On Wilson’s theory of confinement

According to recent results, the Gell-Mann-Low function β(g) of four-dimensional φ⁴ theory is nonalternating and has a linear asymptotics at infinity. According to the Bogoliubov and Shirkov classification, it means the possibility of constructing a continuous theory with finite interaction at large distances. This conclusion is in visible contradiction to the lattice results indicating triviality of φ⁴ theory. This contradiction is resolved by a special character of renormalizability in φ⁴ theory: to obtain the continuous renormalized theory, there is no need to eliminate a lattice from the bare theory. In fact, such kind of renormalizability is not accidental and can be understood in the framework of Wilson’s many-parameter renormalization group. Application of these ideas to QCD shows that Wilson’s theory of confinement is not purely illustrative, but has a direct relation to a real situation. As a result, the problem of analytical proof of confinement and a mass gap can be considered solved, at least on the physical level of rigor.     

弹性薄壁桿件的平衡与稳定的一般理论

In this paper a theory of equilibrium and stability of elastic thin-walled cylinders is proposed. The theory is based on the following assumptions: 1) The cross section of the cylinder is uncleformable. 2) The cylinder is under a system of initial stresses σ_z⁰=- P⁰/F-M_y⁰/I_xx x + M_x⁰/I_yyy. This theory may be regarded as a generalization of V. Z. Vlasoff's theory of stability of thin-walled rods, and includes the theory of Karman-Chien and Adaduroff as a special case. For cases of simply supported cylinders and cantilever cylinders, a method of solution using trigonometric series is proposed which is much simpler than the methods used by Karman-Chien and Adaduroff.     

Reaction field model with free volume for the NMR chemical shift of129Xe dissolved in organic solvents

The temperature dependence of the NMR chemical shift of¹²⁹Xe dissolved in liquid alkanes is examined in the context of the reaction field model. An essential feature of the theory is the inclusion of the temperature dependence of the density of thesolvent. The theory of free volume for liquids is incorporated into the reaction field model to account for this temperature dependence. Comparison of the theory with previously reported measurements indicates the sensitivity of the¹²⁹Xe chemical shift to the free volume of liquids. Incorporation of free volume improves the agreement between measurement and theory for branched alkane solvents, and resolves the origin of the 62 ppm intercept in the plot of reaction field as a function of¹²⁹Xe chemical shift for the n-alkanes.     

Diffusion transport of negative ions through the interface between cryogenic liquids

A theory of electron bubble transport through the interface between cryogenic liquids is developed based on a new approach to calculating the potential of interaction of a bubble with the interface. The theory is in good agreement with experiments on the electric-field dependence of the potential barrier near the interface between liquid ⁴He, ³He, and vacuum, as well as at the interface between ³He and ⁴He saturated solutions. It is found that the interaction potential dependence on the distance between the electron bubble and the interface is isotopically invariant to three versions of such an interface. The dependence of the lifetime of negative ions in ⁴He and ³He on the temperature and electric field has been determined using the Kramers theory.     

Relativistic heavy-ion collisions: An approach based on non-equilibrium thermodynamics

A new theory of particle production in high energy collisions is proposed which is based on non-equilibrium thermodynamics. The non-equilibrium model is a major extension of the equilibrium thermodynamic model of relativistic heavy-ion collisions developed earlier. While the equilibrium thermodynamic theory is appropriate for the formation of light nuclei and for pions, the non-equilibrium theory applies to the creation of particles heavier than the pion, which include such particles as the strange mesons, strange baryons and the anti-nucleons. Using an approach based on the degree of the reaction of kinetic theory, the time evolution of the composition of hadronic systems in incomplete equilibrium is investigated. Densities of produced particles are related to space-time quantities and to the production cross sections of the underlying dynamic processes. An application of the non-equilibrium approach to the production of strange matter is given. The importance of secondary processes, following pion production, in the formation of strange matter is shown. In fact, the secondary production process for kaons is as important as the direct production process arising from initial nucleon-nucleon (NN) collision of a first collision picture. Thus, kaons can be produced in a late stage of the collision of two nuclei and they do not necessarily reflect the early stages of the collision as first thought. Using the experimental number of kaons, the time of reaction is also estimated. No evidence for a long-lived state of the nuclear system is found. Expressions for particle production ratios are developed. The results of an equilibrium theory and a non-equilibrium theory are found to be similar for such ratios. The chemical equilibrium constant is shown to be present in the non-equilibrium theory; the Boltzmann factor in the production threshold energy appears in the equilibrium theory. The K^?/K⁺ ratio is estimated. Surprisingly, reasonable agreement with experiment is found in the K^?/K⁺ ratio using the equilibrium theory, even though the production processes for K⁺'s and K^?'s treated individually, are not ones for which the equilibrium theory applies. It is shown that a fundamental difference between the equilibrium and non-equilibrium theory is lost when particle ratios for non-equilibrium particles are taken. Expressions for the production of complex composite structures made of strange particles are developed. The non-equilibrium model with some modifications may be useful for high energy NN and pion-nucleon collisions.     

