Distribution of electromagnetic transition amplitudes

In this paper the distribution of electromagnetic transition amplitudes 〈W′∥O∥W〉 is described in terms of fluctuations about a gaussian secular variation (as a function of initial and final energies) according to the Porter-Thomas assumption. Explicit formulas are derived both for the case (i) that∑ _w ′¦〈W′∥O∥W〉¦² is replaced by its local average and (ii) that∑ _W ′¦〈W′∥O∥W〉¦² is treated as a stochastic variable showing a χ _d ² -distribution. The resulting distribution function appears to possess a monomial tail. Comparisons with shell-model results are made.     

Statistical mechanics of a bounded,ideal magnetofluid

A statistical model of a three-dimensional, incompressible, cylindrically bounded, current-bearing magnetofluid is presented for the purpose of gaining insight into the nonlinear relaxation process routinely observed in reversed-field-pinch experiments. An absolute equilibrium ensemble is utilized that incorporates energy, magnetic helicity, and magnetic flux constraints. Results are extracted only after an extensive mathematical treatment of the properties of poloidal and toroidal fields. The model predicts the presence of magnetic fluctuations about a cylindrically symmetric, Bessel-function-model, mean magnetic field, which satisfies ▽ × 〈B〉 = μ〈B〉. As Taylor's ∵-parameter approaches 1.56, the model predicts that the significant region of the fluctuation spectrum narrows down to a single (coherent) m = 1 mode. An analogy between the Debye length of an electrostatic plasma and μ^?1 suggests the physical validity of the model's prediction of the magnetic-field-fluctuation autocorrelation tensor 〈δB(r) δB(r′)〉, when |;r ? r′| ≥ μ^?1.     

Axial contraction in toroidal pinches with non-circular plasma cross-sections

The axial contraction of linear pinches with racetrack-shaped and elliptic cross sections is studied byδW-analysis near the equilibrium shape. A surface current profile and a fixed plasma cross-section area are assumed. It is shown for the corresponding special perturbation thatδW is given by the variation of the surface energy(δW=δW _s =1/8B _p ² ξ _b ² ), and thatδW is nearly independent of the shape of the plasma (racetrack or ellipse). The axial oscillation frequency is found to beΩ _ax=1/2√CB _p /√ρ_l with a constantC<1. The model correctly predicts theB _p and ρ_l-dependences of the experimental belt-pinch results and yields theoreticalΩ _ax-values a factor of 2 above the experimental ones.     

On perturbed derivations of C1 algebras

Given a C¹ algebra $\text{U}$, the generator of a group of automorphisms δ, and a derivation D, we examine some situations in which δ+λD is a generator for small real λ.     

Magnetic properties of GaAs/δ〈Mn〉/GaAs/In x Ga1 − x As/GaAs quantum wells

The field and temperature dependences of the magnetization of GaAs/δ〈Mn〉/GaAs/In _x Ga_{1 ? x} As/GaAs quantum wells with the δ〈Mn〉 layer separated from the well by a 3-nm GaAs spacer have been studied in the temperature range of 3–300 K in a magnetic field up to 6 T. An external magnetic-field-induced phase transition to a ferromagnetic state with a magnetization hysteresis loop shifted from a zero magnetic field has been found to occur at a temperature below 40 K. A theoretical model is proposed that implies the coexistence of ferromagnetically and antiferromagnetically ordered regions within the GaAs layers.     

