Field correction

No distortion, neither geometrical neither due to magnetic fields, thanks to proximity focusing. The non sensitivity of the tube to magnetic fields enables software enhancement of the images such as flat field corrections. 

Compute the orientation of the borehole with respect to magnetic north without axial field correction. 

It was pointed out by Cunningham et al.4) that it is strictly necessary to take into account the internal field correction, and define quantities cps instead of A, where... 

The next step to include electron-electron correlation more precisely historically was the introduction of the (somewhat misleading) so-called local- field correction factor g(q), accounting for statically screening of the Coulomb interaction by modifying the polarizability [4] ... 

Figure 3. Local-field correction factor calculations. 

To determine the behavior of g(q) for large q, we performed measurements of iS lq, ) of Li for 1.1 a.u. < q < 2.6 a.u. and performed for each spectrum a fit of the g(g)-modified c° to the experimental data. Figure 10 shows the result of this semi-empirical determination of g(q) together with the shape of the local-field correction factor after Farid et al. [7] calculated for different values ofz solid line (z = 0.1), dashed line (z = 0.5) and dash-dotted line (z = 0.7). One clearly sees that the curve for the surprisingly small value of z = 0.1 fits our experimental findings best. 

We have shown for the case of Li that the step in the occupation number function is surprisingly small z 0.1 and provided semi-empirically obtained values for the local-field correction factor. For the case of Al, we showed the additional cancellation of self-energy and vertex correction. 

Which denotes respectively the short-range penetration corrected electrostatic multipolar (EMTP ) energy, short-range repulsion (Erep ), polarization (Epoi), charge-transfer (Ed), and dispersion (EdiSp) contributions. In presence of an open-shell cation, a ligand field correction is introduced (Elf)-... 

HYSCORE spectra of zeaxanthin radicals photo-generated on silica-alumina were taken at two different magnetic fields B0=3450G and B0=3422G, respectively. In order to combine the data from the two spectra, the field correction was applied (Dikanov and Bowman 1998). The correction consists of a set of equations that allow transformation of spectra to a common nuclear Zeeman frequency. The set of new frequencies was added to that of the former spectrum and plotted as the squares of the frequencies v2a and v2p. Examples of these plots can be found in Focsan et al. 2008. 

Standard data reduction, i.e. bias and flat field correction, has been performed with Iraf. The Iraf task APEXTRACT/APALL was used to extract the spectra, with interactively selected background sampling, in order to avoid contamination for the star spectrum. The wavelength calibration has been done using daily He, Ne, HgCd arcs, and, in order to improve the calibration, wavelengths values for the transitions used were taken from http //physics.nist.gov/. 

N Is the number of molecules per unit volume (packing density factor), fv Is a Lorentz local field correction at frequency v(fv= [(nv)2 + 2]/3, v = u) or 2u). Although generally admitted, this type of local field correction Is an approximation vdilch certainly deserves further Investigation. IJK (resp Ijk) are axis denominations of the crystalline (resp. molecular) reference frames, n(g) Is the number of equivalent positions In the unit cell for the crystal point symmetry group g bjjj, crystalline nonlinearity per molecule, has been recently Introduced 0.4) to get general expressions, lndependant of the actual number of molecules within the unit cell (possibly a (sub) multiple of n(g)). 

In the case of histamine, inclusion of this reaction field correction was found to change the result by almost 4 kJ/mol. Unfortunately, the highly sensitive nature of the histamine monocation results to protocol and parameters used meant that no definite conclusion could be drawn about the importance of long-range forces in these calculations. It does however appear that they do play a role. The correct treatment of long-range forces is... 

Sources of errors in the solution phase dynamics include the usual sources of errors in simulations using empirical force fields. Correct parametrisation is of course essential, and, as always, the description of the electrostatic forces is a particular problem. In addition to these standard problems, FEP requires carefully converged simulations, i.e. correct and sufficient sampling of the relevant phase space must be made. Present computational resources are such that these calculations are no longer a difficult task. It is perhaps time that some of these old problems be reevaluated, and new systems examined. 

For ions in crystals of high symmetry, as in the case of our reference octahedral ABe center, the correction factor is Eioc/Eo = (n + 2)/3 (Fox, 2001), where n is the refractive index of the medium. Although this correction factor is not strictly valid for centers of low symmetry, it is often used even for these centers. Thus, assuming this local field correction and inserting numerical values for the different physical constants, expression (5.21) becomes... 

This expression is exactly coincident with Equation (5.21), which leads to Smakula s formula. Equation (5.22), after inserting numerical values and the local field correction factor for centers of high symmetry. 

In the weak coupling limit, as is the case for most molecular systems, each molecule can be treated as an independent source of nonrlinear optical effects. Then the macroscopic susceptibilities X are derived from the microscopic nonlinearities 3 and Y by simple orientationally-averaged site sums using appropriate local field correction factors which relate the applied field to the local field at the molecular site. Therefore (1,3)... 

F(o>i) are the local field corrections for a"3wave of frequency Generally, one utilizes the Lorentz approximation for the local field in which case (1,4)... 

The measurement of x of solutions can be used to determine the microscopic nonlinearities Y of a solute, provided Y of the solvent is known. This measurement also provides information on the sign of y and (hence x of the molecules if one knows the sign of Y for the solvent (5,7) Under favorable conditions one can also use solution measurements to determine if Y is a complex quantity. The method utilizes two basic assumptions (i) the nonlinearities of the solute and the solvent molecules are additive, and (ii) Lorentz approximation can be used for the local field correction. Under these two assumptions one can write the x of the solution to be... 

The macroscopic polarization of the phase is given by equations 1 and 2, where Di is the number density of the ith conformation, jlj is the component of the molecular dipole normal to the tilt plane when the ith conformation of the molecule is oriented in the rotational minimum in the binding site, ROFj is the "rotational orientation factor", a number from zero to one reflecting the degree of rotational order for the ith conformation, and e is a complex and unmeasured dielectric constant of the medium (local field correction). 

Note that these results are local field corrected... 

A more rigorous theory [40, 41] accounting for an internal field correction yields the following ratio of two field complex amplitudes ... 

The relationship (139), of course, is not rigorous, but it is based on an elementary macroscopic consideration [41] of the internal-field correction. Being widely used (GT, VIG), such a relationship is sufficient for an accurate description of the low-frequency dielectric response of strongly polar fluids. We return to this problem later in this section. 

Finally, we remark that our microscopic approach is mainly aimed at the study of the resonance-interaction mechanisms, which are revealed in the FIR range. In this range, where 3> x 1 and x > 0.1, inclusion of the internal field correction, which is accounted for in Eqs. (139) and (141), gives only a small effect. 

A theory, accounting for an internal field correction [40, 41], gives the relationship % ( ), Eq. (139), between the complex susceptibility and permittivity. For calculation of the wideband spectra it is more convenient to employ the reverse dependence (% ), Eq. (141). 

Taking into account the internal-field correction, replacing % and s by x r and E r, we use the same relationships connecting the complex susceptibility and permittivity as were employed in Sections IV-VI ... 

F(y, T) is a nonequilibrium (induced by a.c. field) correction to the steady-state distribution. 

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