N.M.R. solid echoes in systems of coupled pairs of spins-1/2

Proton solid echo transverse relaxation functions, mapped by measurement of the echo amplitude S _{y x} (t′ = τ) as a function of τ using a P _y (90°)-τ-P _x (90°)-t′ sequence, are reported for a variety of thermotropic mesogens and mesophases (see Table 1). The relationship of the shapes of this function to the structure and dynamics of the mesogen molecule and the mesophase structure is explored. A heuristic approach is adopted. The spin response for an alkyl chain moiety of a mesogen molecule in a uniaxial mesophase is considered to be the sum of the responses for an assembly of representative subsystems each of which consists of two equivalent pairs of spins-½. The response for the latter is calculated by introducing the effects of motional averaging into the expression obtained in Paper I and estimating an ordering matrix from deuterium quadrupole splittings measured on the corresponding deuteriated mesogen. This model, albeit physically unrealistic, qualitatively reproduces the salient features of the observed relaxation functions. The shape functions are found to be rather insensitive to the structure of the mesogen molecule and the type of mesophase involved, but distinguished by the morphological structure of the sample. In homogeneously aligned mesophases, the shape is mainly determined by the distribution in the intersegmental (CH₂) dipolar interactions, whilst in unaligned mesophases the shape is determined by the orientational distribution of the director. A value for M ₂ ^vv(inter-pair) can be obtained from the decay of the relaxation function of unaligned mesophases, but not for aligned ones. There is an exchange process which contributes to the damping of both the FID signal and solid echo relaxation function in unaligned smectic-A mesophases which is absent in the corresponding aligned mesophases. This process must be a consequence of the defect structure of the smectic-A phase and involve rapid diffusion of molecules between regions distinguished by different orientations of the mesophase director.     

N.M.R. dipolar echoes in solids containing spin-1/2 pairs

The proton echo responses to resonant 90°-τ-β_90° (XY) and 90-τ-β_0° (XX) pulse sequences in powdered crystalline hydrates are reported. The echo produced by the XY sequence consists of two components: one is proportional to sin² β and the other to sin² β cos² β; the former component decays much faster than the latter on increasing the pulse spacing τ. In contrast, the XX sequence produces a single component echo of the form - sin² β cosβ. The maximum echo amplitudes for the sequences 90°-τ-90°_90° and 90°-τ-54°44′_0° exhibit a gaussian dependence on τ² over at least 95 per cent of their decays. The decay constant for the 90-τ-90°_90° echo corresponds to M ₂(inter) = 5/6 M ₂ ^vv(inter), where M ₂ ^vv(inter) is the interpair second moment calculated by the van Vleck procedure. These observations can be explained in terms of a simple model consisting of a planar arrangement of two spin-1/2 pairs provided the interpair dipolar hamiltonian is truncated so that [?^o _a(intra) + ?^{o, t} _d(inter), ?_z] = 0 and [?^o _a(intra), ?^{o, t} _d(inter)] = 0.

The model predicts the echo behaviour only if the spin-1 character of the eigenfunctions of ?^o _d(intra) + ?_z is preserved in the presence of the interpair interactions. It is shown that the XX echo and the sin² β cos² β components of the XY sequence originate solely in the interpair interactions and contain no contributions from the intrapair interactions. The decay of the maximum echo amplitude with increasing τ is caused by the incomplete refocusing of the interpair interactions by the XX and XY sequences; the correct decay is only determined provided the interpair dipolar hamiltonian is correctly truncated. The model also accounts for the proton echo behaviour in solid hydrogen reported by Metzger and Gaines.

Interestingly, the N.M.R. behaviour observed for these spin-1/2 pair systems is largely determined by the eigenfunctions of the spin Hamiltonian with M_z = 0.     

Natural orbitals,diatomic molecules and ERD

The effects of molecular motions on spin-echo signals (2n + 1)90°_y—τ—90°_x:—Acq(t) in nuclear spin systems with dipolar interactions have been investigated. It was found that in the case of a rigid lattice (M₂τ² _c: >> 1) and a motionally narrowed NMR line (M₂τ² _c,<< 1) a maximum of echo signals is observed at t_e = 2τ + t₂—t₁/2, where t₁ and t₂ are the widths of the RF pulses. It also was found that in the slow motion region (M₂τ² _c ? 1) an amplitude of the dipolar echo signal is reduced and the maximum of the echo signal is shifted to the end of the second pulse. The theory developed is confirmed by the experimental results obtained for C₆H₆.     

