Renormalized Atom Theory

An approach that is very closely related to the Atomic Sphere Approximation is the Renormalized Atom Theory, introduced first by Watson, Ehrenreich, and Hodges (1970) (sec also Watson and Ehrenreich, 1970, Hodges et al., 1972, and particularly Gelatt, Ehrenreich, and Watson, 1977). The name derives from the way the potential is constructed a charge density for each atom is constructed on the basis of atomic wave functions that are truncated at the Wigner-Seitz, or atomic, sphere. The charge density from each state is then scaled up (renormalized) to make up for that density beyond the sphere which has been dropped. 

MCT can be best viewed as a synthesis of two formidable theoretical approaches, namely the renormalized kinetic theory [5-9] and the extended hydrodynamic theory [10]. While the former provides the method to treat both the very short and the very long time responses, it often becomes intractable in the intermediate times. This is best seen in the calculation of the velocity time correlation function of a tagged atom or a molecule. The extended hydrodynamic theory provides the simplicity in terms of the wavenumber-dependent hydrodynamic modes. The decay of these modes are expressed in terms of the wavenumber- and frequency-dependent transport coefficients. This hydrodynamic description is often valid from intermediate to long times, although it breaks down both at very short and at very long times, for different reasons. None of these two approaches provides a self-consistent description. The self-consistency enters in the determination of the time correlation functions of the hydrodynamic modes in terms of the... 

A theory of finite-order walks has been developed which permits the derivation, from data for such walks, of the coefficient y for self-avoiding walks ((r ) N. In three dimensions, y= 1.203, in agreement with other calculations, but the two-dimensional value (1.469) seemed a little low. The idea of thermal blobs , within which ideal statistics apply, derives from the renormalization-group theory of chain statistics. However, expansion within a short segment of a long Monte Carlo chain is partly caused by interactions of the atoms of the segment with the rest of... 

We calculate the total RHF energy of the ionized metallic final state, the second term on the right side of eq. (25), by the methods described in section 2.1. RHF computations are performed for the 4f" Sd"" 6s free ions, renormalized atom crystal potentials are constructed, and self-consistent band calculations are carried out. Normalization of the wave functions to the WS sphere ensures that the final state cell has charge -l-lle. The q = 0 component of the full crystal potential, which arises from the charge of the other WS cells, is not included in the total energy since our intent is to compare to the completely screened limit where no such term appears (each cell in that case being neutral). Multiplet theory is again employed to place the 4f electrons into their Hund-rule states.. 

In LDA, the electron correlations are taken into account only by a mean field approximation which utilizes the correlation enei of the uniform electron gas. In the Ce compounds where the 4f electrons are believed to be itinerant in the ground state, such as in CeSns, the topology of the Fermi surface can be described by the band structure calculated in LDA. However, the strong intra-atomic correlation effect between the 4f electrons should be considered for consistent explanations of the Fermi surface, the electronic specific heat coefficient and the cyclotron efifective mass. Beyond LDA, there are two approaches by which the correlation effect between the 4f electrons is taken into account in an explicit way. One is p-f mixing theory and the other is renormalized band theory. 

Keywords Density functional theory (DFT) Green s functions Keldysh non-equilibrium Green s functions (NEGF) linear combination of atomic orbitals (LCAO) tunnel junction metal-fullerene-metal junction density of states (DOS) transmission function Landauer formula renormalized molecular levels (RMLs) I-V curves. 

The difference in the energy of the 2 Sand 2 Pjy2 levels in hydrogenic atoms is a purely electrodynamic effect due to the interaction of the bound electron with the quantized electromagnetic field. The measurement of this splitting was a major stimulus for the development of renormalization theory and still provides an important test of Quantum Electrodynamics. The precise measurement of this split-ting is difficult because of the short radiative lifetime of the 2 P 2 state. 

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. 

In atoms, the dominating Uehling potential causes the vacuum polarization effect to be attractive instead of repulsive, as would be expected from classical polarization theory. The polarization of the vacuum can be imagined as in Fig. 8. This can be understood as a result of charge renormalization. The bare charge is unobservable... 

B. R. Johnson, The log derivative and renormalized Numerov algorithms, Algorithms and Computer Codes For Atomic and Molecular Quantum Scattering Theory (L. Thomas, ed.), NRCC Workshop, Lawrence Berkeley Laboratory, Report No. LBL 9501, 1979. 

Power of the renormalization procedure is in the treatment of QED as a fundamental constraint, not as a theory. We can calculate a long-range Coulomb-like interaction (which determines an observable value of the electric charge), we can study electron s kinetic (or complete) energy (which determines an observable value of the electron s mass) and we can measure a number of other properties such as the anomalous magnetic moment of an electron and the Lamb shift in the hydrogen atom. The constraint means that they are correlated and we can calculate the correlation. Learning some of these values from experiment, we can predict the others. 

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