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4302 results in General and Classical Physics

Page 41 of 216

  • 5 - Angular Momentum

  • from Part I - Fundamental Principles
  • Mark Fox, University of Sheffield
  • Book:
    A Student's Guide to Atomic Physics
    Published online:
    21 June 2018
    Print publication:
    14 June 2018, pp 84-105

  • Summary

    The treatment of angular momentum is very important to understand the properties of atoms. It is now time to explore these effects in detail, and to see how this leads to the classification of the quantized states of atoms by their angular momentum.

    Conservation of Angular Momentum

    In the sections that follow, we will consider several different types of angular momentum and the ways in which they are coupled together. Before going into the details, it is useful to stress one very important point related to conservation of angular momentum. In an isolated atom, there are many forces (and hence torques) acting inside the atom. These internal forces cannot change the total angular momentum of the atom, since conservation of angular momentum demands that the angular momentum of the atom as a whole must be constant in the absence of any external torques. The total angular momentum of the atom is normally determined by its electrons. The total electronic angular momentum is written J and is specified by the quantum number J. The principle of conservation of angular momentum therefore requires that isolated atoms always have well-defined J-states. It is this J-value that determines, for example, the magnetic dipole moment of the atom.

    It should be noted in passing that the nucleus can possess angular momentum and that electrons can exchange angular momentum with the nucleus through hyperfine interactions. (See Section 7.8.2.) These interactions are very weak, and can usually be neglected except when explicitly considering nuclear effects. With this caveat, we can safely regard the total electronic angular momentum J as a conserved quantity.

    The principle of conservation of angular momentum does not apply, of course, when external perturbations are applied. The most obvious example is the perturbation caused by the emission or absorption of a photon. In this case the angular momentum of the atom must change because the photon itself carries angular momentum, and the angular momentum of the whole system (atom + photon) has to be conserved. The change in J is then governed by selection rules, as discussed, for example, in Section 5.8. Another obvious example is the effect of a strong external DC magnetic field.

  • 11 - Atomic Physics Applied to the Solid State

  • from Part II - Applications of Atomic Physics
  • Mark Fox, University of Sheffield
  • Book:
    A Student's Guide to Atomic Physics
    Published online:
    21 June 2018
    Print publication:
    14 June 2018, pp 202-225

  • Summary

    Solids are made up of atoms bound together in crystals, and the understanding of their quantized states is a subject in its own right, namely solid-state physics. In this chapter, we briefly look to see how the general principles developed in atomic physics can be applied to solid-state systems. This will enable us to obtain a basic understanding of light emission in solids. The focus of the chapter will be restricted to two main examples of optically active solid-state materials:

  • (i) Semiconductors: Semiconductors lie at the heart of modern technology. The silicon chip underpins the electronics industry, while the optoelectronics industry exploits the optical properties of compound semiconductors such as GaAs. Our task here will be to apply simple principles of atomic physics to understand the electronic states of impurities in semiconductors, and the mechanisms of light emission and detection.

  • (ii) Ions doped into optical hosts: Here we consider materials such as ruby, where chromium is lightly doped into Al2O3, with the Cr3+ ions substituting for the Al3+ ions in the crystal. Pure Al2O3 is a colorless, transparent crystal, and the characteristic red color of ruby arises from transitions associated with the Cr3+ ions. Our task will be to understand how the transitions of the Cr3+ ions in the crystal relate to the atomic states of Cr3+ ions in isolation.

    • In both cases, it will not be possible to give a comprehensive treatment; the aim of the chapter is to explain a few basic principles that can lay the foundations for further study. This author has written another book in which these topics are explained in much greater depth. See Fox (2010).

    Solid-State Spectroscopy

    Chapter 3 developed the basic principles governing optical transitions in atoms. In this section, we shall see how these principles carry over to solid-state systems.

    Selection Rules

    The electric-dipole (E1) interaction is the strongest term in the light-matter Hamiltonian, as discussed in Section 3.3. The selection rules that follow from analysis of the E1 perturbation and the wave functions of atomic states were derived in Section 3.4, and are summarized in Table 3.1. These selection rules carry over directly to optical transitions in solid-state systems.

Page 41 of 216