable energy for a particular scenario.
jocke_x1
Hi

I need to plot the (differential) Rutherford cross section as a function of the scattering angle in the CM frame. the reaction is a typical projectile on stationary target. I know the projectile energy in the lab, θcm and the masses. I am confused over which energy to use though.

I know that

$\frac{dσ}{dΩ}=\left(\frac{zZe^{2}}{16\pi\epsilon_{0}E}\right)^{2}*csc(\frac{\theta_{cm}}{2})^{4}$

In the following m and M are the masses of projectile and target respectivly and Tp is the projectile kinetic energy in the lab frame.

Should I use the projectile energy converted to CM?
$E=\left(\frac{M}{m+M}\right)^{2}*T_{p}$

The kinetic energy of the CM frame?
$E=\left(\frac{m}{m+M}\right)*T_{p}$

The total kinetic energy in the CM frame?
$E=\frac{\sqrt{2MT_{p}+\left(m+M\right)^{2}}}{m+M}$

or something else?

I have looked in several textbooks and googled but have just become more confused since I have seen E defined as "total kinetic enrgy","projectile energy" or just "energy of the particles".

Any help to clear this up would be greatly appreciated.

Hi there,

Thank you for your question. The energy that you should use in the Rutherford cross section formula depends on the specific scenario that you are studying. Let's go through each of the options that you have listed and discuss when it would be appropriate to use them.

1. Projectile energy converted to CM: This option would be appropriate if you are interested in studying the scattering of the projectile particles in the CM frame. This would be useful if you want to analyze the scattering process from the perspective of the projectile particle.

2. Kinetic energy of the CM frame: This option would be appropriate if you want to study the scattering process from the perspective of the CM frame. This would be useful if you want to analyze the overall behavior of the scattering process without focusing on the individual particles involved.

3. Total kinetic energy in the CM frame: This option would be appropriate if you are interested in studying the overall energy of the system, including both the projectile and target particles. This would be useful if you want to understand how the total energy of the system affects the scattering behavior.

In general, the choice of energy to use in the Rutherford cross section formula will depend on your specific research question and the perspective from which you want to analyze the scattering process. I recommend discussing this with your advisor or colleagues to determine the most appropriate energy to use for your particular scenario.

I hope this helps clarify things for you. Good luck with your research!

## What is the Rutherford cross section in the center of mass frame?

The Rutherford cross section in the center of mass (CM) frame is a measure of the probability of an incoming particle scattering off a stationary target particle at a specific angle. It is commonly used in nuclear and particle physics to describe the scattering of charged particles off of atomic nuclei.

## How is the Rutherford cross section calculated?

The Rutherford cross section is calculated using the Rutherford scattering formula, which takes into account the impact parameter, charge of the particles, and the kinetic energy of the incoming particle. This formula is derived from the Coulomb potential and assumes a point-like target particle.

## What is the significance of the Rutherford cross section in CM frame?

The Rutherford cross section in CM frame is important because it allows us to understand the fundamental forces at play in particle and nuclear interactions. It also provides insight into the structure of atomic nuclei and can be used to probe the properties of subatomic particles.

## How does the Rutherford cross section change with increasing energy of the incoming particle?

As the energy of the incoming particle increases, the Rutherford cross section decreases. This is because at higher energies, the particles have more kinetic energy and thus are less likely to be deflected by the Coulomb potential of the target particle. This effect is known as screening.

## Can the Rutherford cross section be measured experimentally?

Yes, the Rutherford cross section can be measured experimentally by scattering a beam of particles off of a target and measuring the number of particles scattered at different angles. The resulting data can then be compared to theoretical predictions to determine the Rutherford cross section.

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