Atomic Photoeffect pp 13-45 | Cite as

# The Structure of the Atom and Its Interaction with an Electromagnetic Field

Chapter

## Abstract

The Hamiltonian of an atom composed of a nucleus (of charge
where
where Ψ

*Z*) and*N*electrons consists of three summations: these are sums over the kinetic and potential energy operators for each separate electron moving in the field of the nucleus and also over the interelectronic Coulomb interaction terms:$$
\widehat H = \sum\limits_{n = 1}^N {\left( {\frac{{\widehat p_n^2}}{2} - \frac{Z}{{{r_n}}}} \right)} + \frac{1}{2}\sum\limits_{n > q = 1}^N {\frac{1}{{\left| {{r_n} - {r_q}} \right|}}} ,{\widehat p_n} = - i{\nabla _n} = - i\frac{\partial }{{\partial {r_n}}}
$$

(2.1)

**r**_{ n }is the radius vector of the*n*th electron. For a neutral atom*N*=*Z*. In (2.1) all relativistic effects have been neglected so all interactions represented are of Coulombic origin. The state of an atom is determined by its wavefunction Ψ_{ E }(*x*_{1}⋯*x*_{ N }), which is a solution of the stationary Schrödinger equation:$$\hat{H}\Psi_E(x_1\cdot\cdot\cdot x_N)=E\Psi_E(x_1\cdot\cdot\cdot x_N)$$

(2.2)

_{ E }depends on the spatial coordinates and spin projection of each electron, i.e.,*x*_{ n }≡**r**_{ n }, σ_{ n }.## Keywords

Orbital Angular Momentum Schrodinger Equation Principal Quantum Number Atomic Electron Photoionization Cross Section
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1990