# Obtaining range from bethe-bloch formula

• Cemil
In summary, the conversation discusses the integration in the range formula used in particle physics. The person is seeking help with understanding how the integration is done, and another person suggests using a programming language and the trapezoidal rule. It is also mentioned that the formula involves velocity instead of energy. A reference to a tutorial on beam loss monitoring is provided as well.

#### Cemil

While studying particle physics, i saw that the range formula is the integration dE/(dE/dx) but as you know that there are no variable E in the formula. how could that integration be done?

well i think we can do it by ourselves and we must use a programming language and i think the trapezoidal rule would be useful to solve that.

But i could not find out how could that integration be done please help me. thank you

Cemil said:
but as you know that there are no variable E in the formula.

But there is a velocity. From velocity you can get energy.

Look at Equation (1) and Figure 1 in
http://beamdocs.fnal.gov/DocDB/0010/001068/001/A%20tutorial%20on%20beam%20loss%20monitoring.pdf [Broken]
Eq (1) is the Bethe Bloch energy loss equation for protons. The independent variable is β. The integrated range is obtained by iteration of

dx = dE/[dE/dx]
E=E-dE
x=x+dx
etc.

Bob S

Last edited by a moderator:

## 1. What is the Bethe-Bloch formula?

The Bethe-Bloch formula is an equation used in particle physics to calculate the energy loss of a charged particle as it passes through a material. It takes into account the particle's charge, velocity, and the properties of the material.

## 2. How is the Bethe-Bloch formula used to obtain range?

The Bethe-Bloch formula can be used to calculate the stopping power of a material for a specific particle. By integrating this value over the distance traveled, the range of the particle in that material can be obtained.

## 3. What factors influence the range calculated using the Bethe-Bloch formula?

The range calculated using the Bethe-Bloch formula is influenced by the charge and mass of the particle, the density and thickness of the material, and the velocity of the particle.

## 4. Are there any limitations to using the Bethe-Bloch formula to obtain range?

Yes, there are limitations to using the Bethe-Bloch formula. It is only applicable for charged particles traveling through a material at high velocities. Additionally, it does not take into account energy loss due to nuclear interactions.

## 5. How accurate is the range obtained from the Bethe-Bloch formula?

The accuracy of the range obtained from the Bethe-Bloch formula depends on the accuracy of the input parameters used, such as the properties of the particle and material. Generally, it is accurate within a few percent for high energy particles.

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