On the equivalence of standard and covariant perturbation series in non-polynomial pion lagrangian field theory

Recently a covariant perturbation approach has been developed to give a perturbation expansion of the chiral-invariant pion theory which does not depend on the choice of pion coordinates. We prove that this covariant approach is equivalent to standard perturbation theory. Our method explicitly shows how one can express covariant graphs by contributions of non-covariant ones and vice versa. We neglect contributions vanishing on the mass shell.     

On ellipsoidal solutions of Liouville's equation in general relativity

A relativistic, collisionless gas of gravitating particles all having the same proper mass (possibly equal to zero) is studied under the assumption that the oneparticle distribution function is locally ellipsoidal in momentum space with respect to some timelike vector field (observer). Liouville's equation implies that the distribution function depends only on a quadratic form in the 4- momenta, whose coefficients are a Killing tensor in the case of non- vanishing proper mass, and a conformal Killing tensor in the case of vanishing rest mass of the particles. It is suggested that cosmological models of Bianchi-type I can be described in terms of ellipsoidal momentum distribution functions whose ellipsoidal tensor is built out of the Killing vectors associated with the spatial homogeneity.     

Spherical shells of positive density - can they be of non-positive mass?

Spherical shells of fluid in general relativity are considered. The density is assumed to be spatially uniform and it is found that there may be three cases of positive, negative and vanishing Schwarzschild mass of the shell although the density and the pressure are both positive throughout. However the negative mass case has to be associated with a singularity representing a negative mass particle and so is unphysical. The zero mass solution has the intriguing feature that the geometry on either side of the shell is Minkowskian and the space is closed. This closure of the space saves the present result from being in contradiction with the positive energy theorems. Earlier investigations claiming zero-mass distributions are also discussed. A short report giving some of the results of the present paper is published inPhys. Lett. A140 285 (1989).     

Nucleon propagator at finite temperature

We study the nucleon propagator at finite temperature in the framework of finite energy QCD sum rules. We find that the nucleon mass is approximately constant over a wide range of temperature, increasing sharply near the critical temperature for deconfinementT _c . The coupling of the nucleon to quarks is a monotonically decreasing function ofT, vanishing atT=T _c .     

Rotating dirty black hole and its shadow

In this paper, we examine the effect of dark matter to a Kerr black hole of mass m. The metric is derived using the Newman-Janis algorithm, where the seed metric originates from the Schwarzschild black hole surrounded by a spherical shell of dark matter with mass M and thickness Δr_s. The seed metric is also described in terms of a piecewise mass function with three different conditions. Specializing in the non-trivial case where the observer resides inside the dark matter shell, we analyzed how the effective mass of the black hole environment affects the basic black hole properties. A high concentration of dark matter near the rotating black hole is needed to have considerable deviations on the horizons, ergosphere, and photonsphere radius. The time-like geodesic, however, shows more sensitivity to deviation even at very low dark matter density. Further, the location of energy extraction via the Penrose process is also shown to remain unchanged. With how the dark matter distribution is described in the mass function, and the complexity of how the shadow radius is defined for a Kerr black hole, deriving an analytic expression for Δr_s as a condition for notable dark matter effects to occur remains inconvenient.     

Experimental study on the 3p size-resonance in thep- wave neutron strength function

Using a silicon filtered fission neutron beam of an energy width of 20 keV around 143 keV we measured the total cross sections for 37 nuclides and elements having mass numbers between 87 and 140 and determined thep-wave strength functions. The 3P-resonance atA=98 shows no splitting into theP _3/2?P _1/2 doublet. The narrow resonance peak and the following broad distribution of thep-strength function (A=103 to 140) can approximately be reproduced by deformed optical model calculations. The spin-orbit term in the optical potential is consistent with the spin orbit force in the shell model. For nuclei around the closed (N=50) neutron shell a shell effect in thep-wave strength function is indicated.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

Exact solutions for spherical gravitational collapse around a black hole:the effect of tangential pressure

Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied.Exact solutions corresponding to different equations of state are given.We find that when taking the tangential pressure into account,the exact solutions have three qualitatively different outcomes.For positive tangential pressure,the shell around a black hole may eventually collapse onto the black hole,or expand to infinity,or have a static but unstable solution,depending on the combination of black hole mass,mass of the shell and the pressure parameter.For vanishing or negative pressure,the shell will collapse onto the black hole.For all eventually collapsing solutions,the shell will cross the event horizon,instead of accumulating outside theeventhorizon,even if clocked by a distant stationary observer.     

