Electron resonance studies of the renner effect

The gas phase electron resonance spectra of NCO in its ground ²Π_3/2 vibronic state and in two excited vibronic states are described. Theoretical analysis of the spectra yields effective g values for the three states. In additon the ¹⁴N magnetic hyperfine and electric quadrupole coupling constants and the electric dipole moment are determined. The theory of the Renner coupling of electronic and vibrational motion is extended, and shown to account for anomalous contributions to the g values. The theory also shows that these contributions are closely related to the Renner coupling constant.     

Strong Coupling Constant to Four Loops in the Analytic Approach to QCD

The QCD analytic running coupling _an which has no nonphysical singularities for all Q ²>0 is considered for the initial perturbation-theory approximations up to four-loop order. The finiteness of the analytic coupling at zero is shown to be a consequence of the asymptotic freedom property of the initial theory. The nonperturbative contributions to the analytic coupling are extracted explicitly. For all Q> they are represented in the form of an expansion in inverse powers of Euclidean momentum squared. The effective method for a precise calculation of the analytic running coupling is developed on the basis of the stated expansion. The energy-scale evolution of the analytic running coupling for the one- to four-loop cases is studied and the higher loop stability and low dependence on the quark-threshold matching conditions in comparison with the perturbative running coupling were found. Normalizing the analytic running coupling at the scale of the rest mass of the Z boson with the world-average value of the strong coupling constant, _an(M _Z ²)=0.1181±0.002, one obtains as a result of the energy-scale evolution of the analytic running coupling _an(M ²)=0.2943^+0.0111 _–0.0106 that is notably lower than the estimations of the coupling strength available at the scale of the mass of the lepton.This work has been partly supported by RFBR under Grant No. 02-01-00601Received November 24, 2002; accepted February 19, 2003 Published online June 27, 2003     

具有D4h对称性构型的C2+4分子的Jahn-Teller效应与能级分裂

依据量子理论与配位场理论,利用群论和对称性分析的方法探讨了C²⁺₄分子在具有D_4h对称性构型时,E×(b_1g+b_2g)系统的Jahn-Teller效应中的相关问题.研究了C²⁺₄分子的电子态与声子态的对称性及其活跃声子态,讨论了系统声子间的耦合与CG系数,构建了E×(b_1g+b_{2g 关键词： 2+4分子')" href="#">C²⁺4分子 对称性 能级分裂 Jahn-Teller畸变}     

Sternheimer shielding in molecules

The effect of perturbing electric fields and electric-field gradients on the nuclear quadrupole coupling in molecules is investigated. The theory for the first-order effects is developed and it is shown that not only a perturbing field gradient but also a perturbing field, and higher terms, induce a finite field gradient at a nucleus in a molecule. The so-called Sternheimer (anti)shielding is thus considerably more complex in molecular than in atomic systems. The different shielding components have been calculated for HCl, HCN and NH₄ ⁺ using a finite perturbation ab initio molecular orbital method. The calculated values are then used to rationalize experimentally determined ¹⁴N quadrupole coupling constants in condensed media for HCN and NH₄ ⁺.     

Kl3 form factors at order p of chiral perturbation theory

This paper describes the calculation of the semileptonic K_l3 decay form factors at order p⁶ of chiral perturbation theory, which is the next-to-leading order correction to the well-known p⁴ result achieved by Gasser and Leutwyler. At order p⁶ the chiral expansion contains one- and two-loop diagrams which are discussed in detail. The irreducible two-loop graphs of the sunset topology are calculated numerically. In addition, the chiral Lagrangian produces direct couplings with the W bosons. Due to these unknown couplings, one can always add linear terms in q² to the predictions of the form factor f _- (q ² ). For the form factor f ₊ (q ² ), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q⁴ counterterm, the q⁴ ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q² our calculation shows that chiral perturbation theory converges very well in this application, as the corrections are small. Comparing the predictions of chiral perturbation theory with the recent CPLEAR data, it is seen that the experimental form factor f ₊ (q ² ) is well described by a linear fit, but that the slope is smaller by about 2 standard deviations than the prediction. The unavoidable q² counterterm of the corrections allows one to bring the predictions of chiral perturbation theory into perfect agreement with experiment. Received: 8 January 2002 / Revised version: 27 March 2002 / Published online: 20 September 2002 RID="*" ID="*" Now at Fraunhofer Gesellschaft, Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, D-53754 Sankt Augustin, Germany, e-mail: peter.post@scai.fraunhofer.de RID="**"     

