Perturbation theory in terms of electron density

When an inhomogeneous electron gas is subjected to a perturbation, its energy and density both change by small amounts. We calculate the changes in the energy explicitly in terms of the density changes within the density-functional theory of many-electron systems. We also derive the equations for the induced densities, and using these show that a density correct up to order n in terms of the perturbation parameter is sufficient to give energy changes up to order (2n + 1). As a corollary, the even-order energy changes E⁽²ⁿ⁾ are variational with respect to the density changes ?⁽ⁿ⁾. The equations for the induced densities also follow from this corollary. The even-order corollary also gives a variational method of calculating the induced densities. The theory is demonstrated by applying it to calculate the polarizability and hyperpolarizability of the hydrogen, helium and neon atoms.     

Interactions between heavy mesons and Goldstone bosons from chiral dynamics

We calculate the S -wave scattering lengths for charmed mesons scattering off Goldstone bosons and explore their quark mass dependence using the chiral perturbation theory up to next-to-leading order as well as a unitarized version of it. The quark mass dependence of all scattering lengths determined in a recent lattice calculation can be reproduced by the unitarized version. We also discuss signals of possible bound states in these observables.     

A Brief Overview of Hard-Thermal-Loop Perturbation Theory

The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades.Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence.The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion,and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions.We discuss HTLpt thermodynamic calculations for QED,pure-glue QCD,and QCD with N f=3 up to three-loop order.The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.     

光纤中双孤子相互作用的等价粒子理论

本文给出了含有一般扰动的非线性薛定锷（Ｓｃｈｒｏｄｉｎｇｅｒ）方程的孤子等价粒子理论，它使人们对孤子的粒子性质有了更深的了解，同时给出了光纤中双孤子相互作用的等价粒子分析，得到了与基于逆散射及微扰变分法完全一致的结果，这一方法可用于多孤子相互作用的解析分析，并能给出这一过程的直观物理图象．     

Scattering of a heavy vector meson on a nucleon in QCD

Using the method of x⁺ ordered perturbation theory we estimate the perturbative QCD contribution to heavy vector meson-nucleon scattering in terms of non-relativistic wave functions. The suppression of the cross section due to the colour singlet nature of the vector meson is investigated. We find that perturbation theory for the Ψ may account for $\text{1}\text{4}$ of the total cross section and that for the υ it may account for the whole cross section. We attempt to allow for final-state interactions by comparing with the relevant non-relativistic calculation.     

Remote polar phonon scattering for hot electrons in Si-inversion layers

The effect of the remote interfacial phonon (R.I.P.) scattering on the carrier drift velocity v is evaluated in function of the effective mobility, i.e. in function of the surface roughness. A perturbation theory using the experimental ν?F relation as a zero order approximation is used to calculate the contribution of the R.I.P. scattering. The calculation shows that the influence of this phonon mode scattering on the transport properties in Si-inversion layers is dependent on the carrier low field mobility and is of the order of 10%. The R.I.P. scattering is particularly significant in the warm electron regime, having no consequence on the saturation velocity.     

The pionium lifetime in generalized chiral perturbation theory

Pionium lifetime corrections to the nonrelativistic formula are calculated in the framework of the quasipotential–constraint theory approach. The calculation extends an earlier evaluation, made in the scheme of standard chiral perturbation theory, to the scheme of generalized chiral perturbation theory, in which the quark condensate is left as a free parameter. The pionium lifetime is calculated as a function of the combination (a₀⁰−a₀²) of the ππ S-wave scattering lengths with isospin I=0, 2.     

Perturbation theories in low energy electron diffraction: t-matrix and τ-matrix approaches

Two perturbation approaches to low energy electron diffraction (LEED) are discussed within the inelastic collision model: t-matrix approach recently proposed by Tong, Rhodin and Tait (all scatterings treated to third order), and τ-matrix approach (layer scattering is treated exactly while all interlayer scatterings are treated to third order). Both approaches are applied to the calculation of rotation diagrams for the (001) surface of Al. In the case of a single layer third-order perturbation results for the magnitude and phase of the scattering amplitude are compared to the exact results and found to be in fairly good agreement over a large range of elastic scattering cross-sections. When all scatterings (up to third order) are considered for an infinite crystal, the differences between the exact and third-order t-matrix perturbation resutls become quite substantial ; marked improvement is achieved if the layer scattering is treated exactly, but the remaining difference may be significant enough (depending on the application) to suggest that interlayer scattering may not always be treated by perturbation, and thus renormalization of the type proposed by Pendry may be necessary.     

The three-boson system with short-range interactions

We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be summed, which leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in one local three-body force counterterm and compute the running of the three-body force with the cutoff. This allows a calculation of the scattering of a particle and the two-particle bound state if the corresponding scattering length is used as input. We also obtain a model-independent relation between binding energy of a shallow three-body bound state and this scattering length. We comment on the power counting that organizes higher-order corrections and on relevance of this result for the effective field theory program in nuclear and molecular physics.     

Vanishing three-loop beta function in N = 4 supersymmetric Yang-Mills theory

We have calculated the beta function of the N = 4 supersymmetric Yang-Mills theory through three-loop order and find that it is zero. The calculation was performed using superspace techniques that also allowed the calculation of the complete three-loop chiral-multiplet propagator, which turned out to be quite simple. These results strongly support the speculations that the theory is finite order-by-order in perturbation theory.     

