Anomalous Electric Moment

Two fields E and B can also be used to build the following potential matrix 

The transformation law of electromagnetic fields under Poincare transformations (as it follows from Maxwell s equations) is almost compatible with the potential transformation law (89). There is a slight mismatch concerning the behavior under the parity transformation. The matrix structure of (91) would require that the fields E and B change their sign under a space reflection, but the electromagnetic field strengths don t. Therefore, the Dirac equation with this potential matrix is not covariant with respect to a parity transformation. 

The next two sections describe potential matrices that appear to have little importance in atomic physics. We list these examples for the sake of completeness. 

---

The fine structure constant a can be determined with the help of several methods. The most accurate test of QED involves the anomalous magnetic moment of the electron [40] and provides the most accurate way to determine a value for the fine structure constant. Recent progress in calculations of the helium fine structure has allowed one to expect that the comparison of experiment [23,24] and ongoing theoretical prediction [23] will provide us with a precise value of a. Since the values of the fundamental constants and, in particular, of the fine structure constant, can be reached in a number of different ways it is necessary to compare them. Some experiments can be correlated and the comparison is not trivial. A procedure to find the most precise value is called the adjustment of fundamental constants [39]. A more important target of the adjustment is to check the consistency of different precision experiments and to check if e.g. the bound state QED agrees with the electrical standards and solid state physics. 

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. 

The value of the relaxation time is based on dielectric constant studies of Oncley (140) at 25 , who showed that the protein underwent anomalous dispersion and conformed nicely to the simple Debye curve, exhibiting a single critical frequency ve — 1.9 X 10 cycles sec"S a low frequency dielectric increment of -f 0.33 g. liter and a high frequency increment of —0.11 g." liter. The data just presented have been discussed by Oncley (141) and by Wyman and Ingalls (241) with the aid of their nomograms. It appears from their analyses that the facts might reasonably well be reconciled with the assumption either of oblate ellipsoids with p = 3 and A = 0.3 — 0.4 or of prolate ellipsoids with p = H and = 0.3 — 0.4. On the assumption of prolate ellipsoids, however, it would be necessary to assume that there was no component of the electric moment parallel to the long axis (axis of revolution). In either case the two dielectric increments correspond to an electric moment of about 500 Debye units (140). 

Based on the fundamental dipole moment concepts of mesomeric moment and interaction moment, models to explain the enhanced optical nonlinearities of polarized conjugated molecules have been devised. The equivalent internal field (EIF) model of Oudar and Chemla relates the j8 of a molecule to an equivalent electric field ER due to substituent R which biases the hyperpolarizabilities (28). In the case of donor-acceptor systems anomalously large nonlinearities result as a consequence of contributions from intramolecular charge-transfer interaction (related to /xjnt) and expressions to quantify this contribution have been obtained (29). Related treatments dealing with this problem have appeared one due to Levine and Bethea bearing directly on the EIF model (30), another due to Levine using spectroscopically derived substituent perturbations rather than dipole moment based data (31.) and yet another more empirical treatment by Dulcic and Sauteret involving reinforcement of substituent effects (32). 

Finally, hydrogenated fullerenes have been proposed as carriers of the anomalous microwave emission recently detected by several experiments on the Cosmic Microwave Background (Iglesias-Groth 2005, 2006). In the interstellar medium these molecules should spin with rates of several to tens of gigaHertz, if as expected they have a small dipole moment, then they would emit electric dipole radiation in a frequency range very similar to that observed for the anomalous microwave emission. 

Much more interesting and informative than Zeeman spectroscopy on atoms with zero electronic spin is the Zeeman effect on electric dipole transitions between states with a nonzero electronic spin moment. For historical reasons, this is called the anomalous Zeeman effect. 

A further structure effect, the proton polarizability, is only estimated to be < 4 ppm [28], of the same order than the value above. The agreement between theory and experiment is therefore only valid on a level of 4 ppm. Thus, we can say that the uncertainty in the hyperfine structure reflects dominantly the electric and magnetic distribution of the proton, which is related to the origin of the proton anomalous moment, being a current topics of particle-nuclear physics. 

Studies were made of A-doublet transitions in levels with 2 = and 2, J values from 1 to 7, and v from 0 to 4. Figure 8.49 shows an example of a high-resolution spectrum, in which the vibrational dependence of the A-doubling is clearly resolved the reasons for the anomalous position of the v = 4 resonance will be explained in due course. The A-doublet splitting ranges from 6.529 MHz in the v = 3, 2 = 2,J = 2 level, to 1150.934 MHz in the v = 0, 2 =, J = 2 level. The electric dipole moments in a number of different v, 2, J levels were also determined they range from 1.375 to 1.378 D. We return later to a more quantitative discussion of the analysis of the results, particularly the A-doublet splittings. 

Yamaoka K, Matsuda K. Reversing-pulse electric birefringence of poly(p-styrenesulfonate) in aqueous solutions effects of molecular weight and concentration on anomalous signal patterns arising from fast- and slow-induced ionic dipole moments. J Phys Chem 1985 89 2779-2786. 

A particle with charge e and anomalous moment /Xa subjected to a spherically symmetric electric field E(x) = would be described by the potential... 

---