Fine-structure effect

Dominant contributions are responsible for the a, fi, and y dispersions. They include for the a-effect, apparent membrane property changes as described in the text for the fi-effect, tissue structure (Maxwell-Wagner effect) and for the y-effect, polarity of the water molecule (Debye effect). Fine structural effects are responsible for deviations as indicated by the dashed lines. These include contributions from subcellular organelles, proteins, and counterion relaxation effects (see text). 

The dielectric properties of tissues and cell suspensions will be summarized for the total frequency range from a few Hz to 20 GHz. Three pronounced relaxation regions at ELF, RF and MW frequencies are due to counterion relaxation and membrane invaginations, to Maxwell-Wagner effects, and to the frequency dependent properties of normal water at microwave frequencies. Superimposed on these major dispersions are fine structure effects caused by cellular organelles, protein bound water, polar tissue proteins, and side chain rotation. 

The physical mechanism underlying the fine-structure effect can be seen if we consider say the excitation of the 2 Po,i,2 fine-structure states of helium from the singlet ground state I Sq. This can only occur by exchange processes, since in the Pj states the atoms have their electron spins aligned, while in the singlet state they are antiparallel. As discussed... 

The fine-structure effect also results in a polarisation of the scattered electron. Since the spin-down electron is preferentially captured, the atomic spin-up electron is preferentially released, and the electron arriving at the detector has an average spin-up component, i.e. positive polarisation, and indeed... 

The existence of the fine-structure effect has been demonstrated for sodium (Hanne, Szmytkowski and van der Wiel, 1982 McClelland et ai, 1985 Nickich et al, 1990) using the time-reversed arrangement. A polarised electron beam is superelastically scattered from sodium atoms excited to 3 P /2 or 3 3/2 states by a single-frequency laser. McClelland et al. (1985) measured the spin asymmetry of polarised electrons that de-excite unpolarised atoms from the 3> P3/2 fine-structure state over the angular range —35° < 6 < 35°. As expected from reflection symmetry, the... 

For heavier atoms the pure fine-structure effect is expected to break down due to relativistic effects. In the very heavy open-shell target atom thallium (Z=81) the ground-state atoms populate only one of the fine-structure levels, and the effect may be important at low energies. In an R-matrix calculation using magnetic potentials derived from the Dirac equation, Goerss, Nordbeck and Bartschat (1991) showed that... 

The presence of two spins in a triplet [70, 71] or biradical [72] species results in additional ESR features, viz. fine structure effects as a result of electron spin-electron spin interactions [69], The phenomena observed and results derived therefrom are best discussed for simple examples, viz., the interaction of two equivalent centers in structurally well-characterized molecules. 

It is evident that the total strain of various conformers of the [Co(sar)]3+ cation is quite similar. Thus, the conformation in the solid state and in solution results from fine structural effects in the... 

In this paper we modify and extend this approach in several ways. In particular, we consider the magnetic fine structure effects in the presence of a uniform electric field F for ls2p Pj- excited states of helium. We introduce two separate differential polarizabihties to describe the quadratic part of the electric field splitting and three differential hyperpolarizabilities to describe the terms the order of in the fine-structure splitting of the atomic multiplet s2p Pj. We have developed a calculational approach that allows correct estimation of potential contributions due to continuum spectra to the dipole susceptibilities j3 and 7. In the next section we briefly outline our method. The details of the calculations of the angular and radial matrix elements have been described elsewhere [8,9] and are omitted here for brevity. Atomic units are used throughout. 

Graff, M.M. and Wagner, A.F. (1990) Theoretical studies of fine-structure effects and long-range forces. J. Chem. Phys. 92,2423-2439. 

Our future work on charge transfer collisions will concentrate on fine-structure effects and on polyatomic targets, which present a whole new range of challenges for the type of methodology presented here. 

Another source of error inherent in the perturbation approach to sensitivity studies is the inadequacy of multigroup methods based on flux-averaged group constants to allow for the fine-structure effects of the perturbation. A detailed description of this problem and of possible ways of reducing or eliminating the errors are described in Section VII. 

Are these in-group spectral effects responsible for the CWD for fertile and fissile isotopes The simple model results (13S) tend to support this assumption. Results of numerical calculations for realistic problems obtained recently by Kier and Zolotar 139) show, however, that even though spectral fine structure effects are significant in the low energy end of the resolved resonance region, they contribute little to the reactivity worth of a Pu and a sample in the ZPR 6 assembly 7 reactor. These results were obtained from a small number of calculations for two specific perturbations. Further investigation seems necessary before the significance of spectral fine structure effects and their connection with the CWD can be firmly established. 

How can the spectral fine structure effects of a perturbation be allowed for in calculations One approach is to avoid using the group formulation. It is possible to apply the continuous energy formulation with Monte Carlo methods 32, 33). They are, however, not practical for routine application. 

There are several approaches that can take into account spectral fine structure effects with multigroup methods that use flux-averaged group constants (a) All calculations (flux, adjoint, and perturbation) are performed... 

The paramount fundamental problem to resolve is that of the central worth discrepancy. It is important not only for its academic interest or for reassuring the reactor physicist in the adequacy of the calculational methods and nuclear data he u.ses, but also for practical reasons. Safety factors that account for the CWD must be included in the design of fast reactors an economic penalty is associated with these safety factors. Related to the question of the CWD is the more general problem of the multigroup calculation of bilinear functionals. The questions arising here are (I) for which applications, and under what conditions, are spectral fine structure effects non-negligible (2) how can these fine structure effects be taken into account in the multigroup formulation. 

A. Ermers, T. Woschnik, W. Behmenbutg, Depolarization and fine structure effects in half-collisions of sodium-noble gas systems. Z. Phys. D 5,113 (1987)... 

Besides making implicit use of these really puzzling properties of the relativistic Kepler problem, the second major impact of Sommerfeld s article lies in several notions introduced which lie at the foundation of relativistic quantum chemistry and have since been instrumental in the field the notion of scalar (kinemat-ical) relativistic effects versus fine-structure effects, the introduction of the fine-structure constant, a = jhc, and the expansion of the relativistic expressions in powers of the square of this constant. The idea that relativistic effects decisively influence the structure of the outer electrons of the atoms is at the root of relativistic quantum chemistry. 

In the following sections we will discuss some of the features mentioned above. The first (Section II) will address itself to the question of the overall accuracy that is generally achieved in excited-state potential surface calculations. The next (Section III) will present examples for species for which the theoretical predictions are sometimes the only data available challenging the experimentalists, or for which computed data have been around prior to measurements and are able to explain and predict general trends. Section IV will deal with the interaction of potential surfaces and the contribution of theoretical methods to this area. Section V will deal with the treatment of short-lived negative ions Section VI will show calculated fine-structure effects in the potential energy curves of simple systems and Section Vll will give a selected but representative set of examples from our own work carried out in conjunction with experiments or examples that have led to a re-evaluation of measured data. 

---