Convergence of rayleigh-schrödinger perturbation theory in calculations of multiphoton processes

Abstract

We have calculated the high-order ac Stark Shift, multiphoton ionization rates, and nonlinear susceptibilities for high harmonic generation for the hydrogen atom in a radiation field. The calculations are done in the framework of Rayleigh-Schrödinger perturbation theory applied to a complex-rotated Hamiltonian. Our intention is to investigate the limitations of perturbation theory in calculations of multiphoton processes. Comparisons are made with results from nonperturbative calculations. For some frequencies the results of lowest-order perturbation theory are found to disagree with nonperturbative calculations even at moderate to low intensities (I ～ 10¹¹ W cm^?2) and in the absence of resonances. We find that the high-order perturbation expansion theory is not a reliable predictor of the behavior of hydrogen atoms in radiation fields with intensities greater than ～ 10¹² W cm^?2.     

Einstein-Cartan引力理论中的广义协变守恒定律

本文从广义Noether定理出发,对Einstein-Cartan引力理论中一般拉氏量所对应的守恒定律作了普遍的讨论,并由广义位移交换x^μ＇=x^μ+e_d^μb^a得到了包含挠率的一般拉氏密度所对应的广义协变能量动量守恒定律,并论述了超势存在的必然性。它是文献[1]和[2]理论的自然推广。 关键词：     

C12(d,p)C13和Ca40(d,p)Ca41基态反应质子的角分布

本实验测量了C¹²(d,p)C¹³及Ca⁴⁰(d,p)Ca⁴¹基态反应质子群的角分布和微分截面。氘核能量为13.3MeV,对C¹²和Ca⁴⁰的反应,其测量角度范围分别为3°—167°和10°—164°,每隔2.5°或5°测量一点,其主要结果如下:(1)对于这两群质子,在主削裂峯附近的实验点和用简单Butler理论算得的理论角分布曲线都符合得相当好;理论计算数据对实验数据在主峯处归一;由此而定得的核能级参数与前人所得到的是一致的。(2)大角度区的实验截面数值没有减小到象Butler理论所要求的那样小,并有非常明显的次极大出现,其位置与Butler理论所预言的不一致;这些特点可以用扭曲波理论来解释,非氘核削裂机制也可能有部分贡献。(3)在C¹²(d,p)C¹³反应中,前角度区的截面有很大下降,而后角区则有明显的增加,这些现象都和Butler理论不一致;然而,这也可以用扭曲波来解释。(4)用主峯处的截面和Butler理论算得的基态的约化宽度,对C¹²(d,p)C¹³和Ca⁴⁰(d,p)Ca⁴¹反应分别为r²=0.17和0.041;用扭曲波理论计算时,则得到较大的r²值,后者更接近于单粒子模型所预言的数值,基于上面这些事实,对本实验的数据使用扭曲波理论来进行分析似乎是值得的。     

流体静压下AlAs合金化的GaAs中Cr2+(3d4)杂质态的理论研究

本文将一个自旋极化的紧束缚格林函数方法发展到用于流体静压和合金下GaAs:Cr²⁺(3d⁴)杂质态的研究。文中给出了GaAs:Cr²⁺系统⁵E激发态和⁵T₂基态受主能级随压力和AlAs合金成份的变化趋势。理论证明了在一定的压力和Al成份下,⁵E激发态将从导带底进入带隙,原在通常条件下观察不到的⁵E→⁵T_关键词：     

