Spectral Sum Rules Research Articles

Scattering theory for general, non-local interactions: Threshold behavior and sum rules

Scattering theory is discussed for Schrödinger Hamiltonians with general, not necessarily separable, non-local interactions without assuming spherical symmetry. The possibility of zero-energy eigenstates is explicitly taken into account. Low-energy expansions are obtained for the scattering amplitude in the different cases. The scattering length and effective range parameter are directly derived from the threshold behavior of the scattering amplitude. Spectral sum rules, generalizing Levinson's theorem, are given.

Spectral sum rule for time delay in R2

A local spectral sum rule for nonrelativistic scattering in two dimensions is derived for the potential class v∈L4/3 (R2). The sum rule relates the integral over all scattering energies of the trace of the time-delay operator for a finite region Σ⊆R2 to the contributions in Σ of the pure point and singularly continuous spectra.

Statistical electron angular correlation coefficients for atoms within the Hohenberg-Kohn-Sham theory.

Statistical electron angular correlation coefficients \ensuremath{\tau}=2〈 ${\mathcal{J}}_{?\phantom{\rule{0ex}{0ex}}}^{}$, have been obtained for the atomic systems $_{2}\mathrm{He}$ through $_{14}\mathrm{Si}$, within the Hohenberg-Kohn-Sham density-functional formalism. These are computed with use of the spectral sum rules obtained from the pseudoexcitation spectrum employing the recent formulation of the time-dependent Kohn-Sham theory due to Bartolotti. Various approximations to the exchange-correlation energy functional are used and for first-row atoms, a comparison is made with the highly accurate correlation coefficients recently obtained by Thakkar. The present \ensuremath{\tau} values show closer agreement with those of Thakkar with increasing number of electrons.

Spectral function sum rules for gluonic currents

We determine the masses and the decay amplitudes of the 2++, 0−+ and 0++ gluonia in anSU(3)c Yang-Mills theory. We estimate the so-called topological susceptibility of theU(1) sector. We discuss theSU(3)F breaking effects to the η′(896) massrelation from current algebra and predict the η′ parameter values.

Meson-gluonium mixing from QCD sum rules

We evaluate the off-diagonal two-point correlation function responsible for the gluonium-meson mixing, including the leading non-perturbative lowest dimension vacuum condensate contributions. Then, using spectral function sum rules approach, we deduce a small meson-gluonium mixing angle. We also derive upper bounds for the η′ and for the strange quark masses.

Chiral symmetry breaking in SQCD

Using a spectral function sum rules approach, we derive some constraints among the Goldstone parameters, the lowest dimension vacuum condensates and the mass of the chiral matter superfield in supersymmetric QCD (SQCD). These relations are consistent with previous results on SQCD and complement them.

Properties of the meson system and chiral-symmetry-breaking parameters from quantum chromodynamics

Some QCD-inspired spectral function sum rules are discussed, in view of the most recent experimental results on scalar and pseudoscalar mesons. Estimates are performed of the weak-decay amplitudes of 0− radial excitations, of the current quark mass ratiomg/md and of the quark vacuum condensate ratio\(\langle \bar \psi _s \psi _s \rangle /\langle \bar \psi _u \psi _u \rangle \).

On the properties of the W-boson within the subconstituent models of electroweak interactions

We discuss some properties of the W-boson using spectral function sum rules within the framework of constituent models of quantum haplo-dynamics (QHD). Constraints on the W-decay amplitude and so its mass and total width have been derived. The results may give a test on possible aspects of this model of electroweak interactions.

Spectral sum rules for the three-body problem

This paper derives a number of sum rules for nonrelativistic three-body scattering. These rules are valid for any finite region $\ensuremath{\Sigma}$ in the six-dimensional coordinate space. They relate energy moments of the trace of the on-shell time-delay operator to the energy-weighted probability for finding the three-body bound-state wave functions in the region $\ensuremath{\Sigma}$. If $\ensuremath{\Sigma}$ is all of the six-dimensional space, the global form of the sum rules is obtained. In this form the rules constitute higher-order Levinson's theorems for the three-body problem. Finally, the sum rules are extended to allow the energy moments to have complex powers.

Spectral mass sum rules for self-coupled Bose fields

Spectral mass sum rules for self-coupled Bose fields

Light Quark Masses

1. Introduction; (a) The mass pitfalls of the old quark model. (b) Perturbative and spontaneous masses in QCD.2. Running masses in QCD; (a) Masses from spectral sum rules. (b) Lower bounds on running masses and upper bounds on non-perturbative masses.3. Isospin and SU(3) violations from the quark mass matrix in radiative meson decays.

