On the Annihilation of Electron and Proton (Dirac – 1930)

Saba Etezad Razavi, Physics Undergraduate Student, Sharif University of Technology

Negative energy states appear in the eigenvalues of a Hamiltonian whenever we work with relativistic Hamiltonian. Nevertheless, in classical theory, these negative energies do not make trouble for us as there is a forbidden area between states with negative and positive energy. However, when we are working with a quantum relativistic equation (Dirac equation), the existence of negative energy states can give rise to a number of paradoxes. In 1931 Dirac tried to eliminate these paradoxes by presenting the Dirac sea model. As a consequence of this model, new particles with exact characteristics of electrons but positively charged, introduced to the physic’s world. Dirac thought that these newly introduced particles could be a description for the known protons, but soon people (including Dirac himself) found out that it cannot be possible, and a new particle called “positron” came to existence. Later in 1931, Anderson found positrons in the laboratory.
In these numbers of presentations, we focus on Dirac’s theory of the electron sea, which appeared in his 1930 paper, “On the theory of electrons and protons.” Then we will start to compute the rate of the electron-positron (as Dirac thought those times, protons) annihilation as Dirac did in another 1930 paper, “On the annihilation of electrons and protons.”

Date: August 31, 2020