Charge composition of a cluster plasma upon irradiation of large atomic clusters by the field of a superatomic femtosecond laser pulse

A theory is developed for calculating the charge composition of a cluster plasma produced upon irradiation of large atomic clusters by the field of a superatomic femtosecond laser pulse. The theory is based on the overbarrier process of a successive multiple internal ionization of atomic ions inside a cluster accompanied by the external field ionization. Collision ionization is also taken into account in the calculations. The theory is illustrated by the example of a cluster consisting of 10⁶ xenon atoms irradiated by a 50-fs laser pulse with a peak intensity of 2×10¹⁸ W/cm². In this case, the Xe²⁶⁺ ions dominate. The amounts of atomic xenon ions with multiplicity up to 31 are calculated.     

Time-dependent density-matrix theory

The mass fluctuations in damped reactions of¹⁶O+¹⁶O are studied in an extended time-dependent Hartree-Fock theory. The theory determines the time evolution of a two-body density matrix as well as that of a one-body density matrix, providing us with a microscopic way to calculate the fluctuations of one-body quantities. The results of the theory are compared with those obtained in a transport model. It is found that the dispersions in fragment mass calculated in the two models are of the same order of magnitude and much larger than those calculated in the time-dependent Hartree-Fock theory. The differences between the microscopic theory and the transport model are also discussed.     

Origin of the high-and low-frequency K-satellites of 31Ga, 32Ge and 33As

The origin of the high- and low-frequency K-satellites of ³¹Ga, ³²Ge, ³³ As is explain on the basis of Hayasi's theory of quasi-stationary states. It is shown that the same QSS difference gives rise to a particular satellite of either type in all the elements. The results are compared with those of multiple ionisation theory.     

Eigenstates of the time-dependent density-matrix theory

An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying 2 ⁺ states in ²⁴O to understand the foundation of the rather successful time-dependent approach. It is found that the calculated strength distribution of the 2 ⁺ states has physically reasonable behavior and that the strength function is practically positive definite though the non-Hermitian Hamiltonian matrix obtained from TDDM does not guarantee it. A relation to an Extended RPA theory with hermiticity is also investigated. It is found that the density-matrix formalism is a good approximation to the Hermitian Extended RPA theory.Received: 26 May 2003, Revised: 30 October 2003, Published online: 26 January 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 21.10.Re Collective levels     

Influence of high-frequency magnetic fields on Mössbauer resonance

The influence of high-frequency magnetic modulation on Mössbauer resonance is investigated using the⁶⁷Zn resonance. A phase-modulation theory theory explaining the experimental results is presented. Implications to magnetic modulation experiments with the⁵⁷Fe resonance are also discussed.     

Multi-level quantum electrodynamic calculation of spontaneous emission and small signal gain in high voltage free electron lasers

Abstract

Using the Weisskopf-Wigner technique, a self consistent quantum electrodynamic (SCQED) theory of spontaneous emission of radiation and single photon small signal gain is developed for high voltage free electron lasers (FEL). Excellent agreement is obtained simultaneously to our knowledge for the first time between the predictions and the experimental observations for lineshift, linewidth and gain. The SCQED theory predicts lineshift and broadening due to quantum mechanical effects for linear, helical and tapered undulator FELs which are not predicted by the classical/conventional FEL theories, but which have been observed ^{4,5,18,22,23,45,46}. Excellent agreement is obtained between the SCQED theory predicted spontaneous emission spectra and the 1980–81 ACO FEL^4,18, ACO Optical Klystron FEL^45,46, Stanford 10.6 μm FEL²² and Stanford 3.4 μm FEL²³ experimental spectra. This agreement is much better than the prediction from the classical/conventional FEL theory which gives errors of many tens of percent. We show that the spontaneous emission spectrum obtained from classical/conventional FEL theories is valid only in the limit of a short undulator containing a small number of periods. The small signal gain derived from the SCQED theory is shown to reduce to Colson's gain formula^12,34 in the classical limit. However, the SCQED theory predicts significant reductions in the small signal gain which agree well with the ACO gain data⁵, and are not predicted well by Colson's formula. Due to the non-neglible finite electron state lifetime, it is discovered that a fundamental physical gain limit exists which is universal to all types of FELs within the limits of the single photon transition scheme considered (i.e. if multiphoton effects are ignored). Finally, the implications of the theoretically obtained results are discussed for practical conditions of experimental interest. It is shown that under practical experimental conditions quantum effects can be quite important in the FEL.     

