The Collective Excitation Spectra of σ, ω and π Mesons in Nuclear Matter

The recent progress on the study of the collective excitation in relativistic nuclear matter is reviewed. The collective excitation modes are derived by meson propagators in nuclear matter. The mesons we studied are σ, ω, γ and π mesons. For pion, we derived not only the relativistic particle-hole, delta-hole excitations but also antiparticle excitations, suchas particle-antiparticle, antidelta-particle, delta-antiparticle excitations. By calculating the dispersion relation and the spin-isospin-dependent response function, the effects of all these excitation are studied.     

Effects of dirac sea on giant resonance states

There are two approximations in relativistic models which keep the continuity equation of the baryon current without renormalization of the divergence. One is the no-free-term approximation (NFA) which neglects the divergent terms, but keeps the Pauli blocking terms coming from nucleon-antinucleon excitations in the RPA correlation functions. The other is the no-sea approximation (NSA) where antiparticle states are assumed to be empty with negative energies. It is shown that both approximations formally satisfy the Ikeda sum rule and the RPA theorem for the β_? and β₊ transition strengths also, but that the NFA requires negative strengths in the positive excitation energy region, while the NSA requires positive strengths in the negative excitation energy region, as a price of neglecting the renormalization of the divergence.     

核物质中π分子引起的粒子－空穴和△－空穴激发

以π介子为例给出了正确计算核物质中粒子－空穴激发的相对论方法，指出了它与通常计算方法的区别及通常计算方法中所作近似的不合理性．并与非相对论的粒子－空穴激发的色散关系进行了比较．我们还用这一方法计算并给出了△－空穴激发的表达式．     

Relativistic Particle-Hole and Delta-Hole Excitations for Pion Propagator in Nuclear Matter

The relativistic particle-hole and delta-hole polarization insertions for pion propagator are calculated by using particle-hole-antiparticle representation of nucleon and delta propagators in nuclear matter. The short-range correlations between nucleon-nucleon, nucleon-delta and delta-delta are included via Landau-Migdal parameter g' in the random phase approximation. We calculate the dispersion relations for pions and find out that the damped pion condensation is removed by the short-range correlation and there is a long gap in the dispersion relation.     

Mass, energy, and the electron

The two-component solutions of the Dirac equation currently in use are not separately a particle equation or an antiparticle equation. We present a unitary transformation that uncouples the four-component, force-free Dirac equation to yield a two-component spinor equation for the force-free motion of a relativistic particle and a corresponding two-component, time-reversed equation for an antiparticle. The particle-antiparticle nature of the two equations is established by applying to the solutions of these two-component equations criteria analogous to those applied for establishing the four-component particle and antiparticle solutions of the four-component Dirac equation. Wave function solutions of our two-component particle equation describe both a right and a left circularly polarized particle. Interesting characteristics of our solutions include spatial distributions that are confined in extent along directions perpendicular to the motion, without the artifice of wave packets, and an intrinsic chirality (handedness) that replaces the usual definition of chirality for particles without mass. Our solutions demonstrate that both the rest mass and the relativistic increase in mass with velocity of the force-free electron are due to an increase in the rate of Zitterbewegung with velocity. We extend this result to a bound electron, in which case the loss of energy due to binding is shown to decrease the rate of Zitterbewegung.     

A generalized quantum kinetic equation for models of relativistic nuclear dynamics

Zubarev’s method of non-equilibrium statistical operator is applied to problems of relativistic kinetic theory. Within this method, a generalized relativistic quantum kinetic equation for the relativistic Wigner function is derived with taking into account the drift term of the Vlasov type and the collision integral of the second order in particle interaction. It is shown that this result holds as well for gauge invariant theories in the case of slowly changing fields. An advantage of the developed approach is exemplified by the consideration of relativistic nuclear matter within the Walecka and Nambu-Jona-Lasinio models. Typical relativistic effects like retardation, spin degrees of freedom and antiparticle evolution are taken into consideration.     