Zum selektiven NMR-Spinecho-Verhalten bei Systemen mit I = 1 im Festkörper am Beispiel des Kaliumoxalatmonohydrats

Investigation of the Selective N.M.R. Spin Echo Response of I = 1 Systems in Solids Demonstrated on Potassium Oxalate Monohydrate The theory of the nonselective spin echo response in solids for dipolar-coupled spins I = 1 with quadrupole interaction by BODEN et al. [5] is modified for the case of selective irradiation to only one line of the n.m.r. spectrum. The theoretical results are compared with ¹H-n.m.r. experiments on dipolar-coupled protonpairs of a (KCOO)₂ · H₂O single crystal. This is possible because in this material the interpair dipolar interaction is substantially smaller than the intrapair dipolar interaction. An echo response results which has some similarities to the behaviour of spin systems with heteronuclear coupling.     

Asymptotic behavior of orbits of C 0-semigroups and solutions of linear and semilinear abstract differential equations

In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t ⁿ f(t, u(t)), where A is the generator of a C ₀-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C ₀-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S ^p-A defined similarly to the case of S ^p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A _u:= A ∩ BUC(ℝ, X) if n = 0 and to t ⁿ A _u ⊕ w _n C ₀ (ℝ, X) if n ∈ ℕ, where w _n(t) = (1 + |t|)ⁿ. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0. Dedicated to the memory of B. M. Levitan     

Systematization of intermediate-mass fragments

We consider the power law dependence of cross-sections of formation of intermediate-mass fragments on the mass number and atomic number, σ (A _f ) ～ A _f ^?τ and σ (Z _f ) ～ Z _f ^?τ . The values of parameter τ are determined for fragments detected by the ΔE ? E and the induced activity methods. It is shown that in “liquid-gas” phase transition τ varies within the limits of 2–3. A conclusion was drawn that at high beam energies parameter τ does not depend on the detection angle of the fragment. At the increase in the energy τ passes through a minimum at E _i ～ 6–7 GeV which is typical “critical behavior” predicted by models.     

Mean lifetimes of excited levels of Ar II. I. Time correlation measurements

Mean Lifetimes of excited levels of Ar II have been measured using the method of time-correlated photons in cascade. The following results were obtained: for 4p⁴S^°_{$\text{3}\text{2}$}, τ = 7·2±0·3ns; for 4p′²F^°_{$\text{7}\text{2}$}, τ = 8·8±0·2 ns; for 4p′²F^°_{$\text{5}\text{2}$}, τ = 8·0±0·2 ns. These results are compared with experimental and theoretical values.     

High resolution absorption and magnetic circular dichroism of spin-forbidden ligand field transitions in Cs3CoBr5

The axial absorption spectrum of Cs₃CoBr₅ has been recorded from 3100 to 6500 Å at 4·2 K with a spectral bandpass of 0·1 Å and the magnetic circular dichroism spectrum at 4·2 K and 47·5 kG over the same wavelength range with a spectral bandpass of 1 Å. The electronic origins of the spinorbit and tetragonal field components of most of the doublet ligand field states are definitively located and assigned. In a number of instances it has also proved possible to determine whether the doublet gains its intensity from the 3/2 U′ or 5/2 U′ spin-orbit component of ⁴ T ₁, and arguments are also presented to show that the higher energy doublets derive the greater part of their intensity from the lowest ⁴ T ₁ charge transfer state and not the ⁴ T ₁(P) ligand field state. The vibronic sidebands accompanying the doublet transitions are also assigned to internal modes of CoBr₄ ^2- and to lattice modes. In a number of the transitions non-totally symmetric modes are excited with greater intensity than totally symmetric.     

