Many-body correlation effect

To ensure this, the-many-body wavefunction can be written as a Slater determinant of one particle wavefunctions - this is the Hartree Fock method. The drawbacks of this method are that it is computationally demanding and does not include the many-body correlation effects. 

Thus, one can think of the R12 wave function as representing many-body correlation effects through two types of terms /(r12)O0 responsible for the short-range two-body Coulomb correlation and y describing conventional many-body correlation. The second term is expanded in terms of Slater determinants composed of orbitals from a finite orbital basis set (OBS) ... 

Eieiat. describes relativistic effects (such as variations in spin couplings - see Chap. A) and 8Econ. other electron-electron (and also electron-vibrational) many-body correlation effects (which are not included in Hartree-Fock calculations). 

It is obvious that more sophisticated relativistic many-body methods should be used for correct treating the NEET effect. Really, the nuclear wave functions have the many-body character (usually, the nuclear matrix elements are parameterized according to the empirical data). The correct treating of the electron subsystem processes requires an account of the relativistic, exchange-correlation, and nuclear effects. Really, the nuclear excitation occurs by electron transition from the M shell to the K shell. So, there is the electron-hole interaction, and it is of a great importance a correct account for the many-body correlation effects, including the intershell correlations, the post-act interaction of removing electron and hole. 

The band calculations with potentials generated from local density functional approximations give the most detailed one electron band structures. As was discussed in section 2, one obtains Fermi surface dimensions in good agreement with experiments. We will mention briefly the basic principle of the calculation in order to illustrate that the calculation is surprisingly unsophisticated in terms of many-body correlation effects to be discussed later. 

The effective mass, introduced in Sect. 3.3 and discussed more in Sect. 3.5, is the factor that corrects a single-particle logic for the many-body correlations. Thus, one can say that the study of the evolution in the level-density parameter a, is one of determination of how m changes with E. This thermal sector was discussed in Sect. 3.5. 

The exchange-correlation potential represents all many-body effects due to electron electron interaction that are not included in the Hartree potential. The correlation problem in metals remains largely unsolved, and in heavy-fermion materials the many-body correlation is thought to be the cause of all the observed anomalous properties. On the other hand, it has been found empirically that one can perform extremely good band calculations for simple as well as transition metals by using the local-density-functional approximation (LDA) for (Kohn and Sham 1965) ... 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

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