# Relativistic Coulomb Scattering

• Trickster2004
In summary, the conversation is discussing an equation for the angle of deflection of a charged particle, found on page 102 of the book "Classical Theory of Fields." The question is raised about the use of arctan in the solution to Problem 1 and how it was derived. The response explains that the equation can be derived using basic trigonometry.

#### Trickster2004

Hi. Landau and Lifgarbages give an equation describing the angle of deflection of a charged particle of a given initial velocity and impact parameter. It's given on page 102 of their Classical Theory of Fields, available here: http://books.google.com/books?id=QI...X&oi=book_result&ct=result&resnum=5#PPA102,M1. It's in the solution to Problem 1, at the bottom of the page.

I'm just curious where the equation in Problem 1 came from, in particular where the arctan came from. It's simple to solve 39.4 for the angle letting r-->infinity, but that gives an arccos, not an arctan. L-L just state that as the answer without working through it, as if it's obvious. Does anyone see how to derive it?

Thanks!

If you have an equation of the form $$\cos\theta=\frac{a}{b}$$, then you can think of $a$ being the adjacent side of a right triangle, $b$ being the hypotenuse and hence $\sqrt{b^2-a^2}$ as the opposite side $$\implies \tan\theta=\frac{\sqrt{b^2-a^2}}{a}$$

## 1. What is Relativistic Coulomb Scattering?

Relativistic Coulomb Scattering is a phenomenon that occurs when a high energy charged particle, such as an electron, passes near a charged nucleus. The electric field of the nucleus causes the particle to deviate from its original path, resulting in a change in its trajectory and energy.

## 2. How does Relativistic Coulomb Scattering differ from non-relativistic Coulomb Scattering?

Relativistic Coulomb Scattering takes into account the effects of special relativity, such as the increase in mass and energy of a high speed particle. Non-relativistic Coulomb Scattering only considers the classical laws of motion and does not take into account the effects of high speeds.

## 3. What is the mathematical equation for Relativistic Coulomb Scattering?

The mathematical equation for Relativistic Coulomb Scattering is given by the Rutherford scattering formula, which takes into account the relativistic effects and is based on the Coulomb force law. It is expressed as F = kQq/r^2, where F is the force, k is the Coulomb constant, Q and q are the charges of the particles, and r is the distance between them.

## 4. What are the applications of Relativistic Coulomb Scattering?

Relativistic Coulomb Scattering has various applications in particle physics and nuclear physics. It is used to study the structure of the atomic nucleus, as well as to investigate the properties of fundamental particles, such as protons and neutrons. It is also used in medical imaging techniques, such as positron emission tomography (PET) scans.

## 5. Can Relativistic Coulomb Scattering be observed in everyday life?

No, Relativistic Coulomb Scattering cannot be observed in everyday life as it requires high energy particles and specialized equipment. It is mostly observed in laboratory settings, such as particle accelerators, where high energy particles can be produced and studied.