129Xe contact shift in oxygen gas

We have determined the temperature dependence of σ₁ of ¹²⁹Xe in oxygen gas. These results were obtained by measurement of the resonance frequency of ¹²⁹Xe in gas samples of known densities in Xe and O₂. The shift of the resonance frequency due to Xe-Xe interactions has been measured in pure Xe gas samples with improved precision. This allows the determination of σ₁(Xe-O₂) by subtracting out the known effect of Xe-Xe interactions in mixed Xe-O₂ samples. σ₁(Xe-O₂) values are reported here for the temperature range 220 to 440 K. The values of σ₁(Xe-O₂) are adequately described by the polynomial function in p.p.m. amagat^-1 σ₁(Xe-O₂) = - 1·061 + 3·64 × 10^-3τ - 2·19 × 10^-5τ² + 9·58 × 10^-8τ³ - 2·08 × 10^-10τ⁴, where τ = (T - 300 K). It is found that the temperature dependence of σ₁(Xe-O₂) can be interpreted in terms of a contact interaction between Xe and the paramagnetic O₂ molecule.     

Desorption kinetics and surface diffusion of potassium,rubidium and cesium on a silicon(111)7 × 7-surface

Using pulsed atomic beam technique and a surface ionization ion microscope, the desorption kinetics and the surface diffusion of the alkalis potassium, rubidium and cesium were investigated on a Si(111)7 × 7-surface at extremely low alkali coverages. In the temperature range 1120 … 800 K, the mean adsorption lifetime τ(T) = τ₀ · exp(E_desⁱ/kT) and the mean diffusion length x(T) - defined in the equilibrium between adsorption, diffusion and desorption - were measured. From these data the diffusion constant D(T) = D₀ · exp(-E_diff/kT) was obtained as D = x^?2/τ. For temperatures T ? 750 K, the diffusion constant was calculated from nonstationary alkali concentration profiles using the Boltzmann-Matano method. From the temperature dependence of these quantities the parameters of desorption (E_des,ⁱ τ₀) and surface diffusion (E_diff, D₀) for K, Rb and Cs on Si(111) were obtained. The values of E_diff and D₀ are comparably high and may be interpreted by non-localized diffusion according to a model proposed by Bonzel (Surf. Sci. 21 (1970) 45).     

Conversion coefficients and E0 transitions in102, 104, 106Pd

In in-beam (p, p′) experiments, electron and γ-spectra were measured in the electron energy range of 500-1840 keV for¹⁰²Pd and¹⁰⁴Pd, and 600–1580 keV for¹⁰⁶Pd. The conversion coefficients of all transitions in this range were obtained with accuracies of about 20%, in some favourable cases 10%. Special attention was given to 0⁺′-0⁺ transitions from the two-phonon triplets to the ground states with the following results for the branching ratios 0⁺′-0⁺ (ground state) to 0⁺′-2⁺ (one-phonon state):¹⁰²Pd:T _k (E0)/T _γ (E2)<(2.1±3.6)·10^{?7 104}Pd:T _k (E0)/T _γ (E2)=(6.0±1.4)·10^{?5 106}Pd:T _k (E0)/T _γ (E2)=(6.0±2.0)·10^?4     

Complexation of bis‐crown stilbene with alkali and alkaline‐earth metal cations. Ultrafast excited state dynamics of the stilbene‐viologen analogue charge transfer complex

The complex formation of bis(18‐crown‐6)stilbene ( 1 ) and its supramolecular donor‐acceptor complex with N,N′‐bis(ammonioethyl) 1,2‐di(4‐pyridyl)ethylene derivative ( 2 ) with alkali and alkaline‐earth metal perchlorates has been studied using absorption, steady‐state fluorescence, and femtosecond transient absorption spectroscopy. The formation of 1 ?Mⁿ⁺ and 1 ?(Mⁿ⁺)₂ complexes in acetonitrile was demonstrated. The weak long‐wavelength charge‐transfer absorption band of 1 · 2 completely vanishes upon complexation with metal cations because of disruption of the pseudocyclic structure. The spectroscopic and luminescence parameters, stability constants, and 2‐stage dissociation constants were calculated. The initial stage of a recoordination process was found in the excited complexes 1 ?M⁺ and 1 ?(M⁺)₂ (M = Li, Na). The pronounced fluorescence quenching of 1 · 2 is explained by very fast back electron transfer (τ_et = 0.397 ps). The structure of complex 1 · 2 was studied by X‐ray diffraction; stacked ( 1 · 2 )_m polymer in which the components were connected by hydrogen bonding and stacking was found in the crystal. These compounds can be considered as novel optical molecular sensors for alkali and alkaline‐earth metal cations.     

