Microwave spectrum,dipole moment,and conformation of 3-methylcyclopentanone

The rotational spectrum of 3-methylcyclopentanone has been observed in the frequency region from 18.0 to 26.5 GHz. Both a-type and b-type transitions in the ground vibrational state and a-type transitions in five excited states have been assigned. The ground state rotational constants are determined to be A = 5423.32 ± 0.18, B = 1949.51 ± 0.01, and C = 1529.59 ± 0.01 MHz. Analysis of the measured quadratic Stark effects gives the dipole moment components ∥μ_a∥ = 2.97 ± 0.02, ∥μ_b∥ = 1.00 ± 0.03, ∥μ_c∥ = 0.18 ± 0.06, and the total dipole moment ∥μ_t∥ = 3.14 ± 0.03 D. These data are consistent with a twisted-ring conformation with a methyl group in the equatorial position.     

The Fritzsch mass matrix and geometrical scaling of quark masses

It is shown by numerical calculation that the best fit of the Fritzsch matrix to present data is found for values of the top-quark mass between 30 and 60 GeV, depending on the value adopted for the strange-quark mass. The value of m_t that produces the best fit is very close to the geometrical scaling prediction of m_t = m_b(m_c/m_s) for current-quark masses. The residuals of the fit obey a surprising scaling rule, being functions of m_sm_t rather than of m_s and m_t separately.     

Measurement of π−p → π0n at large momentum transfer

New results on a high statistics measurement of pion-nucleon charge exchange scattering at 40 GeV/c, extending in momentum transfer up to ?t = 1.8 (GeV/c)², are reported and compared with an optical impact parameter model, together with previous data for the reaction π^?p → ηn at the same energy. The imaginary part of the pole trajectory b₀(s) is determined from the slope of the tangent to the maxima of $\text{(?t)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{d}\text{σ}\text{d}\text{t}$. The linear increase of Im b₀(s) with log s, which has been observed at low energies, continues up to 40 GeV/c.     

Surface demagnetizing field as a source of uniaxial surface anisotropy in GdCoMo thin amorphous films

Surface magnetic anisotropy energy was studied for (Gd_0.26Co_0.74)_0.96Mo_0.04 and (Gd_0.29Co_0.71)_0.96Mo_0.04 thin amorphous films by means of microwave spectroscopy at the X-band within the temperature range 4–295 K. Excitations of surface spin waves were observed in the spin wave resonance spectra. The experiment was performed in a rotating external magnetic field. The angular dependence of the resonance field for the uniform mode (spin wave vector k=0) and the surface mode made it possible to determine the surface uniaxial anisotropy constant K_s and its temperature dependence. An inhomogeneity of the saturation magnetization M_s within a close-to-surface layer of thickness d can generate the surface anisotropy energy with anisotropy constant K_s given by the formula: K_s=4πM^b_s (M^b_s−M^surf_s)d, where the indexes b and surf correspond to the bulk and surface values, respectively. The temperature dependence of K_s calculated by means of the formula agrees qualitatively with temperature dependence of K_s found in the experiment.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

An investigation of unitarity at ISR energies

We analyse the unitarity equation in impact-parameter space using recent ISR data (at s=930 GeV²) on σ_T, dσ/dt (elastic) and d²σ/dtdM² (diffractive) as input. The assumption of s-channel helicity conservation for the diffractive process leads to a diffractive overlap function which is central. Unitarity then restricts single diffraction to satisfy 2σ_d?5.8 mb. The assumption of t-channel helicity conservation, on the other hand, gives the interesting result that diffractive processes are peripheral in b-space if the diffractively produced state has high spin. Unitarity in this case gives no significant bound on 2σ_d. For both cases, non-diffractive processes are peripheral.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

On Asymptotics for the Airy Process

The Airy process t→A(t), introduced by Prähofer and Spohn, is the limiting stationary process for a polynuclear growth model. Adler and van Moerbeke found a PDE in the variables s ₁,s ₂, and t for the probability Pr(A(0)≤s ₁, A(t)≤s ₂). Using this they were able, assuming the truth of a certain conjecture and appropriate uniformity, to obtain the first few terms of an asymptotic expansion for this probability as t→∞, with fixed s ₁ and s ₂. We shall show that the expansion can be obtained by using the Fredholm determinant representation for the probability. The main ingredients are formulas obtained by the author and C. A. Tracy in the derivation of the Painlevé II representation for the distribution function F ₂ plus a few others obtained in the same way.     

