What is the total cross-section for hard sphere scattering?
Example 1: elastic collision of two hard spheres So in this case the total scattering cross section is equal to the area of the circle (with radius r + R) within which the center of mass of the incoming sphere has to arrive for it to be deflected, and outside which it passes by the stationary scattering center.
What is hard sphere scattering?
This type of scattering potential is known as hard sphere scattering, and is illustrated in Figure 2. It describes a light projectile bouncing off of a solid sphere of radius R. While the solid sphere is an extended object, we will assume that the projectile is a point-like mass.
How do you calculate cross-section scattering?
In cases where the radiation is being treated as a continuous classical wave, as in the case of long-wavelength electromagnetic radiation, scattering cross-sections are determined by dividing the power of the scattered wave by the intensity of the incident wave.
What is the differential cross-section in scattering?
In other words, the differential (scattering) cross-section is defined as the ratio of the intensity of radiant energy scattered in a given direction to the incident irradiance and thus has dimensions of area per unit solid angle, dΩ.
What is Rutherford scattering formula?
The “differential cross-section”, dσ/dθ, with respect to the scattering angle is the number of scatterings between θ and θ + dθ per unit flux, per unit range of angle, i.e. dσ dθ = dN(θ) F dθ = π D2 4 cos(θ/2) sin3(θ/2) .
What is a rigid sphere?
Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space.
What is Rutherford scattering cross section?
Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model of the atom and eventually the Bohr model.
What is Rutherford alpha scattering?
Rutherford’s Alpha Scattering Experiment Rutherford, in his experiment, directed high energy streams of α-particles from a radioactive source at a thin sheet (100 nm thickness) of gold. In order to study the deflection caused to the α-particles, he placed a fluorescent zinc sulphide screen around the thin gold foil.
What is alpha ray scattering experiment?
The initial discovery was made by Hans Geiger and Ernest Marsden in 1909 when they performed the gold foil experiment in collaboration with Rutherford, in which they fired a beam of alpha particles (helium nuclei) at foils of gold leaf only a few atoms thick.