Intensity and bandwidth of multiphonon vibronic transitions of rare-earth ions in crystals

The theory of multiphonon vibronic coupling to electronic transitions is applied in analysing fluorescence spectra of Eu²⁺ in BaFCI, which consist of the 4f⁷(⁶P_7/2,) → 4f⁷(⁸S_7/2) and 4f⁶5d → 4f⁷ transitions, and the 4f⁷-4f⁶5d excitation spectrum of Ce³⁺ in YPO⁴. The 4f electrons are weakly coupled to lattice vibration modes so that only weak one- and two-phonon sidebands are observable in the 4f-4f optical transitions, whereas the electron-phonon coupling is significantly stronger for a 5d electron. Accordingly, intensive multiphonon vibronic transitions overwhelmingly dominate the 4f⁶5d → 4f⁷ spectrum. It is shown that the extended Judd-Ofelt theory for weak vibronic coupling in the framework of the M-process is equivalent to the Huang-Rhys theory for the δ-process. In the analysis of experimental data, contributions from local ligand modes and lattice acoustic modes are separated, and the coupling strength is evaluated, in terms of the Huang-Rhys parameter S, for the 4f-4f and 5d-4f vibronic transitions.     

Krein Regularization of <Emphasis Type="Italic">λϕ</Emphasis><Superscript>4</Superscript>

We calculate the four-point function in λϕ ⁴ theory by using Krein regularization and compare our result, which is finite, with the usual result in λϕ ⁴ theory. The effective coupling constant (λ _μ ) is also calculated in this method.     

Higgs as gauge fields on discrete groups and Standard Models for electroweak and electroweak-strong interactions

We complete the construction of the gauge theory on discrete groups coupled to fermions in the spirit of non-commutative geometry. We show that a simple Higgs field is such a gauge field with respect toZ ₂-gauge symmetry overM ⁴ and the Yukawa coupling between Higgs and fermions is automatically introduced via minimum coupling principle. TheZ ₂-symmetry is taken to be ={e, r=(CPT) ²}, a sub-symmetry of the CPT transformations. The Weinberg-Salam model for the electroweak interaction as well as the Standard Model for the electroweak-strong interaction are reformulated in detail.Work supported in part by The National Natural Science Foundation Of China     

Vibronic coupling in the first four electronic states of CH2F+2

Vibronic coupling in the energetically lowest first four electronic states of CH₂F⁺₂ is studied in this paper. A model 4×4 Hamiltonian is constructed in a diabatic electronic representation employing normal coordinates of vibrational modes and standard vibronic coupling theory. Extensive ab initio quantum chemistry calculations are carried out to determine the parameters of the Hamiltonian and energetic ordering of the electronic states. The topographical features of the latter are examined at length and several conical intersections are established. Nuclear dynamics calculations on coupled electronic states are carried out from first principles by propagating wave packet. Theoretically calculated broad band vibronic structure of the four states are found to be in good accord with the experimental results.     

Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

The magneto-optical and magnetic properties of Nd ³⁺ ions in Y ₃Fe ₅O ₁₂ garnet are analyzed by using quantum theory. In the spontaneous state, the magneto-optical effects originate mainly from the intra-ionic electric dipole transitions between the 4 f ³ and 4 f ²5d states split by the spin-orbit, crystal field, and superexchange interactions. For the excited configuration, the coupling scheme of Yanase is extended to the Nd ³⁺ ion. The magneto-optical resonance frequencies are mainly determined by the splitting of the 5d states induced by the crystal field. The theoretical results of both Nd magnetization and Faraday rotation are in good agreement with experiments. The observed Faraday rotation is proved to be of the paramagnetic type. Although the value of the magneto-optical resonance frequency derived from a macroscopic analysis is approximately confirmed by our theoretical study, a new assignment about the transitions associated with this resonance is unambiguously determined. The spin-orbit coupling of the ground configuration has a great influence on both the Faraday rotation and magnetization, but, unlike the theoretical results obtained in some metals and alloys, the relation between the Faraday rotation and the spin-orbit coupling strength is more complex than a linear one. The magnitude of the magneto-optical coefficient increases as the spin-orbit interaction strength of the ground configuration decreases when the strength is not very weak. Finally, the temperature dependence of the magneto-optical coefficient and the effect of the mixing of different ground-term multiplets induced by the crystal field are analyzed. Received 8 November 2000     

Exchange and nuclear symmetry interference in He+-He scattering

A method is described to determine the potential difference, V _g-V _u, that will accurately reproduce the exchange and nuclear symmetry oscillations observed by Aberth et al. in their experimental work on He⁺-He differential scattering. It is demonstrated that at higher energies and angles the experimental results for ⁴He⁺-⁴He, ⁴He⁺-³He and ³He⁺-³He appear incompatible with one another when investigated in terms of a two-state scattering theory. This is an indication that at these energies and angles the theory may require modification to include the effects of coupling to higher states.     

The flexoelectric effect in nematic liquid crystals: A statistical- mechanical approach

The flexoelectric coefficients e₁ and e₃ for polar liquid crystals, such as 4-n-pentyl- 4^′-cyanobiphenyl, are investigated theoretically by means of an integral equation approach, which takes into account translational, orientational correlations as well as their coupling. e₁ and e₃ are evaluated from microscopic expressions derived on the basis of a density-functional method. Received 27 April 2001 and Received in final form 27 August 2001     

Infrared Features of Unquenched Lattice Landau Gauge QCD

The running coupling and the Kugo-Ojima parameter of unquenched lattice Landau gauge are simulated and compared with the continuum theory. Although the running coupling measured by the ghost and gluon dressing function is infrared suppressed, the running coupling has a maximum of α₀ ∼ 2 − 2.5 at around q = 0.5 GeV irrespective of the fermion actions (Wilson fermions and Kogut-Susskind (KS) fermions). The Kugo-Ojima parameter c which saturated to about 0.8 in quenched simulations becomes consistent with 1 in the MILC configurations produced with the use of the Asqtad action, after averaging the dependence on polarization directions caused by the asymmetry of the lattice. The presence of the correction factor 1 + c ₁/q ² in the running coupling depends on the lattice size and the sea quark mass. In the large lattice size and small sea quark mass, c ₁ is confirmed of the order of a few GeV. The MILC configuration of a = 0.09 fm suggests also the presence of dimension-4 condensates with a sign opposite to the dimension-2 condensates. The gluon propagator, the ghost propagator, and the running coupling are compared with recent pQCD results including an anomalous dimension of fields up to the four-loop level.     

Bogoliubov compensation principle in the electro-weak interaction: value of the gauge constant,muon g-2 anomaly,predictions for Tevatron and LHC

We apply the Bogoliubov compensation principle to the gauge electro-weak interaction to demonstrate the spontaneous generation of an anomalous three-boson gauge invariant effective interaction. The non-trivial solution of the compensation equations uniquely defines the values of the parameters of the theory and the form factor of the anomalous interaction. The contribution of this interaction to the running EW coupling, α _ew(p ²), gives its observable value α _ew(M _W ²)=0.0374, in satisfactory agreement to the experiment. The anomalous three-boson interaction gives a natural explanation of the well-known discrepancy in the muon g−2. The implications for EW studies at Tevatron and LHC are briefly discussed.     