Level densities of heaviest nuclei

The intrinsic level densities of superheavy nuclei in the α-decay chains of ^296,298,300120 are calculated using the single-particle spectra obtained with the modified two-center shell model. The role of the shell and pairing effects on the level density as well as their quenching with excitation energy are studied. The extracted level density parameter is expressed as a function of mass number, ground-state shell correction, and excitation energy. The results are compared with the phenomenological values of level density parameters used to calculate the survival of excited heavy nuclei.     

Constituent quarks,soft pions and meson masses

In the constituent quark model, a simple mass formula is given to relate the masses of the vector and pseudoscalar mesons. Good agreement is obtained for all mesons, from the lightest π, ? mesons to the heaviest. In the limit of vanishing pion mass, alower limit of 230 MeV is obtained for the constituent quark mass.     

Improved renormalization group equations with dimensional regularization and the ε expansions

Due to the absence of dimensional cut-off parameters in the dimensional regularization scheme, vanishing of the renormalized mass of the scalar boson implies vanishing of its renormalized mass; thus the masses of both bosons and fermions in renormalizable field theories can be made finite by multiplicative mass renormalizations. The improved renormalization group equations in D dimensions are derived in such a way that both the large (or the small) momentum limits and the Wilson ? expansions can be uniformly treated for the fermion as well as the boson cases. We discuss the improved equations for φ₆³ theory, φ₄⁴ theory, quantumelectrodynamics, massive vector-gluon model, and non-Abelian guage theories incorporating fermions. For the latter three classes of theories, the gauge dependent problem of the coefficient functions in the improved renormalization group equations is discussed.     

New perspectives on the level density of compound resonances

The level density of compound resonances observed at neutron separation energy is subject of closer investigation and interpretation. The structures in the level density parameter as a function of the mass number allow the determination of the hierarchy of the compound states and the definition of a base line which represents the level density parameter of spherical nuclei with no residual interaction and no shell effects. Using the base line a method becomes available enabling the separation of the residual interaction from properties of the average potential defined in the framework of the shell model. The following examples in different mass regions are discussed: the change of the pairing energy due to the blocking effect atA ≈ 70; the breakdown of the pairing correlation atA ≈ 105 is interpreted as neutron-proton interaction; similar effects in the mass region 150<A<170 are discussed with neutron-proton interaction and the backbending phenomen. Finally it will be shown that there is no enhancement of states due to collective properties of nuclei at high excitation energy.     

Pion-nucleon vertex function with an off-shell nucleon

We present a model calculation for the π-N vertex function in the case in which there is a single off-mass-shell nucleon and a (nearly) on-mass-shell pion. We find very strong effects due to the P₁₁ resonance at 1470 MeV. We provide a simple parametrization of the vertex function in the case that at least one nucleon is on its mass shell.     

Rotationally inelastic,classical scattering from an anisotropic rigid shell potential of rotation symmetry

Rotational excitation in collisions of structureless atoms and diatomic rigid rotor molecules interacting by a rigid potential shell is considered in classical mechanics. The double differential cross sectionJ(u ^*,θ) for final (over initial) relative velocityu ^*=ν′/ν and deflection byθ is analytically related to the shell form in the case of vanishing initial molecular rotation.J(u ^*,θ) exhibits the strong structure of “bulge” scattering or “orientational rainbows” which has been observed in the K?N₂ and K-CO systems and is expected to occur in rotationally inelastic collisions of many nonreactive systems under appropriate scattering conditions. The present results elucidate the nature of the sensitive and direct relation of bulge scattering to the anisotropy of the intermolecular potential.     

dc Josephson effect in metallic single-walled carbon nanotubes

The dc Josephson effect is investigated in a single-walled metallic carbon nanotube connected to two superconducting leads. In particular, by using the Luttinger liquid theory, we analyze the effects of the electron-electron interaction on the supercurrent. We find that in the long junction limit the strong electronic correlations of the nanotube, together with its peculiar band structure, induce oscillations in the critical current as a function of the junction length and/or the nanotube electron filling. These oscillations represent a signature of the Luttinger liquid physics of the nanotube, for they are absent if the interaction is vanishing. We show that this effect can be exploited to reverse the sign of the supercurrent, realizing a tunable π-junction.     

