Rational parametrisation of normalised stiefel manifolds,and explicit non-'t hooft solutions of the Atiyah-Drinfeld-Hitchin-Manin instanton matrix equations for Sp(n)

It is proved that normalised Stiefel manifolds admit a rational parametrisation which generalises Cayley's parametrisation of the unitary groups. Applying (the quaternionic case of) this parametrisation to the Atiyah-Drinfeld-Hitchin-Manin (ADHM) instanton matrix equations, large families of new explicit rational solutions emerge. In particular, new explicit non-'t Hooft solutions are presented.     

On the interpretation of heavy-ion sub-barrier fusion data

We study the well-known deviation of measured fusion cross-sections below the barrier from predictions of one-dimensional tunnelling models. A simple parametrisation of measured excitation functions is discussed which allows to identify a smooth general trend depending only on gross nuclear properties. The parametrisation is substantiated by quantum mechanically exact calculations in a two-dimensional tunnelling model. Various possibilities for the geometrical interpretation of the second degree of freedom are discussed. Neck formation is identified as the most probable degree of freedom effecting the overall behavior of sub-barrier fusion.     

An analysis of BCS solutions with realistic interactions

We adopt the principle that the BCS solution can be regarded as a generating function for ground states of neighbouring nuclei. A parametrisation of the binding energy in terms of the number of particles is assumed and the assumption tested. Using an ansatz from statistical mechanics, a formula for the distribution of the number of particles is developed and the formula is shown to give accurate answers. The concept of temperature is introduced and its interpretation in many-particle theory is clarified.     

Electron states and atomic positions at the {001}, {110} and {111} faces of W and Mo

The results of ab initio calculations on the {001}, {110} and {111} surfaces of W and Mo and on the (√2 × √2)R45° reconstructed W {001} surface are presented. A distribution of surface states in reasonable agreement with experiment is found. A simple parametrisation of the short range repulsive force between transition metal atoms is used to predict, for all these surfaces, relaxations which are comparable with those observed. This same parametrisation indicates that the W and Mo {001} surfaces are stable to proposed reconstructive displacements.     

Folded world sheets and the orientable string

Classical solutions for the open relativistic string with a single junction are examined and a new class of kinked solutions presented. An interpretation of the phenomena of reverse parametrisation on one arm is offered in terms of oriented chains and the consequence that this has for folded world sheets is discussed. A physical interpretation for certain junction sites is presented through interaction of the string with an external field.     

Systematic tests of QCD: Non-singlet moments

The comparison of QCD predictions with experiment requires the inclusion of both next to leading order and higher twist terms. We propose a systematic parametrisation of structure function moments, which, in principle, permits the extraction of all these terms, and explicitly allows for the ambiguities inherent in higher order QCD predictions. An analysis of non-singlet moments using this form favours small higher twist terms, agrees closely with the leading order QCD parameters, and is consistent with the presence of next to leading QCD effects. The scale parameter Λ is determined, it ambiguities discussed and its errors estimated.     

Saddles and trajectories,and poles and surface waves in heavy-ion elastic scattering

The terms I_m^±(θ) of the Poisson summation formula are used to describe and classify the oscillatory structures of the heavy-ion elastic cross sections coming from a strong-absorption model. The method of stationary phase, which relates these terms to branches of a deflection function, is shown to be inadequate and is replaced by the saddle-point method in the plane of complex angular momenta. The positions of the saddle points are found to be fairly independent of the parametrisation and define certain “active” regions which contribute to the scattering amplitude. The complex saddle points may be thought of as corresponding to complex trajectories in the nuclear potential. If the strong-absorption parametrisation possesses poles many saddle-point contributions can be simply expressed as the residues of the poles nearest the real axis. One of these leading parametric poles has an energy dependence similar to that of the dominant Regge pole generated by a complex optical potential. Poles lying above the real axis give rise to terms which may be thought of as surface waves, i.e. they are damped as they progress around the nuclear surface. These terms possess classically equivalent paths in the sense that they correspond to deflections less than π. Terms coming from poles below the real axis have no classical equivalent, increase as they progress and can, then, only be thought of as being diffractive. Some useful formulae for the cross section are given and the limiting case of a sharp cut-off is discussed.     