Hysteresis in the nonlinear driven drift and KdV equations

The nonlinear driven/damped differential equation ∂φ/∂t+a∂³φ/∂t∂²y+b∂³φ/∂³y+c∂φ/∂y+fφ∂φ/∂y= −ϵ sin (Ky-ωt)−γφ with a=0 (KdV equation) or b=0 (drift equation) is numerically studied in a parameter region where the energy tends to a constant, E_s, for t→∞. It is found that E_s(ϵ) traces a hysteresis curve when the driving amplitude ϵ is cyclically varied.     

The far-infrared spectrum of tetrahydrothiophene: The bend/twist vibrations and associated barriers

The far-infrared spectrum of tetrahydrothiophene is reinvestigated with a resolution of 0.12 cm^?1 in the region of 50–350 cm^?1. In addition to the bend transitions (ν_b) below 120 cm^?1 reported previously, a number of sequences revealed by the improved resolution are observed for the first time and assigned to transitions of 2ν_b, of the twist (ν_t), and of difference combinations (ν_t - ν_b). Simple one-dimensional modeling of the twist sequence, which is derived from a self-consistent bend-twist energy level diagram, with a quadratic-quartic Hamiltonian suggests a barrier to planarity on the order of 4250 cm^?1. A two-dimensional potential function in the dimensionless coordinates is found to be V(q_b, q_t) = ?249.6q_b² + 4.48q_b⁴ ? 215.5q_t² + 2.73q_t⁴ + 7.00q_b²q_t².     

Entanglement dynamics in Coriolis coupled rovibrational states of formaldehyde

The entanglement dynamics of two vibrational modes of a polyatomic molecule coupled by Coriolis interaction to overall molecular rotation is studied in terms of two negativities, N(t) and N_s(t), respectively, defined by the minimum of the eigenvalues and by the sum of the negative eigenvalues of the partial transpose of a density matrix. Various initial states are the products of Dicke states and the products of coherent states of vibrations and rotations. Formaldehyde is taken as an example, and the von Neumann entropy s(t) is simulated for the comparison with both negativities. It is shown that negativity N_s(t) is positively correlated with entropy s(t), and the correlated behavior between negativity N(t) and entropy s(t) strongly depends on initial states. However, these three indicators of entanglement display a dominantly positive correlation for the coherent states with small or large parameters. In addition, for the latter state two quantities N(t) and s(t) are nearly unchanged for a long time. This time can be further increased by the increasing of vibrational quantum number so that molecular information processing and quantum computing is allowed. These results are useful in quantum information theory.     

Light-front quark model and analysis of the spectrum of photons from inclusive B → X s γ decays

The electroweak-decay width Γ(B → X _s γ) is investigated in a light-front (LF) constituent quark model. A new partonlike formula is derived that establishes a simple relation between Γ(B → X _s γ) and the b → sγ decay width. A treatment of the b quark as an on-mass-shell particle and the inclusion of effects that arise from the transverse motion of the b quark in the B meson are basic features of this approach. Adopting different b-quark LF distribution functions, both phenomenological ones and those that are derived from constituent quark models, and neglecting perturbative corrections, we compute the photon energy spectra and the moments of the shape function. It is shown that the LF approach can be matched completely with a heavy-quark expansion (HQE), provided that the constituent b-quark mass is redefined in a way similar to that used in HQE to define the pole mass of the b quark. In this way, the correction to first order in 1/m _b can be eliminated from the total width in agreement with the general statement of HQE. We also show that the photon energy spectra calculated in the LF approach agree well with those obtained in the model of Altarelli et al., provided that the same distribution function is used as an input in both cases. Despite the simplicity of the model, our results are in fairly good agreement both with HQE predictions and with available experimental data.     

Dynamical spin system: Exact solution and mean recurrence time

A model involving a chain of N ≥ 2 spins s_i = ±1, i = 1,…,N, evolvi ng syncronously in discrete time t via a nonlinear, autonomous transformation s_i(t+1) = s_i(t)s_i+1(t), i = 1,…,N−1; s_N(t+1) = s_N(t), is presented. The transformation equations are solved explicitly and the detailed decomposition of state space into ergodic sets is found. On the assumption of equally likely initial states, the mean recurrence time is calculated and its variance is discussed. The model displays a strikingly sensitive dependence on the number of spins, and this is reflected in the “staircase” behavior of the mean recurrence time. Remarks are made regarding the connection between the behavior of the model and the ground states of a related two-dimensional Ising model.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

