Helium and Other Two Electron Systems

Abstract

After a general introduction and a survey of the experimental observations (Sect. 7.1) the quantum mechanical basis for treating multi-electron systems is reviewed in Sect. 7.2. The reader should know about these tools or get used to them by reading this section. Section 7.3 expands this theme by introducing electron exchange and the characteristic excited state configurations. Fine structure interaction in He and He like ions are addressed in Sect. 7.4 – a consolidation of our knowledge acquired in Chap. 6 which will turn out to be essential also for later chapters. In Sect. 7.5 the most important selection rules for E1 transitions in multi-electron system are treated. This directly leads to “double excitation” in Sect. 7.6. It is of importance far beyond atomic physics: resonances of states imbedded into a continuum are found in all fields of physics. The ensuing interference structures, known as Fano resonances and their origin are described in a practical, easy to access approach. Finally, in Sect. 7.7 the alkaline earth atoms and the Hg atom are treated: they are related to He in an analogous manner as alkali atoms are related to the H atom.

So far our discussions were restricted to atomic systems with effectively one active electron in an attractive Coulomb or screened Coulomb field. For the majority of atoms this simple model cannot be maintained, since the electrons repel each other pairwise and have to obey the Pauli principle. The helium atom (He) is the simplest and purest example for introducing the key problems which one encounters in true multi-electron systems, as well as the methods for describing and understanding them.

Acronyms and Terminology

a.u.:

‘atomic units’, see Sect. 2.6.2.

CI:

‘Configuration interaction’, mixing of states with different electronic configurations in atomic and molecular structure calculations, using linear superpositon of Slater determinants (see Sect. 10.2.3).

E1:

‘Electric dipole’, transitions induced by the interaction of an electric dipole with the electric field component of electromagnetic radiation.

FS:

‘Fine structure’, splitting of atomic and molecular energy levels due to spin orbit interaction and other relativistic effects (Chap. 6).

IR:

‘Infrared’, spectral range of electromagnetic radiation. Wavelengths between $760\operatorname{nm}$ and $1\operatorname{mm}$ according to ISO 21348 (2007).

NIST:

‘National institute of standards and technology’, located at Gaithersburg (MD) and Boulder (CO), USA. http://www.nist.gov/index.html.

SI:

‘Système international d’unités’, international system of units (m, kg, s, A, K, mol, cd), for details see the website of the Bureau International des Poids et Mésure http://www.bipm.org/en/si/ or NIST http://physics.nist.gov/cuu/Units/index.html.

UV:

‘Ultraviolet’, spectral range of electromagnetic radiation. Wavelengths between $100\operatorname{nm}$ and $400\operatorname{nm}$ according to ISO 21348 (2007).

VIS:

‘Visible’, spectral range of electromagnetic radiation. Wavelengths between $380\operatorname{nm}$ and $760\operatorname{nm}$ according to ISO 21348 (2007).

VUV:

‘Vacuum ultraviolet’, spectral range of electromagnetic radiation. Part of the UV spectral range. Wavelengths between $10\operatorname{nm}$ and $200\operatorname{nm}$ according to ISO 21348 (2007).