Comparison between static and adiabatic coupling mechanisms for nonradiative multiphonon transitions in semiclassical approximation

Semiclassical versions of the static (diabatic) and adiabatic coupling schemes are applied to a two-level-one-mode system at total energies above the cross-over level. The corresponding rates of nonradiative multiphonon transitions reduce to alternativemonotonous dependences on the usual Landau-Zener parameter. Static coupling gives an increasing transition probability (per oscillation) of the familiar formP ^st() = 4. Adiabatic coupling associated with a sufficiently low mechanism-specific potential barrier of Born's type produces a decreasing transition probability of the formP ^ad() exp (–2). The underlying Beyond-Non-Condon calculation procedure shows that (1) the weak dependence of the pre-exponential factorP ^ad is a consequence of the-independent normalization of the electronic matrix element governing the non-adiabaticity operator and (2) the occurrence of the mechanism-specific tunnelling factor exp(–2) is due to the avoided crossing of adiabatic oscillator potentials. Ranges of applicability of both alternative coupling schemes are limited by comparison with earlier non-perturbational results.     

56,57,60CoFe NMR/ON,hyperfine anomalies and γ-factors of cobalt isotopes

The results of NMR/ON measurements on^56'57'60Co isotopes in iron are presented. To avoid the uncertainties caused by local demagnetizing field inhomogenities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factor ratios ⁵⁷/ ⁶⁰ = 1.805 (20), ⁶⁰/ ⁵⁶ = 0.761 (20), ⁵⁶/ ⁵⁷ = 0.726 (20) and hyperfine anomalies⁵⁶⁶⁰ = -0.036 (10),^{60 57} = 0.017 (10) and⁵⁷⁵⁶ = 0.018 (10) have been calculated from the experimental results.     

Hyperfine anomalies and nuclear γ-factors of56Co,57Co and60Co isotopes studied by NMR/ON

The results of NMR/ON measurements on^56,57,60Co isotopes in iron are presented in the paper. To avoid the uncertainties caused by local demagnetizing field inhomogeneities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factors ratios ⁵⁷/ ⁶⁰=1·805(20), ⁶⁰/ ⁵⁶ = 0·761(20), ⁵⁶/ ⁵⁷ = 0·726(20) and hyperfme anomalies^{56 60} = –0·036(10),^{60 57} = 0·017(10) and^{57 56} = 0·018(10) have been calculated from the experimental results.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.     

Photon scattering on quasi-free neutrons in the reaction γd→γ′np and neutron polarizabilities

The possibility to obtain information on n scattering at intermediate energies from the reaction dnp is analyzed. To this aim, the differential cross sectiond ³ /d ,d _n dE _n and the scattering asymmetry with linearly polarized photons are calculated at photon energies 100 to 400 MeV in the diagrammatic approach. The pole diagrams of the impulse approximation are evaluated with realistic n and p scattering amplitudes. One-loop diagrams withnp rescattering in the final state and with meson-exchange and isobar currents are taken into account as well. The main contribution to the differential cross sectiond ³ /d ,d _n dE _n in the kinematics of quasi-free n scattering arises from the neutron pole diagram. The correction due to other diagrams is typically –30% to –10% and decreases with increasing photon energy and momentum transfer. The sensitivity of the cross sections to the magnitude of the neutron electric polarizability and to the sign of the ⁰2 decay constant is demonstrated.     

Representations of an algebra of the Gell-Mann-Dashen type

LetG denote the infinitedimensional Lie algebra given by communtation relations [a _m ,a _n ] =c a _m+n (m, n=0, 1, ...), wherec are structure constants of the arbitrary centerless Lie algebra. The paper is devoted to the construction of a certain class of skewsymmetric irreducible representations (so called F-representations) of the algebraG .     

A Democritean phenomenology for quantum scattering theory

The basic operational devices in a particle theory are detectors which show that a particle is here, now rather than there, then. Successful operation of these devices requires a limiting velocity. Given auxiliary devices which can change particle velocities in both magnitude and direction, the Lorentz-invariant mass can be defined. The wave-particle duality operationally required to explain the scattering of particles from a diffraction grating then predicts fluctuations in particle number (the Wick-Yukawa mechanism), if we postulate a smallest mass. We show that this suffices to establish the conventional quantum mechanical scattering formalism without postulating either interactions or analyticity. By introducing the phase change due to external electromagnetic fields, we can describe the auxiliary devices assumed above to an accuracy ofe ²/hc, thus completing the operational definition to that accuracy.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Typical cluster size for two-dimensional percolation processes

The typical cluster size for two-dimensional percolation models is discussed. It is shown that, forW ₀={xZ ²0x}, [–lim _n(1/n) logP _p (W ₀=n)]^–1p–p _c ^– aspp _c , provided thatE _p (W ₀²)/E _p (W ₀)p–P _c ^– aspp _c . Furthermore, we introduce a new quantityf _s (p), which may be thought of as the singular part of the free energy, and show thatf _s (p)¦p–p _c ¦^2v provided that the correlation length ¦p–p _c ¦^–v aspp _c .     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