Radiative decay of the metastable quartet state of copperporphin

In CuP the low temperature luminescence originates from eight transitions between a quartet (M = ±3/2, ±1/2) and a doublet (M′ = ±1/2) with M and M′ denoting the (approximate) eigenvalues of the spin angular momentum S_z along the fourfold axis. Here we report (1) the selection rules governing the polarizations of the transitions; (2) the zero-field splitting ξ between the ±3/2 and ±1/2 components of the quartet for CuP in an n-octane crystal (ξ = 1·1 ± 0·2 cm^-1); (3) a photo-selection experiment on CuP in an isopentane glass from which it is concluded that the ratio of in-plane to out-of-plane polarization in the 0-0 band at 2·1 K amounts to an intensity ratio I _‖/I _⊥ ≈ 2. The implications of these results for the different SOC pathways are analysed.     

Secondary vacuum trajectories and scalar meson exchange

A new second vacuum trajectory passing throughf*(1515) and σ(548), α(t)=? 0.3+t, is proposed, which, together with α_p″(t=0)=? 0.5, overcomes the failure of Igi's original superconvergent πN sum rule and avoids the ghost-state of the conventionalP′-trajectory. The negative residue att=0 confirms the repulsive contribution of a vacuum pole component withJ=0 to the generalizeds-reaction potential, as postulated by Chew (1965). TheP- andP′-poles can build the non resonating background. The Gell-Mann nonsense mechanism at the negative integers with wrong signature explains the dips in the elastic π^± p-scattering att=?0.7, ?2.7 and ?4.5 (GeV/c)². σ(∞) for πN reactions turns out to be 24.3 mb, if α _p (t=0)=1, but the best fits to the total πN cross sections for pion momenta between 2 and 29 GeV/c yield α _p (t=0)=0.93.     

The probability of prompt and delayed fission of muonic237Np

Fission fragments from the reaction²³⁷Np(μ ^?,γ,f) have been measured in coincidence with muonic X-rays. The efficiency of the fission fragment detector is determined from (μ ^?,γ,f)-data of the same experiment. The total fission probability perμ-stopP _t has been measured as well as the fission probabilities P_f of the non-radiative muonic (3d→1s)- and (2p→1s)-transitions; the latter has been divided into two parts leading to different mean excitation energiesE:P _t =(54±17)%,P _f (3d→1s)=(41±21)%,P _f (2p→1s,E=6.218 MeV)=(61±19)%, andP _f (2p→1s,E=6.525 MeV)=(57±18)%. The influence of the muon on the fission barrier is discussed. The fission probability after muon capture is compared with a calculated value using a distribution of nuclear excitation energies following muon capture and the fission probability as measured in a²³⁸U(³He,αf)-reaction.     

Measurement of the spectral functions of vector current hadronic tau decays

A measurement of the spectral functions of non-strange τ vector current final states is presented, using 124 358 τ pairs recorded by the ALEPH detector at LEP during the years 1991 to 1994. The spectral functions of the dominant two- and four-pion τ decay channels are compared to published results of e ⁺ e ^- annihilation experiments via isospin rotation. A combined fit of the pion form factor from τ decays and e ⁺ e ^- data is performed using different parametrizations. The mass and the width of the ρ ^±(770) and the ρ ⁰(770) are separately determined in order to extract possible isospin violating effects. The mass and width differences are measured to be M _ρ ^± ₍₇₇₀₎ - M _ρ ⁰ ₍₇₇₀₎ = (0.0 ± 1.0) MeV/c ² and Γ _ρ ^± ₍₇₇₀₎ - Γ _ρ ⁰ ₍₇₇₀₎ = (0.1 ± 1.9) MeV/c ².     

Unitary Correlations and the Fejér Kernel

Let M be a unitary matrix with eigenvalues t _j , and let f be a function on the unit circle. Define X _f (M)=f(t _j ). We derive exact and asymptotic formulae for the covariance of X _f and X _g with respect to the measures |(M)|²dM where dM is Haar measure and an irreducible character. The asymptotic results include an analysis of the Fejér kernel which may be of independent interest.     

