Collective isoscalar monopole and quadrupole oscillations with l-pole—l-pole interactions: A sum rule approach

Appropriate sum rules are shown to reproduce the results of microscopic calculations made in the random phase approximation for the soluble Hartree model with l-pole—l-pole interactions. This approach has the merit to avoid the problem of studying ground state correlations.     

Fourier transform and CARS spectroscopy of the ν1 and ν3 fundamental bands of 14NH3

The ν₁ and ν₃ fundamental bands of ¹⁴NH₃ have been measured using the techniques of Fourier transform and coherent anti-Stokes Raman spectroscopy. The effective values of the band origins, rotational and centrifugal distortion constants, and parameters of the vibrational-rotational interactions have been obtained by analyzing these bands as essentially regular parallel and perpendicular bands, with the “off-diagonal” local resonance interactions excluded from the fit. The “diagonal” l-type resonance effects have been included into the analysis of the ν₃ band for the +l, K = 1 and ?l, K = 2 levels.     

Role of the substrate thickness for the structural properties of organic-organic heterostructures

F₁₆CuPc deposited on pentacene is characterized by the coexistence of two different configurations: F₁₆CuPc is found in the standing up phase (“s-configuration”) on top of pentacene terraces and in a lying down phase (“l-configuration”) at pentacene step edges. By combining AFM and grazing incidence X-ray diffraction we show that the ratio between F₁₆CuPc in l- and s-configurations increases with thickness of the pentacene substrate film, demonstrating the role of the pentacene steps as nucleation centers for the F₁₆CuPc l-configuration. Experiments performed with ultra-thin pentacene thicknesses disclose that the F₁₆CuPc l-configuration does not grow on top of the first and second pentacene layers, pointing to the action of long-range interactions with the substrate.     

The democratic nuclear interaction in relative S states

A simple relative l=0 interaction is obtained by setting all relative matrix elements of a given spin equal to each other. The nuclear matrix elements are nearly equal for this interaction and the standard l=0 interactions such as the Kallio-Koltveit interaction, although the relative matrix elements are quite different.     

Phase diagrams of competing quadruple and binary interactions on Cayley tree-like lattice: Triangular Chandelier

We study the phase diagrams for the Ising model on a Cayley tree-like lattice, called Triangular Chandelier, with competing nearest-neighbour interactions J₁, prolonged next-nearest-neighbour interactions J_p and one-level next-nearest-neighbour quadruple interactions J_l1. The phase diagrams display the multicritical points (the Lifshitz points) that are at nonzero temperature and many modulated phases. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular case, previous work of Vannimenus extension result given by Ganikhodjaev and U?uz for k=3. At vanishing temperature, the phase diagram is fully determined for all values and signs of J₁,J_p and J_l1. At finite temperatures several interesting features are exhibited for typical values of J_l1/J₁ and −J_p/J₁.     

CP violation andZ boson decays

We present a general discussion ofCP-violating effects in the following two and three body decays of theZ boson:Z→l ⁺ l ^?,Z→l ⁺ l ^?γ, wherel=e, μ, τ andZ→2 jets,Z→ 2 jets+γ, andZ→ 3 jets. Experimental observables sensitive toCP violation in these decays are discussed systematically for the case that polarizations of final state particles are not observed. It is shown that the standard model predicts only extremely smallCP-violating effects for the above decays. PossibleCP-violating interactions beyond the standard model are parametrized in terms of aCP-odd effective Lagrangian containing coupling constants proportional to Λ _P ^-1 and Λ _P ^-2 . Here Λ _CP is the mass scale associated with the assumed new interactions. We give estimates of the bounds obtainable for Λ _CP in experiments at LEP1.     

Rare meson decay in supersymmetric theory with nonconservation of <Emphasis Type="Italic">R</Emphasis>-parity

The decay of mesons K ⁺ → π ^? l ⁺ l′⁺ and D ⁺ → K ^? l ⁺ l′⁺ (l, l′ = e, μ) involving a change of lepton number ΔL = 2 is considered in a supersymmetric extension of the standard model in which R-parity is not conserved due to trilinear Yukawa interactions. The obtained estimates for the probabilities of these decays are significantly lower than the direct experimental upper limits.     

On the Lorentz structure of Z→ττ

Together with the vector and axial vector couplings, the general Lorentz structure of leptonicZ decays, e⁺e^?→Z→l ⁺ l ^?, allows various additional types of interactions which are studied here. A way to measure these contributions in the reactionZ→τ⁺τ^? is described. This measurement may be performed at LEP and the SLC.     

On the magnetic moment inZ→ττ

Together with the vector and axial vector couplings, the general Lorentz structure of leptonicZ decays,Z→l ⁺ l ^?, allows for two types of interactions which correspond to weak magnetic and electric dipole moments. A way to measure the anomalous weak magnetic moment in the reactionZ→τ ⁺ τ ^? is described. This measurement may be performed at LEP and the SLC.     

