Core Calculations

The core calculations consist of neutronic and thermal-hydraulic parts. These parts are coupled to evaluate the core characteristics such as the core power or coolant temperatures. 

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ADF uses a STO basis set along with STO fit functions to improve the efficiency of calculating multicenter integrals. It uses a fragment orbital approach. This is, in essence, a set of localized orbitals that have been symmetry-adapted. This approach is designed to make it possible to analyze molecular properties in terms of functional groups. Frozen core calculations can also be performed. 

All calculations were performed on the Cray-2 computers at the Minnesota Supercomputer Center. In some cases the two-electron Integrals could be kept in the 256 megaword central memory of the Cray-2, and in these cases an "in-core" integral and SCF code(53) was used. The largest in-core calculations possible in... 

In G3(MP2) theory, the MP2(fu)/G2Large calculation of G3 is replaced with a frozen core calculation with the G3MP2Large basis set [23] that does not contain the core polarization functions of the G3Large basis set. 

Since the (Fen05(0H)6> unit is stable, it has been speculated(8b,17b) that it might also be present in the ferritin core. Since the majority of phosphate in ferritin is adventitious, surface bound and the metallic core can be reconstituted in the absence of phosphate groups with no change in the X-ray powder diffraction pattem(l), replacement of bridging phosphate by bridging carboxylate groups should not influence the three dimensional structure of the core. Calculations show that -409 Fell nnits could fill the apoferritin inner cavity. Further details can be found in reference 17. 

Adams and Clark78 used a large basis set of better than DZ quality and calculated core binding energies and shifts for several fluoro- and chloro-methanes, including CF4. These were obtained using Koopmans theorem, hole state calculations, and equivalent cores calculations,79 the latter giving the best results for minimal basis sets, but there was little difference between the three methods for the more extended basis sets. NF4+ was also studied in this paper. 

The four-fold ionization energies for these two full potential rigid core calculations are listed in the first row of Tables I and II. The relaxation... 

One of the best ways to determine whether an itinerant or localized picture is applicable is to compare experimental and theoretical determinations of the Fermi surface topology and effective masses. It has been known for many years that the Fermi surfaces of most elemental 4f metals can be represented by an f core calculation (15t. 

It is interesting to contrast the case of hep UPtg to the case of UPdg, which has a closely related crystal structure (dhep). It turns out that the UPdo Fermi surface is well-represented by an f core calculation (24). Thus one could say that UPtg is on the verge of a localization (Mott) transition. In conclusion, it is clear that the LDA calculations have been very helpful in sorting out the nature of the ground states for those f electron metals which show anomalous behavior. 

A frozen-core calculation involves choosing a particular state (for example the one lowest in energy), performing a Hartree—Fock calculation to find the best orbitals, then using the orbitals of the core to generate a nonlocal potential (5.27), which is taken to represent the core in calculations of further states. 

A good example is provided by the alkali-metal atoms, which consist of one electron outside a closed-shell core in the single-configuration model. If the frozen-core approximation is valid a frozen-core calculation of the orbital occupied by one electron will give the same result as a Hartree—Fock calculation and the core orbitals will not depend on the state. 

Table 5.1 illustrates the frozen-core approximation for the case of sodium using a simple Slater (4.38) basis in the analytic-orbital representation. The core (Is 2s 2p ) is first calculated by Hartree—Fock for the state characterised by the 3s one-electron orbital, which we call the 3s state. The frozen-core calculation for the 3p state uses the same core orbitals and solves the 3p one-electron problem in the nonlocal potential (5.27) of the core. Comparison with the core and 3p orbitals from a 3p Hartree—Fock calculation illustrates the approximation. The overwhelming component of the 3p orbital agrees to almost five significant figures. 

Fig. 4 Relative change (%) of major SCCP homolog groups in three lake sediment cores calculated from the percentage in the surface slice and the percentage in the sediment horizon dated to pre-1950. A negative number indicates higher proportion in surface than the deep slice...

Figure 16. Core-core repulsion correction in Hgj for two-valence electron Hg ECPs. Errors per atom due to a superposition of pairwise eorrections in larger highly-symmetric Hg clusters (n=3 equilateral triangle n=4 tetrahedron n=6 octahedron n=13 icosahedron) are also shown. The underlying core-core repulsion corrections were determined from small-core (20-valence electron) PP frozen-core calculations on the Hg + core systems. The interatomic distances in Hg2 and the bulk are indicated by vertical lines.

The prediction of molecular Rydberg spectra, as well as the analysis of the available laboratory data, has constituted a challenge on the theory. A number of ab initio calculations have been carried out on transition probabilities of Rydberg molecules, such as the frequently quoted Hartree-Fock (HF) study of H3 by King and Morokuma (15), the self-consistent-field frozen-core calculation with floating-spherical-Slater-type orbitals (FSSO) on the second-row Rydberg... 

Dillon, P. J. H. E. Evans, 1993. A comparison of phosphorus retention in lakes determined from mass balance and sediment core calculations. Wat. Res. 27 659-668. 

Fig. 1. (a) The two-particle Pauli operator for a No-Core calculation (b) for a standard model-space calculation, where the wings have been taken to the same dimension as in the No-Core calculation. 

Independent core calculations performed at the Nuclear Engineering Institute (lEN, Rio de Janeiro) pointed out to discrepancies -with respect to calculations done at lEAv- which were mainly attributed to the differences in nuclear data sets. 

Core calculations have shown that the combination of the most extreme voiding pattern and the complete melting and slumping of fuel from the upper half into the lower half of the core in one of the central subassemblies results in less than 400 increase in reactivity. Since this reactivity, and obviously the reactivity insertion rate, is less than that of the control rod ejection just discussed, this accident will be of no consequence to the rest of the core with respect to reactivity addition when followed by a normal scram. There is a need for development of an adequate method for prevention of, or detection of, a local channel blockage. 

Data acquisition for process information, and the interface to process actuators, utilizes the simplest types of microprocessors, whereas the top level of the I C system hierarchy uses powerful minicomputers, eg., for core calculations. Intermediate types of microcomputers are utilized for control and operation, logic and signal treatment. 

The effects of neutron scattering and neutron absorption within the reactor core was investigated by reactivity measurements. The sarnies were positioned in a sample changer so constructed that measurements could be Conducted at the center of the reactor or at specific positions out through the reactor corp. The spatial effects of reactivity for materials with varying ratios of scattering tp absorption cross section were measured. The reactivity data are combined with U-235 foil traverses to determine the extrapolated radius of the reactor and to experimentally measure the (Juantlty used in core calculations as the adjoint flux. 

RA-8 is a critical facility located at the Pilcaniyeu Technological Complex (Centro Tecnologico de Pilcaniyeu), about 60 km from San Carlos de Bariloche. The reactor, which reached criticality for the first time in June 1997, can be operated during steady state conditions at any constant power up to 10 W, or at 100 W in short transients. The reactor was developed with the specific objective to validate codes used for neutronic core calculations, and to study the nuclear design parameters of a modular Argentinian LWR power reactor named CAREM. 

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