Fröhlich 极化子的非经典基态

本文计及波矢 q,q' 声子间动力学关联效应,采用双模-压缩(声子)相干态作为再一次正则变换方案,基于Huybrechts变分近似,求解 Fröhlich 大极化子的非经典基态.由于双模-压缩(声子)相干态导致声子相干态-压缩声子态关联效应,相干参量 f_q 与双模压缩角 φqq' 关键词： 双模-压缩(声子)相干态 位移-声子压缩态 Frö hlich 极化子 非经典基态     

Tests of the infinite mass effective theory and properties of the charming and beautiful mesons

Using an operator product expansion (OPE) in the inverse of the heavy quark massM _Q and a dispersive approach, we rederive theB andB ^* couplings and the Isgur-Wise function predicted by the infinite mass effective theory (IMET). We find that, at the subtraction pointM _Q and using VDM for the spectral function, these observables are governed by the universal light quark condensate. We also find that the corrections induced by finite values ofM _c andM _b are large and are due to the splitting _b between the ground state and its radial excitation. We review the determinations of the different decay constants, couplings and masses from QCD spectral sum rules (QSSR). Forf _B andf _D , we conclude the optimum average:f _B =(1.59±0.09±0.27)f andf _D =(1.31±0.12)f , where the main error is due to the quark mass, while the first one inf _B is due to the non-perturbative terms and to the choice of the continuum thresholdt _c from the onset of sum rule variable stability until thet _c -stability regions. We also find that the vector coupling _V satisfies approximately the IMETM _Q ^3/2 mass dependence scaling law, whilef _P obeys in units of GeV:f P/f(4.6±0.4)M _Q ^–1/2 (1–1.56/M _Q +0.88/M _Q ² ), forM _Q M _c . We also predict the flavour independence:M _P -M _Q 0.6-0.7 GeV andM _V -M _Q 0.7-0.8 GeV of the mass differences between the mesons and the corresponding quark. Finally we find that theBDev _e form factorf ₊(0)(0.55±0.10) deviates from the naive expectation (f ₊(0)=1).     

Strongly positive semigroups and faithful invariant states

Let (?, τ, ω) denote aW*-algebra ?, a semigroupt>0?τ _t of linear maps of ? into ?, and a faithful τ-invariant normal state ω over ?. We assume that τ is strongly positive in the sense that $$\tau _t (A^ * A) \geqq \tau _t (A)^ * \tau _t (A)$$ for allA∈? andt>0. Therefore one can define a contraction semigroupT on ?= \(\overline {\mathcal{M}\Omega } \) by $$T_t A\Omega = \tau _t (A)\Omega ,{\rm A} \in \mathcal{M},$$ where Ω is the cyclic and separating vector associated with ω. We prove 1. the fixed points ?(τ) of τ are given by ?(τ)=?∩T′=?∩E′, whereE is the orthogonal projection onto the subspace ofT-invariant vectors, 2. the state ω has a unique decomposition into τ-ergodic states if, and only if, ?(τ) or {?υE}′ is abelian or, equivalently, if (?, τ, ω) is ?-abelian, 3. the state ω is τ-ergodic if, and only if, ?υE is irreducible or if $$\mathop {\inf }\limits_{\omega '' \in Co\omega 'o\tau } \left\| {\omega '' - \omega '} \right\| = 0$$ for all normal states ω′ where Coω′°τ denotes the convex hull of {ω′°τ _t } _t>0. Subsequently we assume that τ is 2-positive,T is normal, andT* _t ?₊Ω \( \subseteqq \overline {\mathcal{M}_ + \Omega } \) , and then prove 4. there exists a strongly positive semigroup |τ| which commutes with τ and is determined by $$\left| \tau \right|_t \left( A \right)\Omega = \left| {T_t } \right|A\Omega ,$$ 5. results similar to 1 and 2 apply to |τ| but the τ-invariant state ω is |τ|-ergodic if, and only if, $$\mathop {\lim }\limits_{t \to \infty } \left\| {\omega 'o\tau _t - \omega } \right\| = 0$$ for all normal states ω′.