Classical Scattering Formalism

In summary, the Classical Scattering Formalism is a theoretical framework used to describe the interactions between particles, based on classical mechanics and electrostatics. It differs from other scattering theories by not accounting for quantum mechanical effects and assuming non-relativistic particles governed by classical electromagnetic forces. Its key assumptions include point-like, non-relativistic particles interacting through classical electrostatic forces, and no external influences during scattering. It is commonly used in nuclear physics, astronomy, and atmospheric physics, but has limitations in accurately describing behavior at small scales and high energies or speeds.
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So the standard way to introduce scattering classically is through the two body problem for a central force where we move to the centre of mass reference frame and all the dynamics is explained by a one body problem for the separation vector ##r_{12}=r_1-r_2## with a reduced mass ##\mu=\frac{m_1 m_2}{m_1+m_2}##

However then the cross sectional area is introduced by talking about a beam of particles incident on a target with a central potential V(r).

So my question is about relating these two ideas, if we want to calculate the cross sectional area for two bodies scattering off of each other is our beam of particles really a beam of pseudo particles with mass ##\mu## and position vector ##r_{12}## or am I misunderstanding something?
 
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I would like to clarify the relationship between the two concepts mentioned: the two-body problem and the cross sectional area for scattering.

The two-body problem is a classical approach to understanding the dynamics of two bodies interacting through a central force. By moving to the center of mass reference frame, we can simplify the problem to a one-body problem for the separation vector r12. The reduced mass, μ, is used in this approach because it takes into account the relative masses of the two bodies.

On the other hand, the concept of cross sectional area is commonly used in scattering experiments, where a beam of particles is incident on a target with a central potential V(r). This area represents the effective target area for the particles to interact with the target.

To calculate the cross sectional area for two bodies scattering off of each other, we can consider the beam of particles as a beam of pseudo-particles with a reduced mass μ and a separation vector r12. This approach allows us to use the same formalism as in the two-body problem, but now we are considering the interaction between the beam and the target.

In summary, the two-body problem and the concept of cross sectional area are related in the sense that they both involve the interaction of particles through a central potential. However, in the case of scattering, we are considering the interaction between a beam of particles and a target, where the reduced mass and separation vector can be used to calculate the cross sectional area.
 

What is the Classical Scattering Formalism?

The Classical Scattering Formalism is a theoretical framework used to describe the interactions between particles, such as atoms or subatomic particles, when they collide or scatter off of each other. It is based on classical mechanics and electrostatics.

How does the Classical Scattering Formalism differ from other scattering theories?

Unlike other scattering theories, such as the Quantum Scattering Formalism, the Classical Scattering Formalism does not take into account quantum mechanical effects. It also assumes that the particles are non-relativistic and that the interactions between them are governed by classical electromagnetic forces.

What are the key assumptions of the Classical Scattering Formalism?

The Classical Scattering Formalism assumes that the particles involved in the scattering process are point-like, non-relativistic, and that they interact solely through classical electrostatic forces. It also assumes that the particles are not influenced by any external fields during the scattering process.

How is the Classical Scattering Formalism used in practical applications?

The Classical Scattering Formalism is often used in practical applications, such as in the study of nuclear physics, to understand the interactions between particles and to predict the outcomes of experiments involving scattering. It is also used in fields such as astronomy and atmospheric physics to analyze the scattering of light by particles in the atmosphere.

What are the limitations of the Classical Scattering Formalism?

The Classical Scattering Formalism is limited in its ability to accurately describe the behavior of particles at the atomic or subatomic level. This is because it does not take into account quantum mechanical effects, which become more significant at smaller scales. It also cannot accurately describe the scattering of particles at high energies or speeds where relativistic effects come into play.

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