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# 物理代写|粒子物理代写Particle Physics代考|PHYS125 Scattering in Classical and Quantum Physics

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## 物理代写|粒子物理代写Particle Physics代考|Scattering in Classical and Quantum Physics

Almost every act of observation involves a scattering experiment. In everyday life it is usually the scattering of visible light by the object under study and its resolution is limited by the light’s wavelength. During the last century the quest for higher resolution forced us to abandon light as a probe and, following Rutherford’s pioneering experiment, to use more and more energetic particle beams. Today all information we have about the structure of matter at the deepest accessed level comes from high energy scattering experiments. The probes are particles we can accelerate, which are essentially protons (or ions) and electrons. A particle accelerator is, in fact, a “microscope” whose spatial resolution is determined by its maximum energy. The CERN Large Hadron Collider ( $\mathrm{LHC})$, with proton beams up to $7 \mathrm{TeV}$, has a resolution reaching $10^{-19} \mathrm{~m},{ }^{1}$ and is today – in 2021 – the most powerful microscope man has ever built. In this chapter we shall introduce the basic concepts necessary to describe and understand the results of scattering experiments in particle physics. Only the main ideas will be presented, with no detailed proofs. Some of the proofs are proposed as exercises at the end of the chapter.

## 物理代写|粒子物理代写Particle Physics代考|The Scattering Cross Section

We start by considering the case of two colliding particles. The laboratory frame is defined to be the reference frame in which one of these particles, called the target, is at rest. The other is the projectile. By contrast, in the centre of mass reference frame nothing distinguishes the target from the beam. ${ }^{2}$

In the simplest case a projectile, idealised as a hard sphere of radius $r$ in straight motion, will hit the target, a sphere of radius $R$, if the trajectory of the centre of the projectile intersects the disk of radius $r+R$ perpendicular to it and centred at the centre of the target. The surface area of this disk, $\sigma_{\text {tot }}=\pi(r+R)^{2}$, is called the total cross section of this collision process.

In actual experiments the situation is more complex. First, we are not interested only in collisions of hard spheres. Even in classical physics we may want to compute the results of scattering among particles interacting through a potential, for example two electrically charged particles. Second, we do not usually consider the collision of just one particle against another. We send, instead, a beam of particles against a target containing many particles and place a detector in the direction $\Omega(\theta, \phi)$ with an acceptance of $\mathrm{d} \Omega$, which counts the number of particles $\mathrm{d} \mathcal{N}(\Omega) / \mathrm{d} \Omega$ going through it per unit solid angle and per unit time. We want to extract out of such a measurement a quantity, like the cross section we introduced previously, which refers to the collision of one particle in the beam and one particle in the target.

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