Investigating the impurity structure for Fe3+ ions doped into rutile titanium dioxide single crystal

The local environment around Fe³⁺ centers in rutile TiO₂ crystals is studied by employing fourth-order perturbation theory formula based on the dominant spin–orbit coupling mechanism. The zero-field splitting parameters (ZFSPs) D and E and crystal field parameters are modeled for the Fe³⁺ ions not only at the substitution Ti⁴⁺ site, but also at the interstitial site with local symmetry D_2h. In order to acquire the best agreement between the calculated ZFSPs and those measured by electron magnetic resonance, the model parameters are adjusted on the basis of several approaches. This enables us to determine the feasible values of the structural distortions resulting from dopant Fe³⁺ ions. Consequently, it is confirmed that Fe³⁺ ions substitute for Ti⁴⁺ sites in rutile TiO₂ crystals.     

Direct calculation of transition intensities in LiYF<Subscript>4</Subscript>: Nd<Superscript>3+</Superscript>

Duan’s simple model is extended to analyze the mixing of the 4f ^{N − 1}5d configuration with the 4f ^N states. The explicit static coupling and traditional dynamic coupling are considered, and the parameters are fitted according to the absorption spectrum in LiYF₄: Nd³⁺. The parameter values obtained are as follows: T ₃₂ = −28i × 10⁻⁷, T ₅₂ = −1151i × 10⁻⁷, A ₃₂² = 192i × 10⁻¹² cm, A ₅₂⁴ = i × 10⁻¹² cm, A ₇₂⁶ = 54i × 10⁻¹² cm, and A ₇₆⁶ = −680i × 10⁻¹² cm. Compared to the experimental measurements, the present model yields better results than those obtained from the Judd-Ofelt theory. The text was submitted by the authors in English.     

Study of spin–phonon coupling in LiFe1 − xMnxPO4olivines

LiFe_{1 − x}Mn_xPO₄ olivines are promising material for improved performance of Li‐ion batteries. Spin–phonon coupling of LiFe_{1 − x}Mn_xPO₄ (x = 0, 0.3, 0.5) olivines is studied through temperature‐dependent Raman spectroscopy. Among the observed phonon modes, the external mode at ~263 cm⁻¹ is directly correlated with the motions of magnetic Fe²⁺/Mn²⁺ ions. This mode displays anomalous temperature‐dependent behavior near the Néel temperature, indicating a coupling of this mode with spin ordering. As Mn doping increases, the anomalous behavior becomes clearly weaker, indicating the spin–phonon coupling quickly decreases. Our analyses show that the quick decrease of spin–phonon coupling is due to decrease of the strength of spin–phonon coupling, but not change of spin‐ordering feature with Mn doping. Importantly, we suggest that the low electrochemical activity of LiMnPO₄ is correlated with the weak spin–phonon coupling strength, but not with the weak ferromagnetic ground state. Our work would play an important role as a guide in improving the performances of future Li‐ion batteries. Copyright © 2015 John Wiley & Sons, Ltd.     

Non-collinear spin DFT for lanthanide ions in doped hexagonal NaYF4

Trivalent lanthanide ions (Ln³⁺) doped in hexagonal (β)-NaYF₄ nanocrystals (Na₂₄Y₂₃Ln₁F₉₆, Ln = La, Ce, Pr, Nd, Pm, Sm, Eu, Gd) were systematically studied by density functional theory (DFT) with a perturbative account for spin–orbit coupling. The simulated results, including the optimised molecular structures, electronic and magnetic properties, are compared to previous spin-polarised DFT studies in the same system. The spin–orbit coupling effects become significant with the increase in the number of unpaired 4f electrons in the doped lanthanide ions, particularly for the Sm³⁺-, Eu³⁺- and Gd³⁺-doped nanocrystals. Abnormal behaviour of Eu³⁺-doped nanocrystals was observed due to the Wybourne–Downer mechanism. A ‘sandwich-like’ 2p–4f–4d,5d electronic structure for Na₂₄Y₂₃Ln₁F₉₆ and the energies of the highest occupied 4f electrons from Ce³⁺ to Gd³⁺ are consistent with Dorenbos's relationship. The energy difference between the first and second Russell–Saunders terms (^2S+1L) of the lanthanide dopant is consistent with Carnall's experimental results and with earlier spin-polarised DFT calculations.