Many-body Hamiltonians model

The electronic many-body Hamiltonian in equation (1) is treated in the framework of the independent-electron frozen-core model. This means that there is only one active electron, whereas the other electrons are passive (no dynamic conelation is accounted for) and no relaxation occurs. In this model the electron-electron interaction is replaced by an initial-state Hartree-Fock-Slater potential [37]. This treatment is expected to be highly accurate for heavy collision systems at intermediate to high incident energies. The largest uncertainties of the independent-electron model will show up for low-Z few-electron systems, such as H -F H and H + He° or for high multiple-ionization probabilities. 

Methods for Solving Model Many-Body Hamiltonians... 

Model Many-Body Hamiltonians for tt Conjugated Systems... 

Following Anderson (1963), the model Hamiltonian of Eq. (17.12) can be deduced easily by using second quantization. Let us consider a simple model for a system of N electrons described within a basis set of N orthonormal spatial orbitals. Each electron is assumed to be localized on one orbital (site). The many-body Hamiltonian of this model is ... 

In order to improve the theoretical description of a many-body system one has to take into consideration the so-called correlation effects, i.e. to deal with the problem of accounting for the departures from the simple independent particle model, in which the electrons are assumed to move independently of each other in an average field due to the atomic nucleus and the other electrons. Making an additional assumption that this average potential is spherically symmetric we arrive at the central field concept (Hartree-Fock model), which forms the basis of the atomic shell structure and the chemical regularity of the elements. Of course, relativistic effects must also be accounted for as corrections, if they are small, or already at the very beginning starting with the relativistic Hamiltonian and relativistic wave functions. 

To reasonably limit the focus here it the survey is primarily of many-body solution techniques as applied to a particular VB model, the covalent-space Pauling-Wheland VB model, represented by the Heisenberg spin Hamiltonian... 

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