The form factors of the decays π− → e−¯veγ and K− → e−¯veγ

In the special type of the quark model we obtain the ratio=h _A/h_V of the axial (h_A) and vector (h_V) form factors for the decays ^– e^– ¯v_e and K^– e^–¯v_e different from unity. The low-energy theorem, relating the electric polarizability of the charged pion with the ratio, is analyzed. It is shown that < 1 corresponds to , calculated by accounting the contribution of the scalar meson(700) into the amplitude of the Compton effect on the pion. In the absence of the(700) contribution we have=1.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

KL,S → l+l− decays in the quark model of superconductivity type

The probabilities of K_L,S l⁺l^– decays are calculated by considering only the dominant two-lepton channel K_L,S ^{* *} l⁺l^–. The transitions K⁰ X, where X=⁰,, or (700) dominating in the K_L,S ^{* *}decay amplitudes, are described by the effective weak Lagrangian. The matrix elements of four-quark operators are calculated within the framework of the quark model of superconductivity type. It is shown that the leading contribution to matrix elements of K⁰ X transitions comes from the penguin operator matrix elements.     

Existence of a Constant for Finite System Extinction

We show the existence of a constant (0, ) such that if ⁿ is the extinction time for a supercritical contact process on [1, n] ^d starting from full occupancy, then {log(E[ ⁿ])}/n ^d tend to as n tends to infinity.     

The one dimensional anderson model with off diagonal disorder: band centre anomaly

We study theE-dependence of the Lyapounov exponent <(E)> of an electron with energyE in the one dimensional Anderson model with off diagonal disorder. In the neighbourhood of the band centre we find for nonzero disorder E)>log^–1 E0 forE0, but all even moments of Re(E) diverge logarithmically. As the probability of Re (E)=0 decreases to zero forE0 we conclude that the electron is always exponentially localised.     

Compressible Flow: Turbulence at the Surface

In a study of compressible flow, we have tracked the motion of particles that float on a turbulent body of water. The second moment of longitudinal velocity differences scales as in incompressible flow. However the separation R ²(t) of particle pairs does not vary in time according to the Richardson–Kolmogorov prediction R ²(t)t ³. As expected, the self diffusion d ²(t) shows a crossover between ballistic motion d ²(t)t ² at small t and uncorrelated motion d ²(t)t in the longtime limit.     

Bianchi V imperfect fluid cosmology

Bianchi V, spatially homogeneous imperfect fluid cosmological models which contain both viscosity and heat flow are investigated. The Einstein field equations are established in the case that the equations of state are given byp-(-1),=o ^m, and=o ⁿ (where, o, o,m andn are constants). The physical constraints on the solutions of the Einstein field equations, and, in particular, the thermodynamical laws and energy conditions that govern such solutions, are discussed in some detail. Simple power law solutions and solutions in which there is no heat conduction are studied first. Exact solutions are then investigated in more generality, and it is shown that there exist two first integrals of the field equations for certain values of the physical parameters, m andn. Finally, it is shown that in a special case of interest (in whichm =n = 1/2) the imperfect fluid Bianchi V field equations can be written as a plane-autonomous system, thus facilitating the qualitative analysis of these cosmological models.     

Solution of coupled differential equations of soliton theory

We present the complete set of solutions of the coupled differential equations of the form ()²=(), ² =(). Equations of this form appear in several physical situations.     

Short distance scale invariance and high-energy processes in field theory

The dynamics of short distance interaction is considered from viewpoint of the quark field theory. If the effective coupling of quarks (the invariant charge(p ²)) decreases with distance (with increasingp ²) the field picture unifies different phenomenological models: reggeology in the region of smallp and partonology in the region of highp but(p ² ) lnp ² 1 and predict deviations with a subsequent increase ofp . A character of the deviations depends on the behaviour of whenp ². The variants of the asymptotic freedom (0) and scale invariance (g ₂ ⁰ ) are discussed. The strong suppression of—3 decay is considered as a support for the latter.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

The van der Waals limit for classical systems. I. A variational principle

We consider the thermodynamic pressurep(, ) of a classical system of particles with the two-body interaction potentialq(r)+ ^v K(r), where is the number of space dimensions, is a positive parameter, and is the chemical potential. The temperature is not shown in the notation. We prove rigorously, for hard-core potentialsq(r) and for a very general class of functionsK(s), that the limit 0 of the pressurep(, ) exists and is given by where the limit and the supremum can be interchanged. Here is a certain class of nonnegative, Riemann integrable functions,D is a cube of volume |D|, anda ⁰() is the free energy density of a system withK=0 and density . A similar result is proved for the free energy.     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049