How does one find interaction radius for Coulomb barrier?

In summary, the Coulomb barrier must be overcome for a proton to strike an atomic nucleus. This barrier can be calculated using the formula U = kZ1Z2e2/r, where r is the interaction radius. To find r, one can use formulas that estimate the sum of the nuclear radii. Ultimately, the Coulomb barrier is the electrostatic potential for two electric charges at a distance r.
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eigenmax
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For a proton striking an atomic nucleus (in a Cockcroft-Walton accelerator, for example), the Coulomb barrier must be overcome. The calculation of the Coulomb barrier is U = k Z1Z2 e2 / r
r is interaction radius. How can I find that? For a proton to enter the atomic nucleus what would it be?
 
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  • #2
It is simply the electrostatic potential for two electric charges at distance r. What is unclear?
r will typically be about the sum of the nuclear radii, there are formulas to estimate that.
 
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  • #3
mfb said:
It is simply the electrostatic potential for two electric charges at distance r. What is unclear?
r will typically be about the sum of the nuclear radii, there are formulas to estimate that.
Ok, thank you! So it ought to be the radius of the proton + the target radius. Thank you!
 

1. How is the interaction radius for Coulomb barrier calculated?

The interaction radius for Coulomb barrier can be calculated using the equation r = k * Z1 * Z2 / E, where k is a constant (usually taken to be 1.44 for simplicity), Z1 and Z2 are the charges of the two interacting particles, and E is the total energy of the system.

2. What is the significance of the interaction radius in the Coulomb barrier?

The interaction radius represents the distance at which the Coulomb repulsion between two particles is equal to the kinetic energy of the particles. This means that if the particles come within this distance, they will be repelled and not able to interact with each other.

3. How does the interaction radius affect nuclear reactions?

The interaction radius plays a crucial role in nuclear reactions as it determines whether two particles will be able to overcome the Coulomb barrier and fuse together. If the particles have enough kinetic energy to reach the interaction radius, nuclear fusion can occur.

4. How does the interaction radius change with different particles?

The interaction radius is dependent on the charges and energies of the particles involved. As the charges and/or energies change, the interaction radius will also change. For example, particles with higher charges and/or higher energies will have a smaller interaction radius, making it easier for them to overcome the Coulomb barrier.

5. Can the interaction radius be measured experimentally?

Yes, the interaction radius can be measured experimentally by studying the cross-section of nuclear reactions. By varying the energy of the particles and observing the cross-section, the interaction radius can be determined. This can also be done through theoretical calculations using the aforementioned equation.

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