Effective field theory approach to structure functions at small $x_{\mathrm{Bj}}$

We relate the structure functions of deep inelastic lepton-nucleon scattering to current-current correlation functions in a Euclidean field theory depending on a parameter r. The r-dependent Hamiltonian of the theory is P ⁰ -(1-r)P ³ , with P⁰ the usual Hamiltonian and P³ the third component of the momentum operator. We show that a small in the structure functions corresponds to the small r limit of the effective theory. We argue that for there is a critical regime of the theory where simple scaling relations should hold. We show that in this framework Regge behaviour of the structure functions obtained with the hard pomeron ansatz corresponds to a scaling behaviour of the matrix elements in the effective theory where the intercept of the hard pomeron appears as a critical index. Explicit expressions for various analytic continuations of the structure functions and matrix elements are given as well as path integral representations for the matrix elements in the effective theory. Our aim is to provide a framework for truly non-perturbative calculations of the structure functions at small for arbitrary Q². Received: 16 July 2002 / Published online: 9 December 2002 RID="a" ID="a" e-mail: O.Nachtmann@thphys.uni-heidelberg.de     

Semiclassical analysis of the spin polarization of 12B in the 100Mo(14N, 12B)102Ru reaction

Polarization of ¹²B in the ¹⁰⁰Mo(¹⁴N, ¹²B)¹⁰²Ru reaction at 90 MeV incident energy is studied on the basis of the semiclassical theory of transfer reactions proposed by Brink. Gross behaviors of both the polarization and the cross section as functions of product kinetic energy can be predicted successfully by the theory. But disagreement in the numerical values of the polarization is found for low-energy ¹²B.     

Relativistic Hartree-Bogoliubov description of the lithium isotopes

Here we report the development of the relativistic Hartree-Bogoliubov theory in coordinate space. Pairing correlations are taken into account by both density dependent force of zero range and finite range Gogny force. As a primary application the relativistic HB theory is used to describe the chain of Lithium isotopes reaching from ⁶Li to ¹¹Li. In contrast to earlier investigations within a relativistic mean field theory and a density dependent Hartree Fock theory, where the halo in ¹¹Li could only be reproduced by an artificial shift of the 1p _1/2 level close to the continuum limit, the halo is now reproduced in a self-consistent way without further modifications using the scattering of Cooper pairs to the 2s _1/2 level in the continuum. Excellent agreement with recent experimental data is observed.     

Multidimensional Unified Theories

An extended spacetime, M^4+N, is a Riemannian (4 + N)-dimensional manifold which admits an N-parameter group G of (spacelike) isometries and is such that ordinary spacetime M⁴ is the space M^4+N/G of the equivalence classes under G-transformations of M^4+N. A multidimensional unified theory (MUT) is a dynamical theory of the metric tensor on M^4+N, the metric being determined from the Einstein-Hilbert action principle: in absence of matter, the Lagrangian is (essentially) the total curvature scalar of M^4+N. A MUT is an extension of the Cho-Freund generalization of Jordan's five-dimensional theory. A MUT can be faithfully translated in four-dimensional language: as a theory on M⁴, a MUT is a gauge field theory with gauge group G. A unifying aspect of MUT's is that all fields occur as elements of the metric tensor on M^4+N. When the isometry generators are subjected to strongest constraints, a MUT becomes the De Witt-Trautman generalization of Kaluza's five-dimensional theory; in four-dimensional language, this is the theory of Yang-Mills gauge fields coupled to gravity. With weaker constraints, a MUT appears to be more natural than a Yang-Mills theory as a physical realization of the gauge principle for an exact symmetry of gauged confined color. Such weakly-constrained MUT leads to bag-type models without the need for ad hoc surgery on the basic. Lagrangian. The present paper provides a detailed introduction to the formalism of multidimensional unified gauge field theory.