Asymptotic chiral symmetry, meson masses and decay constants

Weinberg’s spectral function sum rules are examined to study the axial vector mass spectrum at the level of SU(4). New mass relations and general mass constraints are derived to predict the masses of the charmed axial vector mesons and theI=0 pseudoscalar decay constants.

Solid States Effects in X-Ray Photoemission

Many-body description of the X-ray photoemission process from solids is discussed qualitatively, and also formulated in terms of a correlation function that contains the effects of inelastic scattering of both the excited photoelectron ("extrinsic") and photohole ("intrinsic"). The dynamical concepts, like the sudden and adiabatic limits, are discussed and obtained as limiting cases of the full description. The spectral sum rules are shown to be modified due to the extrinsic scattering. The emphasis is on the quantitative description of the inelastic effects characteristic of the solid state photoemission, and several possible scattering mechanisms are analyzed in more detail.

Spectral Function Sum Rules and Situation of Axial Vector Mesons

Spectral Function Sum Rules and Situation of Axial Vector Mesons

Spectral function sum rules in quantum chromodynamics: (I). Charged currents sector

The Weinberg sum rules of the algebra of currents are reconsidered in the light of quantum chromodynamics (QCD). We derive new finite-energy sum rules which replace the old Weinberg sum rules. The new sum rules are convergent and the rate of convergence is explicitly calculated in perturbative QCD at the first non-trivial order. Phenomenological applications of these sum rules in the charged current sector are also discussed.

Spectral function sum rule and onium

Spectral function sum rule and onium

Photoelectron spectroscopy of localized levels near surfaces: Scattering effects and relaxation shifts

We calculate the spectrum of photoelectrons excited from localized levels in solids far into the continuum (XPS situation), in a model that takes into account exactly their interaction with a boson-like spatially non-uniform field. The general results are applied to discuss the spectra of photoelectrons in metals, where the dominant interaction is the coupling to bulk and surface plasmons. In particular, we study the modification of spectral sum rules connecting the strength of inelastic processes with the energy shifts in the spectrum, showing that the electron (“extrinsic”) scattering changes the average position of the spectrum with respect to the pure “intrinsic” result in the “sudden approximation”, which leads also to its dependence on the excitation energy and position of localized level. We estimate these deviations in a simple model which nevertheless reproduces correctly the dynamical aspects of the problem.

Axial vector mass spectrum and mixing angles

Spectral sum rules of the axial-vector current and axial-vector current-pseudoscalar field are used to study the axial-vector mass spectrum and mixing angles, as well as the decay constants and mixing angles of the pseudoscalar mesons. In general, the result is quite persuasive for the existence of the J PC =1 ++ multiplet in which one has a canonical D-E mixing.

Spectral sum rules for the quantized sine-Gordon field

The sine-Gordon field as quantized by the procedures of Coleman is studied by means of spectral representations. A sum rule for the parameter $\ensuremath{\gamma}$ is derived from which it is shown that a breakdown in spectral conditions occurs for ${\ensuremath{\beta}}^{2}>8\ensuremath{\pi}$. A Lehmann-type mass formula is obtained which places an upper bound on the physical boson mass in terms of the finite parameters $\ensuremath{\gamma}$ and ${\ensuremath{\beta}}^{2}$.

ChemInform Abstract: A PHOTOELECTRON SPECTROSCOPIC STUDY OF THIOFORMAMIDE

Chemischer InformationsdienstVolume 7, Issue 30 Physical Organic Chemistry ChemInform Abstract: A PHOTOELECTRON SPECTROSCOPIC STUDY OF THIOFORMAMIDE KATSUMI KIMURA, KATSUMI KIMURASearch for more papers by this authorSHUNJI KATSUMATA, SHUNJI KATSUMATASearch for more papers by this authorTAKAHIKO ISHIGURO, TAKAHIKO ISHIGUROSearch for more papers by this authorAKIKO Y. HIRAKAWA, AKIKO Y. HIRAKAWASearch for more papers by this authorMASAMICHI TSUBOI, MASAMICHI TSUBOISearch for more papers by this author KATSUMI KIMURA, KATSUMI KIMURASearch for more papers by this authorSHUNJI KATSUMATA, SHUNJI KATSUMATASearch for more papers by this authorTAKAHIKO ISHIGURO, TAKAHIKO ISHIGUROSearch for more papers by this authorAKIKO Y. HIRAKAWA, AKIKO Y. HIRAKAWASearch for more papers by this authorMASAMICHI TSUBOI, MASAMICHI TSUBOISearch for more papers by this author First published: July 27, 1976 https://doi.org/10.1002/chin.197630032AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume7, Issue30July 27, 1976 RelatedInformation