Isotopieverschiebungskonstanten von Th,U, Pu und Am

The isotope shifts of unperturbed electron configurations have been determined from isotope shift measurements in the spectra of Th, U, Pu, and Am. The screening of the 7s electron charge density at the nucleus by 6d, 7s, and 7p electrons is discussed. It turns out that the same screening factors as for the 6s electron in lighter elements can be used. The screening of the 7s electron charge density at the nucleus by one 5f electron amounts to about 25%: [δT(f ⁿ s)?δT(f ⁿ )]/[δT(f ⁿ }s)?δ(f ^n} )]=0.7₅. The charge density at the nucleus due to the filleds (andp _1/2) shells is considerabely screened by anf electron. The isotope shiftδT(f^n}-1 d ^m +2)?δT(f ⁿ d ^m ) produced by this effect is of the same order of magnitude as the isotope shiftδT(f ⁿ d ^m s)-δT(f ⁿ d ^m ) due to ans electron. The experimental isotope shift constants are found to be:Β C _exp(Th²³⁰–Th²³²)=880±120;Β C _exp(U²³³–U²³⁵)=1000±180;Β C _exp(U²³⁴–U²³⁶)=1070±200;Β C _exp(U²³⁶–U²³⁸)=1080±180;Β C _exp(Pu²³⁸–Pu²⁴⁰)=1200±120;Β C _exp(Pu²³⁹–Pu²⁴¹)=1060±100;Β C _exp(Pu²⁴⁰–Pu242)=900 ±90;Β C _exp(Am²⁴¹–Am²⁴³)=890±50 [10^?3cm^?1]. The ratiosΒ C _exp/C _th are discussed.     

On the connection of the Independent-Pair Model with a variational principle

It is shown thatBrenig's method of deriving the basic equations of the Independent-Pair Model can also be understood from a variational principle applied to the pseudoexpectation value 〈п¦H¦Ψ〉 (п=model wave function,Ψ=true wave function). Deviations from a vanishing first and second variation of 〈п¦H¦Ψ〉 with respect to the model wave functionп are shown to be due only to the independent-pair approximation, and thus permit us to make a qualitative estimate of the accuracy of this method.     

Microcanonical ensemble study of a gas column under gravity

The study of a classical ideal gas column of finite height H in a uniform gravitational field g is made by the microcanonical ensemble at energy E. The primary functions of this ensemble, the phase volume and the density of states, are derived. Related statistical quantities, such as the entropy, the temperature and the heat capacity, are also reported. The equivalence in the thermodynamic limit between the calculated microcanonical expressions and those obtained from the canonical ensemble is shown numerically. The expression for the temperature is used to analyze the temperature change when the gas is permitted to expand into an evacuated region increasing the height of the column from H ₁ to H ₂. The microcanonical single-particle momentum and height distributions are also reported.     

任意两个相干态的叠加态的相位分布和Wigner函数(英文)

从相位分布和Wigner函数两个方面研究了任意两个相干态|β〉and |mβeiδ〉的叠加态的量子统计性质.结果表明这种叠加态的非经典特性与β2,振幅系数m,相干态间的位相差δ以及叠加系数间的位相差都有关.当参量选择合适,这种叠加态存在着量子效应.计算了两个相干态等几率混合系综的相位分布和Wigner函数,经过与前者比较,结果表明由于相干项的存在,使得叠加态具有很好的量子力学行为.     

Changes in nuclear mean square charge radii of stable Krypton isotopes

The isotope shifts of stable even Kr isotopes (A=78 throughA=86) in the optical transitions at 432 nm and 557 nm were measured by means of polarization laser spectroscopy. The observed shifts are consistent with earlier results for other transitions. From the isotope shifts the changes in the nuclear mean square charge radiiδ〈r ²〉 were inferred using preliminary muonic isotope shift data. Starting from⁷⁸Kr, a monotonic decrease of 〈r ²〉 with increasing mass number is found throughout theg _9/2 neutron shell. The effect onδ〈r ²〉 of nuclear deformations as well as possible contributions due to changes in the skin thickness of the nuclear charge distribution are discussed.     