X-ray determination of the mean-square vibrational amplitudes of atoms in nearly perfect CdS crystals

The mean-square amplitudes of Cd and S atoms in CdS were determined for vibrations parallel as well as perpendicular to the c-axis. The results were obtained by measuring the temperature dependence of X-ray integrated intensities for reflections from both basal and prismatic planes in nearly perfect crystals. The analysis of the experimental data is given in detail. The following results were found for T = 295°K: 〈u²_Cd〉_∥ = 2.85±0.04×10^?18cm², 〈u²_s〉_∥ = 1.94 ± 0.08 × 10^?18cm², 〈u²_Cd〉_⊥= 2.39 ± 0.04 × 10^?18cm² and 〈u²_s〉⊥ = 1.63 ± 0.08 × 10^?18cm². The fact that Cd atoms have a larger vibrational amplitude than the S atoms is briefly discussed.     

L ∞ estimates for the space-homogeneous Boltzmann equation

This paper studies the boundedness of solutionsf of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, whenk>5, and under angular cutoff. The main result is that if the initial value isf ₀ ? 0 with (1 + ¦υ¦²)φ₀ εL ¹ and (1 + ¦υ¦)^s f ₀ε L^∞ for somes > 2, then (1 + ¦υ¦^s'f _tεL ^∞ fort>0 and ess_υ,t sup(1 + ¦υ¦)^s'f(υ, t,) < ∞ for anys′ ? s whens ? 5, and anys′ ? s ifs > 5.     

Approximately linear relations between two-nucleon and three-nucleon parameters

The correlation between the triton binding energyE _t and then-d scattering length² a and the zero energy singlet and triplet wound integral I_os and I_ot is investigated, with phaseequivalent separableNN interactions obeying all the important off-shell constraints. It is found that the correlation betweenE _t and² a is stronger than betweenE _t (² a) andI _os ,I _ot separately. A strong correlation is also found between the percentageD-state in the deuteronP _d andI _ot . Fixing all the other off-shell parameters but allowing variations ofI _os andI _ot leads to surprisingly accurate linear relations betweenE _t(² a) andI _os ,I _ot (P _d). These relations depend strongly on the other off-shell parameters.     

The anomalous quasi isotropic [g] tensor found for CdBr2:Ag2+ and AgBr0.15Cl0.85:Ag2+: An explanation through strong covalency

The “anomalous” quasi-isotropic [g] tensor observed in systems containing the elongated AgBr⁴⁻₆ unit (g_∥ = 2.078 ± 0.003; g⊥ = 2.065 ± 0.003) is reasonably explained, within a rigorous Molecular Orbital framework, in terms of a very high covalency, consistent with the optical electronegativity of Ag²⁺ and previous results on other Cu²⁺ and Ag²⁺ complexes. For the antibonding level 3b_1g(x² − y²) about 90% of the electronic charges should be on bromine ions. The present analysis reveals that g_∥ − g₀ is dominated by charge-transfer excitations while g_⊥− g₀ is dominated by crystal-field excitations.     

Peripheral pn production and decay angular distributions in the reaction π−p → (pn)p at 12 GeV/c incident momentum

The reaction $\text{π}{}^{\mathrm{?}}\text{p}\text{→ (}\text{p}\text{n}\text{)}\text{p}{}_{\mathrm{s}}$, where p_s is a slow proton, was measured at 12 GeV/c incident momentum with the CERN-OMEGA spectrometer. Both antiproton and proton were identified uniquely by electronics information. We obtained 1844 events with four-momentum Transfer squared in the range 0.13 ? |t| ? 0.33 GeV² and with invariant masses $\text{M(}\text{p}\text{n}\text{)}$ up to 2.5 GeV. The corresponding cross section in this t range is determined to be σ = 4 ± 0.4 μb. Extrapolating the differential cross section over the whole t range assuming dσ/dt ≈ exp(5.3t) we estimate a cross section of σ = 9.3 ± 2.0 μb. Comparison with data on $\text{π}{}^{\mathrm{?}}\text{p}\text{→ (}\text{p}\text{p}\text{)}\text{n}{}_{\mathrm{s}}$ (where n_s is a slow neutron) in the same t range shows that the $\text{(}\text{p}\text{n}\text{)}\text{p}{}_{\mathrm{s}}\text{and}\text{(}\text{p}\text{p}\text{)}\text{n}{}_{\mathrm{s}}$ cross sections have approximately the same magnitude.