Brueckner theory

In the framework of the Brueckner theory a rigorous treatment of TBF would require the solution of the Bethe-Faddeev equation, describing the dynamics of three bodies embedded in the nuclear matter. In practice a much simpler approach is employed, namely the TBF is reduced to an effective, density dependent, two-body force by averaging over the third nucleon in the medium,... 

N. C. Handy, J. A. Pople, M. Head-Gordon, K. Raghavachari, and G. W. Trucks, Chem. Phys. Lett., 164, 185 (1989). Size-Consistent Brueckner Theory Limited to Double Substitutions. 

Handy, N. C. Pople, J. A. Head-Gordon, M. Raghavachari, K. Trucks, G. W. Size-consistent Brueckner theory limited to double substitutions, Chem. Phys. Lett. 1989,164, 185-192. 

In 1958, Nesbet extended Brueckner s theory for infinite nuclear mat-ter to nonuniform systems of atoms and molecules. By consideration of the CISD problem in which the electronic Hamiltonian is diagonalized within the basis of the reference and all singly and doubly excited determinants, Nesbet explained that Brueckner theory allows one to construct a set of orthonormal molecular orbitals for which the correlated wavefunction coefficients for all singly excited determinants vanish. Unfortunately, the construction of the set of orbitals that fulfill this Brueckner condition can be determined only a posteriori from the single excitation coefficients computed in a given orbital basis. As a result, the practical implementation of Brueckner-orbital-based methods has... 

V. A. Kozlov and V. I. Pupyshev, Chem. Phys. Lett., 206, 151 (1993). Self-Consistent Brueckner Theory for Molecular Orbitals. 

R. Kobayashi, R. D. Amos, and N. C. Handy,/. Chem. Phys., 100,1375 (1994). Large Basis Set Calculations Using Brueckner Theory. 

During recent years, there has been much development in the other many-body problems of physics, e.g. nuclear matter (Brueckner theory) and the electron gas. > The possibility of applying these theories to atomic and molecular problems has been considered. It turns out, however, that in atoms and most molecules the many-body problem is physically very different from the other problems. 

The Brueckner theory is a generalized SCF method - in which orbitals are adjusted to correlation. Why such adjustment is not necessary in the case of atoms and molecules is shown in Sections XV and XIX. Sections XV, XVIII, and XIX compare such theories with the many-electron theory of this article. 

Brout has used a similar diagram technique but with a C.I. formalism and in connection with the Brueckner theory for infinite nuclei. The technique used here has little to do with the usual field-theoretic methods or statistical mechanics. ... 

Originally, the Brueckner theory was derived in a very different way for infinite nuclear matter where the orbitals are plane waves. The Hartree-Fock method cannot be taken as a starting point for nuclear matter, because there the matrix elements over the hard-core nucleon-nucleon repulsions are infinite. These interactions are so strong that it cannot be simply assumed that particles move independently in an undisturbed sea . Brueck-ner s theory essentially cancelled these infinities by including a correlation potential in the potential of the sea . This was... 

From the success of Brueckner theory in relation to shell model calculations one may conclude that the interaction of the particle with the other particles in the system will be well represented by a Brueckner G-matrix. Indeed, this consideration leads to a Hartree-Fock like choice for the self-energy in which the bare interaction is replaced by the energy-dependent G-matrix. Since the... 

The result for the occupation number for k = 0 calculated according to (14) for the Reid soft core potential at kp = 1.36 fm" is 0.83. Results from other methods such as Brueckner theory [44,45]... 

Starke Wechselwirkung, BRUECKNERSche Theorie, strong interaction, Brueckner theory 461. 

Breit-Wigner formula, Breit-Wigner-Formel 20, 123, 403, 405, 406. Bremsstrahlung 472f., 476, 509, 524. Brueckner theory, BruecknerscA Theorie... 

Strong interaction, Brueckner theory, star-ke Wechselwirkung, BruecknerscA Theorie 461. /... 

Breit interaction, relativistic effects, 210 Brillouins theorem, 104 Brownian dynamics, 389 Broyden-Fletcher-Goldfarb-Shanno (BFGS) update in optimizations, 321 Brueckner theory, 138 Buckingham potential, 19... 

Chapter 13 discusses coupled-cluster theory. Important concepts such as connected and disconnected clusters, the exponential ansatz, and size-extensivity are discussed the Unked and unlinked equations of coupled-clustCT theory are compared and the optimization of the wave function is described. Brueckner theory and orbital-optimized coupled-cluster theory are also discussed, as are the coupled-cluster variational Lagrangian and the equation-of-motion coupled-cluster model. A large section is devoted to the coupled-cluster singles-and-doubles (CCSD) model, whose working equations are derived in detail. A discussion of a spin-restricted open-shell formalism concludes the chapter. 

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