Isotope shifts and hyperfine splitting in HfI changes in nuclear charge radii of stable isotopes and182Hf

Isotope shifts and hyperfine structures in three optical transitions of HfI are investigated. Magnetic dipole coupling constant A and electric quadrupole coupling constant B of four atomic levels for both stable odd-even isotopes¹⁷⁷Hf and¹⁷⁹Hf are determined. Nuclear charge radii changesδ〈r ²〉 of the stable Hf isotopes and¹⁸² Hf (T _1/2=9×10⁶ y) are extracted using the standard semiempirical procedure. Strong deviation from muonic atom data onδ〈r ²〉 is observed. The course of theδ〈r ²〉 dependence on mass number indicates changes in nuclear deformation at A=174 and influence of higher order deformations on nuclear shape in this region.     

A two-particle exchange interaction model

The magnetisation reversal of two interacting particles was investigated within a simple model describing exchange coupling of magnetically uniaxial single-domain particles. Depending on the interaction strength W, the reversal may be cooperative or non-cooperative. A non-collinear reversal mode is obtained even for two particles with parallel easy axes. The model yields different phenomena as observed in spring magnets such as recoil hysteresis in the second quadrant of the field-magnetisation-plane, caused by exchange bias, as well as the mentioned reversal-rotation mode. The Wohlfarth’s remanence analysis performed on aggregations of such pairs of interacting particles shows that the deviation δM(H_m) usually being considered as a hallmark of magnetic interaction vanishes for all maximum applied fields H_m not only at W=0, but also for sufficiently large values of W. Furthermore, this so-called δM-plot depends on whether the sample is ac-field or thermally demagnetised.     

Itô's stochastic calculus and the bosonic string

A new perturbative technique for solving a scalar φ^2P theory consists of expanding a φ^2(1+δ) interaction in powers of δ. The Green functions are computed as a power series in δ by applying a linear differential operator to the Green functions of a specially constructed intermediate Lagrangian. We confront this linear procedure with the quadratic requirement of perturbative unitarity. We verify up to order δ³ that unitarity is indeed satisfied, by virtue of the precise structure of the intermediate Lagrangian. Unitarity gives constraints on that structure, but does not fix it uniquely.     

Amplitudes of thermal vibrations in molecular solids

The mean-square nuclear displacements 〈U²〉 _T have been evaluated for the molecular (rare-gas) solids by a lattice dynamical rigid-atom Model. The model derives the inter-molecular interaction from a “two-piece four parameter” pair-potential, includes the contribution of zero-point vibration through potential parameters by a self-consistent method, and accounts for the cubic and quartic anharmonic potential terms as perturbations to the harmonic Hamiltonian. The effect of many body interactions has been included on the basis of Axilrod-Teller approximation. The effect of including three-body forces as well as anharmonicity is found to decrease the values of 〈U²〉_T at all temperatures for all the solids. However, the ratio of the root mean-square nuclear displacements at melting to the nearest-neighbour distance, i.e. the Lindemann parameter (δ) is approximately the same for all the solids under study, which shows that the Lindemann parameter is structure as well as interaction dependent. The results are consistent with the other conventional calculations.     

Mössbauer conversion spectroscopy: Measurements on the first excited states of180, 182W and145Pm

The Mössbauer Conversion (MBC) Spectroscopy and criteria for its useful application are discussed and compared with other MB-techniques. By help of the MBC spectroscopy the isomer shift of the first excited state in¹⁸²W was measured and a change in radius ?0.05 · 10^?4>Δ 〈r ²〉/〈r ²〉>?0.28 · 10^?4 derived. The ratio of quadrupole moments of first excited states in¹⁸⁰W and¹⁸²W turns out to be¹⁸⁰ Q/¹⁸² Q=0.976 (30). Due to the excellent statistical quality of the spectra the interference parameter of the 100keVE2 transition in¹⁸²W could be determined to 2β=0.0165(9) for theL-shell. The MB-effect for the 61 keV transition in the instable¹⁴⁵Pm has been detected for the first time. A widthΛ _exp=2.15(58) mm/s was obtained.     

Intermittency in the atmospheric surface layer: Unresolved or slowly varying?

