The Theory of Many-Electron Atoms

It has not been possible to solve the Schrodinger equation exactly for atoms with two or more electrons. Although the orbitals for a many-electron atom are not quite the same as the hydrogen orbitals, we do expect the number of orbitals and their angular dependencies to be the same. Thus the hydrogen orbitals are used to describe the electronic structure of an atom with more than one electron. The procedure is simply to assign to each electron in the atom a set of the four quantum numbers n, I, mi, and ms (s is always 5), remembering that no two electrons can have the same four quantum numbers. This is a statement of the Pauli principle. 

What we actually do, then, is to fill up the hydrogen orbitals with the proper number of electrons for the atom under consideration (the aufbau, or building up, principle). One electron can be placed in each orbital. Since an electron can have ms equal to -f- or — two electrons may have the same orbital quantum numbers. The total number of electrons that the different orbital sets can accommodate is given in Table 1-2. 

The J-, p, d, /, etc., orbital sets usually are called subshells. The group of subshells for any given n value is called a shell. 

Type of orbital Orbital quantum numbers Total orbitals in set Total number of electrons that can be accommodated 

---

The role of graphical methods to represent angular momentum, 3 nj- and jm-coefficients was emphasized in the Introduction as one of the most important milestones in the theory of many-electron atoms and ions. 

Coefficients of fractional parentage play a fundamental role in the theory of many-electron atoms. There are algebraic formulas for them (see Chapter 16), however, they are not very convenient for practical utilization, and normally tables of their numerical values are used. They can be generated in the recursive way, starting with the formula... 

Second-quantization formalism was introduced into the theory of many-electron atoms by Judd [12]. This formalism enables one to give a simple and elegant description of both the rotation symmetry of a system and its permutational symmetry the tensorial properties of wave functions are translated to electron creation and annihilation operators, and the Pauli exclusion principle stems automatically from the anticommutation relations between these operators. 

In the theory of many-electron atoms, the particle-hole representation is normally used to describe atoms with filled shells. To the ground state of such systems there corresponds a single determinant, composed of one-electron wave functions defined in a certain approximation. This determinant is now defined as the vacuum state. In the case of atoms with unfilled shells, this representation can be used for the atomic core consisting only of filled shells. Then, the excitation of electrons from these shells will be described as the creation of particle-hole pairs. 

Global methods in the theory of many-electron atoms... 

This monograph presents a complete, up-to-date guide to the theory of modern spectroscopy of atoms. It describes the contemporary state of the theory of many-electron atoms and ions, the peculiarities of their structure and spectra, the processes of their interaction with radiation, and some of the applications of atomic spectroscopy. 

Recently the situation has become incomparably better. There is no problem publishing the main ideas and results in prestigious international journals in English. However, it would be very useful to collect, to analyse and to summarize the main internationally recognized results on the theory of many-electron atoms and their spectra in one monograph, written in English. This book is the result of the long process of practical realization of that idea. Many scientists from an international community of atomic... 

The data of atomic spectroscopy are of extreme importance in revealing the nature of quantum-electrodynamical effects. For the investigation of many-electron atoms and ions, it is of great importance to combine theoretical and experimental methods. Therefore, the methods used must be universal and accurate. A number of physical characteristics of the many-electron atom (e.g., a complete set of quantum numbers) may be found only on the basis of theoretical considerations. In many cases the mathematical modelling of physical objects and processes using modern computers may successfully replace the corresponding experiments. In this book we shall describe the contemporary state of the theory of many-electron atoms and ions, the peculiarities of their structure and spectra as well as the processes of their interaction with radiation, and some applications. 

Although the material contained in this book concerns the theory of many-electron atoms and ions, its many ideas and methods (e.g., graphical methods, quasispin and isospin techniques, particle-hole formalism, etc.) are fairly universal and may be easily applied (or already are) to other domains of physics (nuclear theory, elementary particles, molecular, solid state physics, etc.). 

The monograph is dedicated to those who are interested in the theory of many-electron atoms and ions, including very highly ionized ones, in the fundamental and applied spectroscopy of both laboratory (laser produced, thermonuclear, etc.) and non-atmospheric astrophysical low-and high-temperature plasma. To some extent it may serve as a reference book and textbook for physicists and astrophysicists. 

---