Study of airfoil gust response alleviation using an electro-magnetic dry friction damper. Part 1: Theory

An electro-magnetic controllable dry friction damper has been designed and numerically simulated. The gust response of a three degree-of-freedom typical airfoil section with a control surface using this non-linear damper has been studied theoretically. The effects of the different gust excitations and parameter variations of the non-linear damper on the non-linear aeroelastic response are discussed. The numerical results show the present electro-magnetic dry friction damper can be used to alleviate the dynamic response to both a periodic and a linear frequency sweep gust excitation, especially for the plunge and pitch responses. The results are also verified by an experimental investigation in a wind tunnel presented in a companion paper, Part 2.     

Time-dependent variance and covariance of responses of structures to non-stationary random excitations

In this paper techniques for the analysis of non-stationary random responses of linear structures, discretized by the finite element method so that they can be analyzed as multi-degree of freedom systems, subjected to non-stationary random excitation are developed. The non-stationary random excitation is represented as a product of (a) an exponentially decaying function and a white noise process, and (b) a modulating function in the form of an exponential envelope and a white noise process. Closed form expressions for the time-dependent variance and covariance of response of structures are presented. Application of these expressions is made for the analysis of non-stationary random responses of a physical model of a class of mast antenna structures subjected to base excitation. It is concluded that (a) the coupling terms do have a definite influence on the response; the magnitude of the influence is proportional to the amount of damping in the structure and proximity of the modes excited; (b) the non-stationary random excitations considered are general in that the modulating functions are not necessarily identical, and therefore the influence of various modulating functions of the excitations applied to different locations of the structure on responses can be examined quantivatively; and (c) for a given damping parameter the magnitudes of the modulating function parameters cannot be chosen arbitrarily though the shapes of normalized modulating functions can be selected to best fit the excitation realizations.     

Particle and antiparticle spectra of hadronic atoms

The problem on the relativistic spinless and spin-1/2 particle motion in the Coulomb field is analyzed. The eigenvalues and eigenfunctions of particle and antiparticle bound states are calculated. The calculated spectra include the deeply bound states with the binding energy approximately equal to the particle rest mass. The antiparticle bound states play an important role in the atomic capture, radiative decay of hadronic atoms, and collision processes accompanied by recharging of reaction fragments.     

Quantum Tunneling Time: Relativistic Extensions

Several years ago, in quantum mechanics, Davies proposed a method to calculate particle’s traveling time with the phase difference of wave function. The method is convenient for calculating the sojourn time inside a potential step and the tunneling time through a potential hill. We extend Davies’ non-relativistic calculation to relativistic quantum mechanics, with and without particle-antiparticle creation, using Klein–Gordon equation and Dirac Equation, for different forms of energy-momentum relation. The extension is successful only when the particle and antiparticle creation/annihilation effect is negligible.     

Isoscalar Giant Monopole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant monopole resonance （ISGMR） in nuclei is studied in the framework of a fully consistent relativistic continuum random phase approximation （RCRPA）. In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green＇s function technique. The negative energy states in the Dirac sea are also included in the single particle Green＇s function in the no-sea approximation. The single particle Green＇s function is calculated numerically by a proper product of the regular and irregular solutions of the Dirac equation. The strength distributions in the RCRPA calculations, the inverse energyweighted sum rule m-1 and the centroid energy of the ISGMR in ^120Sn and ^208Pb are analysed. Numerical results of the RCRPA are checked with the constrained relativistic mean field model and relativistic random phase approximation with a discretized spectrum in the continuum. Good agreement between them is achieved.     

相对转动非线性动力学方程的稳定性及在一类非线性弹性系数下的解

建立一类含非线性弹性力的二端面转轴相对转动非线性动力学方程.对相对转动非线性自治方程进行定性分析，研究方程的稳定性.用参数变换法求得相对转动非线性非自治方程在强迫激励下的高次近似解.     

Model basis states for photons and "empty waves"

From the perspective of physical realism (PR), a photon is a localized entity that carries energy and momentum, and which is surrounded by a wave packet (anempty wave) that is devoid of observable energy or momentum. In creating quantized PR basis states for a photon wave packet, three requirements must be met:(1) The basis states must each carry the frequency of the wave;(2) They must closely resemble the photon, so that e.g. they scatter in the same manner from an optical mirror;(3) They must have infinitesimal energy, linear momentum, and angular momentum. An essentially zero-energy "empty wave" quantum-a "zeron"-is defined which meets these requirements. It is created as an asymmetric single-particle (or single-antiparticle) excitation of the vacuum state, with the "particle" (or "antiparticle") and its associated "hole" (or "antihole") forming a rotational bound state. The photon is reproduced as a symmetric particle-antiparticle excitation of the vacuum state, with the "particle" and "antiparticle" also forming a rotational bound state. The relativistic transformation problem is discussed. A key point in this development is the deduction of the correct equation of motion for a "hole" state in an external electrostatic field.     

