Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

We present an analytic calculation of the paramagnetic and diamagnetic contributions to the one-loop effective action in the SU(2) Higgs model. The paramagnetic contribution is produced by the gauge boson, while the diamagnetic contribution is produced by the gauge boson and the ghost. In the limit, where these particles are massless, the standard result of - 12 for the ratio of the paramagnetic to the diamagnetic contribution is reproduced. If the mass of the gauge boson and the ghost become much larger than the inverse vacuum correlation lengths of the Yang–Mills vacuum, the value of the ratio goes to - 8 . We also find that the same values of the ratio are achieved in the deconfinement phase of the model, up to the temperatures at which the dimensional reduction occurs.

Кинетика изменения концентраций магнитных ионов примеси в сплавах Pb-=SUB=-1-x-y-=/SUB=-Sn-=SUB=-x-=/SUB=-V-=SUB=-y-=/SUB=-Te при легировании

The field and temperature dependences of the magnetization (magnetic fields B ≤ 7.5 T, temperatures T = 2.0–75 K) of samples from a Pb_1– x – y Sn_ x V_ y Te ( x = 0.08, y = 0.01) single-crystal ingot synthesized by the Bridgman–Stockbarger method. It is established that the sample magnetization contains two main contributions, notably, the paramagnetism of vanadium ions and diamagnetism of the crystal lattice. The field and temperature dependences of the magnetization are approximated by the sum of modified Brillouin functions corresponding to the paramagnetic contributions of vanadium in two different charge states and the diamagnetic contribution linear in terms of field. The concentrations of vanadium ions in two different magnetic states and the character of their variation along the ingot are determined within the scope of the alloy’s electronic-structure rearrangement because of doping. The results are compared with the data of X-ray fluorescence microanalysis and the results of studying the galvanomagnetic properties of the samples.

Multivariate Regression with Substituent Shift Increments. III. 2,5-Disubstituted Furans

Six series of 2-X-5-Y-substituted furans were used for multivariate regression of 13C NMR chemical shifts with four substituent shift increments (SSI). Some of these series were measured in CDCl3 and DMSO-d6 on different spectrometers to exclude possible sources of deviation from the general trends. Program ASSIGN was written for visual and numerical estimation of correct assignment of 13C NMR spectra in the series of derivatives. Multivariate regression proved that the corresponding position in benzenes and furans are not affected by the substituents in the same way: in 2-X-5-Y-substituted furans, the "ortho" position requires correction for the different bond order, the "meta" 13C chemical shift is probably affected by change in diamagnetic contribution of the Y group, and "para" position behaves like another "ortho" position in the molecule.

A Mathematical Formulation for Diamagnetism in Tetrahedrally Bonded Semiconductors

An expression for the magnetic susceptibility tensor corresponding to diamagnetic contribution in tetrahedrally bonded semiconductors is derived; this formulation refers to the crystalline state. In addition, a comparison with the amorphous case is outlined.

Cyclopentadienyl complexes with transition metal – main group metal bonds. VII. 207Pb and 95Mo nuclear magnetic resonance studies on molybdenum and tungsten complexes [(η5-C5H5)(CO)3M]nPbR4−n (n = 1, R = Me, Et, Ph; n = 2, R = Ph)

Nuclear magnetic resonance measurements of metallic nuclei (δ 207Pb, δ 95Mo, and 1J(W–Pb)) have been carried out on dimetallic Cp(CO)3MPbR3 (M = Mo, W; R = Me, Et, Ph) and trimetallic [Cp(CO)3M]2PbPh2 (M = Mo, W) complexes. 207Pb chemical shifts increase in the sequence PbEt3 < PbMe3 < PbPh3 and are observed at higher fields in the tungsten compounds than in the molybdenum ones. It is suggested that both paramagnetic and diamagnetic contributions determine the overall shielding of lead, and that the higher field resonances of 207Pb in the case of W–Pb compounds are due to an efficacious operation of the Z/r dependent diamagnetic term (higher atomic number Z of tungsten and roughly the same Mo–Pb and W–Pb distances resulting from the 4f level induced lanthanide contraction). 95Mo chemical shifts (−1838 to −2007 ppm) lie in the region typical of the molybdenum – main group metal bonded complexes but at lower fields than in the corresponding Mo–Sn compounds. It is concluded from this observation that the Z/r dependent diamagnetic contribution does not operate efficaciously for 95Mo shieldings, which are hence primarily dominated by the paramagnetic term. The nature of metal–metal interactions is discussed.