Φ3 theory in six dimensions and the renormalization group

Φ³ field theory in six space-time dimensions is used as a testing ground for the renormalization group. The consistency of the new method devised by 't Hooft is verified at the two-loop level by exhibiting certain cancellations among single pole coefficients, and also relations among double and single pole coefficients. This calculation is contrasted in efficiency with one using the Gell-Mann-Low equation in dimensionally regularized form for which a solution is obtained at the one-loop level, without neglecting mass dependence.The theory shares with asymptotically free ones the virtue of an asymptotically vanishing effective coupling constant. Indeed, the next to leading term in the beta function is also of opposite sign to the coupling constant.     

Towards transport theory of hadron gases

An important role of hadron resonances for determining the characteristics of hadron gases is argued. A kinetic theory model of hadron gas is developed. A classical, nonquantum, distribution function of a resonance is defined with the help of the profile function being an analogue of the mass shell delta function of stable particles. The Boltzmann equation is generalized to include the resonance decay and resonance formation processes. To determine the unknown profile function, the transition rates are assumed to satisfy the bilateral normalization or the detailed balance condition. The profile function is expressed through the resonance formation cross section and the decay width. The H-theorem is proved, and it is shown that the form of the equilibrium distribution function of a resonance coincides with that of a stable particle. Macroscopic equilibrium characteristics are studied. Significance of the resonance mass smearing effect is demonstrated.     

Vacuum polarization in a hydrogen-like relativistic atom: g factor of a bound electron

The contribution of vacuum polarization to the g factor of a bound electron is considered for the ground state of a hydrogen-like atom. A final expression for the correction is obtained in terms of generalized hypergeometric functions and represents a function of parameter Zα and the ratio of the mass of the orbital particle (electron or muon) to the mass of a particle in the vacuum loop. Different asymptotic forms of this expression are derived for both common and muon atoms.     

Paradoxes of unstable electron

The hypothesis that an electron is unstable — when we try to make it consistent with the vanishing mass of the photon-leads to a number of paradoxical statements. The lifetime of the electron is determined by emission of a huge number of longitudinal photons and depends exponentially on the amount of emitted energy. This suggests to discuss searches for charge nonconservation in experiments with high energy particles.     

Inner shell excitation,valence excitation and core ionization in NF3 studied by electron energy-loss and X-ray photoelectron spectroscopies

Electron energy-loss Spectroscopy (EELS) at impact energies of 2.5–3 keV has been used to obtain the electron excitation spectra for the N 1s (K-shell), F 1s (K-shell) and valence shell regions of NF₃. The inner shell spectra were recorded using small angle scattering (?1° ) while the valence shell spectrum was obtained at zero degree scattering angle. The inner shell excitation spectra show a strongly enhanced 1s→ δ^* type transition and continuum features which are typical for molecules with highly electronegative ligands. One of the peaks in an earlier published photoabsorption study of the N 1s region has been shown to be due to a N₂ impurity. The valence shell electron energy-loss spectrum shows a number of transitions which are considered to be mainly due to valence-valence type transitions, with also some evidence of Rydberg structure.The X-ray photoelectron spectra (XPS) of the N 1s and F 1s electrons along with their associated satellite structures have also been recorded using Al Kα (1486.58 eV) radiation. The vertical ionization potentials for the N 1s and F 1s electrons were found to be 414.36 (10) eV and 693.24 (10) eV, respectively. Both spectra exhibit a rich and different satellite structure. These “shake-up” features in the satellite XPS spectra are compared with continuum features of the inner shell electron energy-loss spectra and also with the valence shell spectrum.