Theory of atomic bound states

The problem of N bound electrons interacting under the Coulomb attraction of a single nucleus is the basis of the extensive field of atomic spectroscopy. For many years experimental information about the bound eigenstates of an atom or ion was obtained mainly from the photons emitted after random excitations by collisions in a gas. Energy-level differences are measured very accurately. We also have experimental data for the transition rates (oscillator strengths) of the photons from many transitions. Photon spectroscopy has the advantage that the photon interacts relatively weakly with the atom so that the emission mechanism is described very accurately by first-order perturbation theory. One disadvantage is that the accessibility of states to observation is restricted by the dipole selection rule. 

Photon spectroscopy associates two numbers with the pair of states involved in a transition, the energy-level difference and the transition rate. The correlated emission directions of photons in successive transitions are determined trivially by the dipole selection rule. In most cases it is impossible to solve the many-body problem accurately enough to reproduce spectroscopic data within experimental error and we are left wondering how good our theoretical methods really are. 

Because our description of differential cross sections for momentum transfer in a reaction initiated by an electron beam depends on our ability to describe both the structure and the reaction mechanism, scattering provides much more information about bound states. This is even more true of ionisation. The information is less accurate than from photon spectroscopy and is obtained only after a thorough understanding of reactions, the subject of this book, is achieved. The understanding of structure and reactions is of course achieved iteratively. A theoretical description of a reaction is completely tested only when we know the structure of the relevant target states with accuracy that is at least commensurate with that of the reaction calculation. The hydrogen atom is the prototype 

We are concerned here with the use of the theoretical descriptions of atomic eigenstates in the calculation of a reaction. It is necessary to know in principle how the structure calculations are done and to know the detail of the different forms that can be adapted to reaction calculations. 

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Theory of atomic bound states 5.6 Configuration interaction... 

The other powerful stimulus for further development of the bound state theory is provided by the spectacular experimental progress in precise measurements of atomic energy levels. It suffices to mention that in about a decade the relative uncertainty of measurement of the frequency of the 1S—2S... 

The present state of the theories of atomic and molecular processes in condensed phases is characterized by great non-uniformity of its development. Matters are much problematic in the theory of the kinetics of processes at a molecular level. The kinetics of surface processes mainly employs models taking no account of the interaction of the adsorbed particles (the law of masses or surface action) [14-16]. This does not reflect the real properties of a gas solid interface. There is also a diversity of models when considering the interaction of the particles because various approximations are used (equilibrium is described with a view to the correlation effects, while kinetics ignores them). The problem of approximations is of a fundamental significance in the theory of condensed systems. Interaction between the particles causes all the particles to be bound to... 

Abstract. Muonium is a hydrogen-like system which in many respects may be viewed as an ideal atom. Due to the close confinement of the bound state of the two pointlike leptons it can serve as a test object for Quantum Electrodynamics. The nature of the muon as a heavy copy of the electron can be verified. Furthermore, searches for additional, yet unknown interactions between leptons can be carried out. Recently completed experimental projects cover the ground state hyperfine structure, the ls-2s energy interval, a search for spontaneous conversion of muonium into antimuonium and a test of CPT and Lorentz invariance. Precision experiments allow the extraction of accurate values for the electromagnetic fine structure constant, the muon magnetic moment and the muon mass. Most stringent limits on speculative models beyond the standard theory have been set. 

In chapter 6 we described the theory of molecular electronic states, particularly as it applies to diatomic molecules. We introduced the united atom nomenclature for describing the orbitals, and pointed out that this was particularly useful for tightly bound molecules with small intemuclear distances, like H2. We also discussed the more conventional nomenclature for describing electronic states, which is based upon the assumption that the component of electronic orbital angular momentum along the direction of the intemuclear axis is conserved, i.e. is a good quantum number. The latter description is therefore appropriate for molecules in electronic states which conform to Hund s case (a) or case (b) coupling. 

The spectra may also be described in the language of solid state theory. The atomic excited states are the same as the excitons that were described, for semiconductors, at the close of Chapter 6. They are electrons in the conduction band that are bound to the valence-band hole thus they form an excitation that cannot carry current. The difference between atomic excited states and excitons is merely that of different extremes the weakly bound exciton found in the semiconductor is frequently called a Mott-Wannier exciton-, the tightly bound cxciton found in the inert-gas solid is called a Frenkel exciton. The important point is that thecxcitonic absorption that is so prominent in the spectra for inert-gas solids does not produce free carriers and therefore it docs not give a measure of the band gap but of a smaller energy. Values for the exciton energy are given in Table 12-4. 

The mathematical problem associated with the Dirac Hamiltonian, i.e. the starting point of the relativistic theory of atoms, can be phrased in simple terms. The electron-positron field can have states of arbitrarily negative energy. As a general feature of the Dirac spectrum this instability occurs even in the case of extended nuclei and even in the absence of any nucleus (free Dirac spectrum), the energy is not bounded from below. This gives rise to the necessity of renormalization and well-established renormalization schemes have been around for many decades. Despite their successful applications in physics, we may ask instead whether there exist states that allow for positivity of the energy. 

The second aim concerns a presentation of the theory of one-electron atoms starting from its relativisitic foundation, the Dirac equation. The nonrelativis-tic Pauli and Schrodinger theories are introduced as approximations of this equation. One of the major purpose, about these approximations, has been to display, on the one side, the enough good concordance between the Dirac and the Pauli-Schrodinger theories for the bound states of the electron furthermore, but to a weaker extent, for the states of the continuum close to the freedom energy and, on the other side, the considerable discordances for... 

A relativistic consistent quantum-theoretical description of electronic bound states in atoms was first introduced in atomic physics as early as the late 1920s and has been pushed forward since that time. It was believed, however, that effects stemming from Einstein s theory of relativity were of little or even no importance to chemistry. This changed in the 1970s when it was recognized by Pyykkd, Pitzer, Desclaux, Grant and others that several unusual features in heavy-element chemistry and spectroscopy can only be explained in terms... 

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