The binding energy of 184 476 X in the droplet model

The positron spectrum emitted in the U-U-reaction at subthreshold energy could be interpreted in terms of the formation of a giant nucleus if the binding of the latter is 100 MeV stronger than predicted by the usual droplet model parametrisation. We analyse the extrapolation to giant nuclei by accounting properly for the error propagation when the parameters are fitted to measured binding energies and radii. The influence of higher order terms is discussed.     

Inclusive production of antihyperons in nC-interactions

The inclusive production cross-sections of , , and in neutron-carbon interactions at GeV mean energy of neutrons have been measured. The parameters n and b of differential cross-section parametrisation , where x_F is the Feynman variable, p_t is the transverse momentum, have been obtained. The kinematic region of validity of the parametrisation has been defined. Results are compared with published experimental data. Received: 7 June 2002 / Revised version: 23 January 2003 / Published online: 3 March 2003     

Threshold π+ electroproduction at high-momentum transfer: A determination of the nucleon axial vector form factor

Threshold π⁺ electroproduction has been measured at momentum transfers 6k²6 of 0.45, 0.58 and 0.88 (GeV/c)², extending the range of earlier measurements. Using PCAC and current algebra-based models we have deduced the axial vector form factor of the nucleon G_A(k²), and find that the dipole parametrisation is favoured over the monopole. The value of M_A in the dipole parametrisation is, in a weak PCAC model, 0.96 ± 0.03 GeV, in excellent agreement with neutrino measurements. The threshold cross section is also in excellent agreement with the predictions of a fixed-t dispersion relation model.     

Charge distribution in a two-chain dual model

Zeitschrift für Physik C Particles and Fields - Charge distributions in the multiple production processes are analysed using the dual chain model. A parametrisation of charge distributions for...     

类氢原子的强电场电离

强电场情况下,微扰论不再适用,要精确求解Ｓｃｈｒｏｄｉｎｇｅｒ方程．本课题组用数值方法对强电场下类氢原子电离进行了计算,得到基态氢原子的共振态解,与更精确的结果作了比较,证明Ｂｒｅｉｔ－Ｗｉｇｎｅｒ近似在一定误差下是可以接受的． The Schrdinger equation of hydrogen like atoms in a strong electric field is solved by the numerical method instead of perturbation. The resonance ionization of hydrogen atom ground state is computed and comparing with exact result and Breit Wigner parametrisation is useful.     

Anomalous three gauge boson couplings in e+e− → W+W− and “optimal” strategies for their measurement

We discuss how to measure anomalousWWZ- andWWγ-couplings with minimal statistical error using integrated observables, without having to assume that the anomalous couplings are small. We propose a parametrisation of these couplings which is well suited for the extraction of both single and many parameters, and which leads to a very simple form of the integrated cross section, from which additional information on the couplings can be obtained.     

Conditional and unconditional Gaussian quantum dynamics

This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as ‘general-dyne’) quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.     

Gluon shadowing and charmonium/bottonium production on nuclear targets

We examine the suppression ofJ/ω, ω′ and Ψ production on nuclear targets, as observed for proton and pion beams of energies from 200 to 800 GeV. We find that this suppression leads to a universal scaling curve, which indicates that it is due to nuclear modifications of the gluon density (“shadowing”). A parametrisation of the nuclear effect on the gluon density is extracted from the data and used to obtain quantitative estimates for corresponding effects in high-energy heavyion collisions.     

Nahm's equations and the classification of monopoles

Solutions of Nahm's system of ordinary differential equations are produced by variational methods. This leads to an explicit parametrisation of the solutions to the Bogomolny equation over ³.