Résistivité électrique due aux macles dans les métaux monovalents

Crystals off. c. c. sodium twinned in the direction of (111) planes at low temperatures, are studied in the approximation of nearly free electrons. The potential of the lattice is treated as a perturbation. The scattering of electrons by the twinning plane occurs in the direction of two particular wave vectors characterized by their coefficients of reflexion. The electrical resistivity arising from this scattering is calculated with the variational method. The use of this method is justified for certain experimental conditions where the resistivity due to the twinning is a small part of the total one. The numerical calculation shows that the resistivity, given in tensor form, is consistent with the experimental results on the resistivity of stacking faults of other monovalent metals.     

Virtual Compton scattering off the pseudoscalar meson octet

We present a calculation of the virtual Compton scattering amplitude for the pseudoscalar meson octet in the framework of chiral perturbation theory at O(p ⁴). We calculate the electromagnetic generalized polarizabilities and compare the results in the real Compton scattering limit to available experimental values. Finally, we give predctions for the differential cross section of electron-meson bremsstrahlung.     

Inclusive and Deep-Inelastic Scattering from a Dressed Structureless Nucleon

Nonperturbative polaron variational methods are used to study inclusive scattering in the context of the scalar Wick-Cutkosky model. We derive the structure functions for a scalar point-like nucleon surrounded by a cloud of strongly interacting mesons from the Compton amplitude that is obtained in a recent variational calculation based on the particle (or worldline) representation. In zeroth variational order, a covariant exponentiated form is obtained, which is identical to the one suggested by Vineyard for scattering of slow neutrons from quantum liquids. In first order, the much richer dependence of the structure function on momentum and energy transfer, which emerges, is evaluated numerically. We study the -evolution and the perturbative as well as the scaling limit of our variational structure functions. Finally, the momentum sum rule is derived and evaluated in order to determine the momentum fraction carried by the neutral mesons inside the dressed nucleon. Received May 30, 1997; revised December 19, 1997; accepted for publication January 30, 1998     

Pion-kaon scattering near the threshold in chiral SU(2) perturbation theory

In the context of chiral SU(2) perturbation theory, pion-kaon scattering is analysed near the threshold to fourth chiral order. The scattering amplitude is calculated both in the relativistic framework and by using an approach similar to heavy baryon chiral perturbation theory. Both methods lead to equivalent results. We obtain relations between threshold parameters, valid to fourth chiral order, where all those combinations of low-energy constants which are not associated with chiral-symmetry breaking terms drop out. The remaining low-energy constants can be estimated using chiral SU(3) symmetry. Unfortunately, the experimental information is not precise enough to test our low-energy theorems.     

Ground state energies of bound exciton for all mass ratios

We report on a calculation of the ground state energy of bound excitons using states from a model Hamiltonian and correcting the variational results by treating the difference between the model and actual Hamiltonian in second order perturbation theory. The resulting procedure is valid for all mass ratios.     

Correlation corrections based on the Schrödinger equation with a local potential

A compromise version of calculation of the ground state electronic energy is proposed that combines both the density functional theory and the wave function formalism. Single-particle orbitals and energies are determined by solving the Kohn-Sham equations with a local effective potential, which depends on the parameters determined by the variational principle. Correlation corrections are calculated using the Rayleigh-Schrödinger perturbation theory in the zero-order approximation of the Möller-Plesset theory. The specific features of the expressions for the corrections to the wave function and the energy determined in terms of the Kohn-Sham orbitals are considered. This approach, in contrast to the well-known optimized effective potential method, can be applied with equal computational expenditures to both atoms and molecules. A comparative analysis for 20 helium-like atoms showed that the scheme proposed provides better agreement with the “exact” values of the energy in the second order of the perturbation theory in comparison with the results obtained using the conventional exchange-correlation potentials BLYP and PW91. A similar trend is also observed for diatomic hydrides (from LiH to FH), although, in contrast to the atoms, the deviations from the experimental estimates of the energy are less systematic.     

Neutron–Triton Elastic Scattering

The Kohn variational principle and the hyperspherical harmonics technique are applied to study the n ? ³H elastic scattering at low energies. In this contribution the first results obtained using a non-local realistic interaction derived from the chiral perturbation theory are reported. They are found to be in good agreement with those obtained solving the Faddeev–Yakubovsky equations. The calculated total and differential cross sections are compared with the available experimental data. The effect of including a three-nucleon interaction is also discussed.     

Equation of state and interaction potential of helium under high temperatures and high densities

Based on the thermodynamics statistic method, the improved variational perturbation theory and the modified quantum mechanics correction model have been used to calculate the equation of state of liquid helium at pressure from 0.7 to 108 GPa. The calculation results are in good agreement with the experimental data. The EXP-6 potential (α = 13.1) can more accurately describe the interaction of helium atoms than other potentials in the scheme. Finally, a comparison is shown between our interatomic potentials and other potentials.     

The (p, 2p) reaction for slightly deformed nuclei

A perturbation approach for the calculation of (p, 2p) angular correlations for slightly deformed nuclei is developed using the formalism of the distorted wave t-matrix approximation (DWTA) in the static limit where approximations that incorporate absorption and focussing effects are used for the spin-orbit independent optical-model waves. Using a finite-range off-shell t-matrix that fits p-p scattering at 90° to approximate the p-p interaction inside the nucleus, a zero-order calculation is performed and normalized to ¹⁹F(p, 2p)¹⁸O angular correlation data at 42.7 MeV. A rms study is undertaken in order to parametrize the bound-state and the sensitivity of the shape of the angular correlation to the rms value is observed. The deformation of the bound-state is introduced using normalized perturbation theory and calculations with various values of the deformation parameter β for prolate and oblate deformations are performed and the results are compared. The shape of the (p, 2p) angular correlation is shown to be highly sensitive to the degree of deformation and is consistent with the shape dependence of the correlation to the rms value of the bound-state wave function.