The Photoelectric Effect: Hydrogen Atom

Abstract

As our second example, let us calculate the cross section for the photoelectric effect for an atom. For simplicity, we will choose the simplest atom, hydrogen. We assume we have an incoming beam of photons of definite , hence definite energy, ħω, and definite polarization. We also assume the incident photon beam is linearly polarized, with polarization in the direction of , and ħω is greater than the ionization energy of hydrogen, $((\mu {e^4})/(2{\hbar ^2})$. Therefore, when a photon of energy ħω is absorbed, the hydrogen atom makes a transition from the 1s ground state into the continuum, (see Fig. 64.1). For simplicity, let us further assume $\hbar\omega>>(\mu{e^4})/2{\hbar^2})$ so the final electron kinetic energy$p_f^2/2\mu$ is large enough the final electron continuum wave function can be approximated by a plane wave. For the moment, therefore, we shall avoid the more complicated exact Coulomb relative motion function discussed in the appendix to Chapter 42. To calculate the differential cross section for the photoelectric process, we need to know the flux in the incoming photon beam, and the transition probability per second that the hydrogen atom makes a transition from the 1s ground state to a continuum state with the absorption of a photon.