Short-range interaction in three-dimensional quantum mechanics

We show that it is possible to define shape-independent three-dimensional short-range quantum interactions in two-parameter form for non-spherical angular momentum channels through double rescaling of potential strength. Unlike the special case of l=0, where the zero-range limit of the system is renormalizable, the effective ranges diverge for l≠0 channels, and the system becomes trivial at zero-size limit. It is also shown that the two-parameter representation with finite interaction range is useful in analyzing phase shifts and describing resonances with accuracy in non-spherical scatterings.     

Fundamental length hypothesis and new concept of gauge vector field

Through an analysis of quantum field theory with “fundamental length” l[1–10], a new concept of gauge vector field is determined. The electromagnetic field is considered in detail. The new electromagnetic potential turns out to be a 5-vector associated with the De Sitter group SO(4,1). The extra fifth component, called τ-photon, similar to the scalar and longitudinal photons, does not correspond to an independent dynamical degree of freedom. Gauge-invariant equations of motion for all components of the electromagnetic 5-potential are found. Though the new gauge group remains Abelian, it is nevertheless larger than the conventional gauge group. In particular, the new gauge transformations intrinsically depend on the fundamental length l. Therefore one can consider them as a base for modification of QED at small distances (?l) in a profound way. The underlying physics becomes much richer due to the appearance of new interactions mediated by the τ-photons [14].     

Weak four-fermion interaction in terms of SU(3) invariants. I

The four-fermion weak interaction is formulated in terms of invariants of the groups G₂=L?SU (2) and G₃=L?SU(3). The four-fermion Hamiltonian is constructed as a four-fermion invariant of the group G₃ on the basis of the spin tensorsψ _#x03B1;βγ ^lmn , whereα, β, γ=1, 2, 3, 4 are the spinor indices andl, m, n=1, 2, 3 are the unitary indices of the representation of G₃. It is shown that in the case of one multipletψ _#x03B1;βγ ^lmn one can construct one nontrivial invariant and in the case of two multipletsψ _#x03B1;βγ ^lmn and? _#x03B1;βγ ^lmn , nine nontrivial invariants. Of these, only in the case of two of the invariants, which contain two multiplets, are the lepton and baryon numbers conserved independently. One of these invariants is considered in detail. In the case of SU(2) there is no fundamental difficulty and a number of relations are obtained for the constants of the weak interactions and the probabilities of processes. In the case of SU(3) it is shown that the known breakings of SU(3) in weak interactions can be localized in the lepton octet by choosing it in a special way.     

Mixed lump-stripe,bright rogue wave-stripe,dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev–Petviashvili equation in fluid mechanics

Under investigation in this paper is a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics. We derive the mixed lump-stripe waves, bright mixed rogue wave-stripe, dark mixed rogue wave-stripe and dark rogue waves solutions by virtue of the symbolic computation. We observe the fission and fusion phenomena between the lump and one-stripe wave through the mixed-stripe wave solutions. Then, we observe that the influence of l₁, l₂, l₃, l₄, l₅, l₆, l₇ and l₈ on the mixed lump-stripe waves, where l₁ and l₂ represent the dispersion and nonlinear effects, l₃, l₆, l₇ and l₈ are the perturbed effects, while l₄ and l₅ stand for the disturbed wave velocities along the transverse spatial coordinates y and z, respectively. We graphically present the interaction between a rogue wave and a pair of stripe waves through the mixed rogue wave-stripe solutions. We derive a dark mixed rogue wave-stripe when l₁ < 0. We study the influence of l₁, l₂, l₃, l₄, l₅, l₆, l₇ and l₈ on the rogue wave and a pair of stripe waves. We present the dark rogue wave with certain parameters and observe that two stripe waves merge into one stripe wave.     

The Rotational Spectrum of SiHF3 in the Vibrational State υ6=2: Observation of Direct l-Type Resonance Transitions