Construction of Non-Perturbative,Unitary Particle–Antiparticle Amplitudes for Finite Particle Number Scattering Formalisms

Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle–antiparticle amplitude. This process differs from conventional on-shell Mandelstam s, t, u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel non-perturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle–antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the non-relativistic Coulomb problem, including the forward scattering singularity, the essential singularity in the phase, and the Bohr bound-state spectrum.Work supported in part by Department of Energy contract DE-AC03-76SF00515     

Generalized relativistic Fock space

We consider a generalized Fock space obtained by eliminating the restriction to symmetric components for bosons or antisymmetric ones for fermions. In this space we can extend the many times formalism of relativistic quantum mechanics to quantum field theory, in which each particle has a time parameter that has to be included in any exchange of variables. Physical states in which all particle times, or all antiparticle times, are equal, still have the right symmetry. We define creation and annihilation operators for numbered particles in this space, and relate them to the usual operators.     

Scattering of atomic particles at relativistic energies

This article is concerned with excitation, ionization and electron capture collisions between charged particles and atomic systems involving a single active electron, at impact energies which are so great that Lorentz transformations between the frames of reference of the incident and target particles must be carried out as well as relativistic dynamics employed. For excitations and ionization it is sufficiently accurate to use the relativistic generalization of the first Born approximation, but for electron capture it is necessary to carry through the analysis using a relativistic generalization of the second Born approximation. Also relativistic wave functions are employed to describe the active atomic electron.     

Implementation of low-kurtosis pseudo-random excitations to compensate for the effects of nonlinearity on damping estimation by the half-power method

Pseudo-random excitation with low crest factor is less likely to force a structure under test into nonlinear behavior, which should be avoided, or at least minimized, in the practice of experimental modal analysis. However, simply cutting high peaks and removing them from the excitation time history is not an option because such clipping of the signal introduces frequency distortions of the amplitude spectrum. A better approach is to manipulate phases of the harmonics before generating the time history instead of clipping it afterwards. To do so a new parameter, kurtosis, is used in this paper to characterize the high peak behavior of pseudo-random excitations. An analytical solution is obtained for how the phases should be selected in order to reduce kurtosis and make modal testing excitations smoother with less extreme peaks. This solution was implemented for evaluation of the damping ratio of a SDOF system by the half-power method in the presence of an additional cubic term in the equation of motion. The system response obtained by numerical integration was treated as modal analysis data and the result is that the kurtosis-optimized excitation has compensated for the effect of nonlinearity and allowed to identify the damping ratio with good precision whereas an ordinary Gaussian excitation with randomized phases caused an error of 75 percent. Comparison with the numerical crest factor minimization by time-frequency-domain swapping has been made and experimental results from a modal testing rig with a realistic turbine blade are also presented in the paper.     

H2O和HLi分子的双光子激发

用全相对论量子力学计算H2O和HLi的双光子偶极激发。为对比起见,同时用非相对论的对称匹配团族-组态相互作用法(SAC-CI)计算其单光子激发。对于无对称中心的H2O和HLi,符合相应群的对称选择原则。双光子跃迁几率一般比单光子跃迁的小3～5个数量级。在计算双光子偶极激发时,应采用同时包含了空间的对称性和时间反转对称性的全相对论。     

Quantum ion-acoustic solitary waves in weak relativistic plasma

Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized two- species relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive perturbation method. A linear dispersion relation is also obtained taking into account the relativistic effect. The properties of quantum ion-acoustic solitary waves, obtained from the deformed KdV equation, are studied taking into account the quantum mechanical effects in the weak relativistic limit. It is found that relativistic effects significantly modify the properties of quantum ion-acoustic waves. Also the effect of the quantum parameter H on the nature of solitary wave solutions is studied in some detail.