We present streamwise velocity structure functions 〈δv_L(τ)〉=〈|v(t+τ)−v(t)|^p〉 (with p=1:5) obtained in the near neutral atmospheric surface layer at the Utah SLTEST site at the highest terrestrial Reynolds number Re_τ=O(10⁶). We show that the occurrence of very large scale coherent oscillations in the streamwise velocity throughout the wall region, interpreted as genuine structural features of the canonical turbulent boundary layer, affects the scaling exponents of the p>3 order structure functions. This results in a slight alteration of the intermittent behavior of the velocity field. It was found that for positive (fast) large scale oscillation of the low-pass filtered velocity signal, deviations from the Kolmogorov K41 prediction (absence of multiscaling) are more marked, as compared to negative (slow) excursion. The results are discussed in terms of convergence of statistics from atmospheric boundary layer measurements.     

Neutrino magnetic moment inN=1 minimal supergravity

The complete one-loop supersymmetric (SUSY) correction to the magnetic moment (NMM) of a Dirac neutrino is calculated with allowance for mixing between the scalar leptons and for mixing between theW-gaugino and Higgs fermions. The contribution from the charged Higgs loop is negligible for all practical purpose. We thoroughly study the dependence of NMM on the SUSY parameters. The SUSY contribution to the NMM can be a few times less than or comparable to the value of the standard model (with a right-handed neutrino singlet added). The SUSY correction to the NMM increases with decreasing β value (tan β=〈H ₂〉/〈H ₁〉), and is not very sensitive to the charged scalar lepton mass.     

Electroweak quantum effects in theM w -M z relation

Quantum effects in theM _w -M _z relation are studied in the framework of the standard SU(2)×U(1) electroweak theory. After reviewing this relation in detail, numerical analysis is carried out by using recent data of ALEPH, DELPHI, L3, OPAL and MARK II collaborations onM _z , and those of CDF and UA2 collaborations onM _w . For the weighted averageM _z ^exp =91.157±0.032 GeV, theW mass is calculated asM _w ⁽⁰⁾ =80.90±0.04 GeV,M _w ^(l.l) =79.75±0.04±0.02 GeV andM _w =80.21±0.04±0.04 GeV at the tree, leading-log and full correction level (form _top=140 GeV andm _Higgs=100 GeV) respectively. Remarkable is that only the fully correctedM _w is consistent withM _w ^exp =80.24±0.37 GeV, which clearly demands the heavy top-quark correction, and therefore gives a strong phenomenological support, independent of the neutral current data, to the electroweak theory as a renormalizable quantum field theory with the spontaneous symmetry breakdown.     

Electric and magnetic hyperfinestructure investigations in the 5s 25p 3 and 5s 25p 26s Configurations of121, 123Sb

Optical hyperfinestructure investigations in several spectral lines were carried out in the Sb-I spectrum from which for the first time accurate values of the hfs-splitting constantsA andB of the ground configuration 5p ³ and also for five of the eight levels of the first excited configuration 5p ²6s were obtained. With these parameters the influence of core polarization effects is calculated to bea _c= ?6.6(4) mK, (equivalent to a magnetic field of ?283(20) kG perp-electron spin). The quadrupole momentQ ₁₂₁= ?0.36(4) b (including Sternheimer correction) was obtained with the experimental valuesb _3/2= ?14.3(1.0) mK and 〈r ^?3〉 =11.2(3) a.u. andQ ₁₂₃= ?0.49(5) b withb _3/2= ?19.9(1.0) mK resp. This evaluation also yields the relativistic correction factor η= ?(C″/C′) · S _r/R′ _r=1.13(2). —For the first time, too, isotope shift investigations in Sb-I lines were possible which permit to determine the isotope shift constant βC _exp= 40(10) mK, and a value δ〈r ²〉^{121, 123}=0.12(4) fm² for the change in the mean square nuclear charge radius between¹²¹Sb and¹²³Sb which is about 50 percent of the prediction of the unified nuclear model.