The υ₆=2 vibrational state of the main isotopomer of trifluorosilane, ²⁸SiHF₃, has been investigated in the centimeter- and millimeter-wave ranges. Rotational spectra following the Δ J=1, Δk=Δ l=0 selection rule have been measured up to J=24 and K=23 and for both values of ∣l∣. Two types of direct l-type resonance transitions induced by the (Δ l=Δk=±2) interaction could be observed by means of waveguide Fourier transform microwave spectroscopy in the range 8-26 GHz: 252 transitions following the Δ J=0, Δl=Δk=±2 selection rule covering values of J=7-39 and G=∣k-l∣ from 1 to 18 and 90 transitions following the Δ J=0, Δl=Δ k=±4 selection rule covering values of J=17-52 and G from 1 to 4. Due to the strong (2,2) resonance, 18 A₁-A₂ splittings of the k=l=±2 states from J=36-53 could also be observed. Accidental near-degeneracies lead to strong perturbations due to Δ (k-l)=±3 interactions, enabling the observation of perturbation-allowed transitions with selection rules k=±3(l=±2)↔±4(±2), ±2(±2), A₊↔ ±1(?2), A₋ and ± 1(0)↔± 6(±2). In a multiple-fit analysis the experimental data have been refined using five reduced forms of the effective Hamiltonian as proposed by Sarka and Harder [J. Mol. Spectrosc.197, 254-261 (1999)]. Parameters up to seventh order have been determined including the axial rotational constant C for both values of ∣l∣ and the vibrational separation of the ∣l∣=0 and 2 states. The unitary equivalence of the determined parameter sets has been demonstrated up to fifth order. Differences of the rotational constants in the various parameter sets have been explained by the theory of reduction. Sign relations of the fitted parameters and general features of the direct l-type resonance spectrum in a υ_t=2 level are discussed.     

The millimeter-wave rotational spectrum of CF3CCD in the excited vibrational state v10=2

The millimetre-wave rotational spectra of the excited vibrational state v₁₀=2 of the symmetric top molecule, CF₃CCD, have been recorded for J^′′=12 up to J^′′=25. The l=±2 and l=0 series have been assigned and the spectra analysed to give rotational parameters including x_ll=7716.975 MHz. The main interactions between states of different l are the r_t(2,−1)=0.158 MHz and q_t⁺(2,2)=3.308 MHz. Two type of l-resonance are identified, one of which is due to an avoided crossing between the l=0 and l=+2 series. The spectra are qualitatively similar to the corresponding ones of CF₃CCH.     

Overview of the CKM physics opportunities beyond K^ + \to \pi ^ + \nu \bar \nu

A new experiment CKM is accepted by Fermilab for a very sensitive study of rare kaon decay $K^ + \to \pi ^ + \nu \bar \nu $ on an intense separated kaon beam. The high quality of the beam and CKM setup make it possible to perform an important set of other kaon-decay measurements in parallel with the main research program: (1) the search for new physics effects beyond the Standard Model (search for new P, S, T interactions and lepton flavor violation in kaon decays); (2) further search for direct CP violation in charged kaon decays; (3) study of low-energy hadron physics in pure conditions of decay processes (K ⁺ → π ⁺ l ⁺ l ^?; ππlν _l; π ⁰ γγ, etc.). The expected results of these studies are compared with other experimental programs.     

The perturbative approach to the critical behaviour of two-matrix models in the limit N → ∞

We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders. If the multiplication operators B_1,2 tend to differential operators of order l_2,1, respectively, the singularity is characterized by (l₁, l₂). Let l₁ ⩾ l₂. Then the two cases, (A) “l₂ does not divide l₁” and (B) “l₂ divides l₁”, need a different treatment. The universality classes are labelled [p, q] where [p, q] = [l₁,l₂] in case (A) and [p, q]=[l₁ + 1,l₂] in case (B).     

Relativistic shift of the linear Zeeman effect

The efficiency with which a magnetic field acts on sublevels of the first and second doublets of a hydrogen-like atom is shown to vary because of relativistic effects by a factor of 1 ? 2γ(l + 1)/(2l + 3) and 1 ? 2γl/(2l ? 1), respectively, where γ is the ratio of the electron binding energy to the rest energy and l is the quantum number of the orbital angular momentum.     

Interaction de l'oxygène aux basses pressions avec la solution solide niobium-oxygène à haute température: I. Èquilibre de segrégation — chimisorption

Interactions between oxygen under low pressure and a niobium-oxygen solid solution had been studied, in the regime where adsorption is the rate-determining step, from 1000 to 1700 K. It is shown that at saturation of solid solution, there exists a constant limiting value Θ_l of superficial coverage, comparable to a limiting bulk concentration c_l. The ratios θ = Θ/Θ_l and ? = c/c_l are called “relative ratio of occupation” (superficial and bulk). $\text{K}$_SV is the equilibrium constant of segregation between adsorbed and dissolved oxygen atoms: (O_diss^?v) + σ ? (O_chim?σ) + v (σ and v being respectively surface and bulk sites), $\text{K}$_SV = [(1 ? θ)/θ] [?/(1 ? ?)]. The experimentally determined expression: $\text{K}$_SV = 5.7 exp[?(22.1 ? 12.1 θ)/ RT] shows that lateral superficial interactions have a large influence on the enthalpy of transfer between the bulk and the surface of the sample. Adsorption is direct and non activated. At the solubility limit, only a fraction of the superficial sites is occupied. We estimate it to be one half. The sticking probability b of oxygen on a niobium oxygen solid solution is given by b = (1 ? θ/2)², its value at zero coverage being estimated as unity.