Sum rules in QCD for g ηΛΛ and g πΛΣ

New relations between the Borel QCD sum rules for the strong couplings of the Σ⁰ and Λ hyperons are derived. It is shown that, using the sum rules for g _MΣΣ, M = π ⁰, η, as a starting point, one can readily obtain the corresponding sum rules for the coupling constants g _ηΛΛ and g _πΛΣ ⁰. The values of these constants are calculated in a specific parameter region.     

Rotational energy levels of symmetric top molecules in 2 E states

Expressions are derived for the rotational energy levels of a symmetric top molecule in a ² E state which take into account a spin-orbit interaction and vibronic Jahn-Teller interactions. Some group theoretical aspects of the Jahn-Teller problem for a general symmetric top molecule are discussed. In addition, the overall selection rules and formulae for the relative intensities of rotational lines in a ² A-² E transition are derived and the possibility of applying them to two recently published experimental examples is considered.     

Sum rules for the decays of the c-even charmonium states

Sum rules for the decays of the C-even charmonium levels (¹S₀, ³P₀, ³P₂, ¹D₂) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers J^PC=0^?+,0⁺⁺,2⁺⁺,2^?+. The contribution of the continuum to some of the sum rules is small, and they are saturated by the contribution of the lowest charmonium levels. In this way we predict the widths of the two-photon decays of the charmonium states and estimate their total hadronic widths.     

Sum rules including first order quantum corrections for neutron scattering experiments on isotopic mixtures of monatomic fluids

The sum rules for neutron scattering experiments on monatomic isotopic mixtures are studied. The scattering is separated into a self part and a distinct part rather than into an incoherent part and a coherent part. Exact expressions for the moments are derived in terms of polynomials in ? ². The coefficients in these polynomials are sums of averages of hermitean operators that have a classical analogue. For the interpretation, the coefficients are approximated including first order quantum corrections.

It is argued that the separation into coherent and incoherent scattering is not justified in the presence of ‘isotopic incoherence’. Approximate expressions for the sum rules are proposed, in which combined averages (over the isotopic composition) appear of the scattering amplitudes and masses of the scattering atoms. These expressions, including first order quantum corrections to the sum rules, are not available in the literature.

The importance of correct averaging over the isotopic composition of expressions that involve scattering amplitudes and masses is discussed for the case of a maximum incoherent mixture of ³⁶Ar and ⁴⁰Ar.     

An analysis of energy differences in atomic multiplets in connection with the inequality formulation of Hund's rules

A detailed consideration is given of a recent reformulation of Hund's rules in terms of inequalities. The interpretation of Hund's rules is reconsidered assuming that each energy level is known exactly in the restricted Hartree-Fock approximation. Some general theorems and series expansions are derived for energy differences between atomic states. As is now well known, the state of lower energy in a multiplet has the higher expectation value for the electron-electron repulsion, especially in neutral systems. The behaviour of this repulsion is analysed in terms of the Fermi hole and the contraction of the wavefunction which one finds for the state of lowest energy. Numerical examples are given for the ¹P and ³P states of the He isoelectronic series, the ¹S, ¹D and ³P states of the C and O series and the ²P, ²D and ⁴S states of the N series.     

Sum rules for recoilless lambda production in nuclei

Simple sum rules for the (K ^?,π ^?) reaction on nuclei are derived by analogy with the Mössbauer effect. The relative contribution of the recoilless and quasi-freeδ production in the (K ^?,π ^?) reaction in nuclei is estimated.     

New relations between Borel sum rules for the magnetic moments of the Σ<Superscript>0</Superscript> and Λ hyperons

New relations between the Borel sum rules in QCD for the magnetic moments of the Σ⁰ and Λ hyperons are derived. It is shown that, on the basis of the sum rule for the magnetic moment of the Σ⁰ hyperon, one can directly obtain the corresponding sum rule for the magnetic moment of the Λ hyperon, and vice versa, as well as the corresponding sum rule for the Σ⁰ → Λ_γ transition.     

Non-energy weighted electron scattering sum rules for 3He

Electron scattering sum rules for ³He are derived with a realistic ground-state wave function. The theoretical results are compared with the experimentally measured integrated cross sections.     

Symmetry Analysis of Molecules Consisting of Two Coaxial Rotors Using the Extended Permutation–Inversion Groups

A general method for constructing permutation-inversion groups and their extensions to molecules containing two coaxial rotors is presented. Symmetry species of the dipole moment, tensor of polarizability, and total angular momentum operator are determined. General infrared and Raman selection rules, symmetry classifications of rotorsional, rotational, and torsional wavefunctions are derived. Theory is illustrated for the H₃D⁺₂complex.     

Blackbody radiation shift of the Al<Superscript>+</Superscript> clock transition

The blackbody radiation shift of the Al⁺ 3s^{2 1}S^e ₀ ↦ 3s3p ³P^○ ₀ clock transition is evaluated. The polarizabilities of the two states are determined by means of configuration interaction calculations in conjunction with oscillator strength sum rules. The ground state polarizability was 24.14 ±0.12 a.u. while the metastable state polarizability was 24.62 ±0.25 a.u. The derived frequency shift at 300 K was Δν= -0.0042 ±0.0032 Hz. Some auxiliary sum rules are evaluated that allow for the conversion of a finite frequency polarizability difference to a static polarizability difference.     

QCD sum rules for the coupling constants <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">KYN</Emphasis></Subscript> and <Emphasis Type="Italic">g</Emphasis><Subscript>KYΞ</Subscript>

New relations between Borel QCD sum rules for the strong couplings of baryons to kaons are derived. It is shown that, on the basis of the sum rules for the coupling constants g _πΣΣ and g _πΣΛ, the corresponding sum rules can be directly obtained for the coupling constants g _KYN and g _KYΞ, Y = Σ,Λ. The values of these coupling constants are calculated in the fiducial interval 1.0 ≤ M ² ≤ 1.4 GeV² at t = ?1.     

An empirical study on the importance of a speed-dependent Voigt line shape model for tropospheric water vapor profile remote sensing

We use high quality ground-based solar absorption spectra measured in close coincidence with Vaisala RS92 radiosonde in situ water vapor profiles to demonstrate that a Voigt line shape model yields systematic errors in the remotely sensed tropospheric water vapor profiles. We analyse absorption signatures of 4 H₂¹⁶O and 2 HD¹⁶O bands situated between 790 and 4710 cm⁻¹. We find that applying a speed-dependent Voigt line shape model instead of a Voigt line shape model significantly improves the agreement between the water vapor profiles obtained by the radiosondes and by infrared remote-sensing in the different bands. An optimal agreement is obtained for a Γ₂ (relaxation rate for speed-dependence) of 6-21% of Γ₀ (Voigt relaxation rate), which is consistent to the values derived from laboratory experiments. Our study suggests that further extensive laboratory investigations of line shape models are a key for improving the quality of modern water vapor remote sensing products.     

Duality in the current propagator

The idea of local duality between generalized vector dominance and light cone algebra or parton model is applied to the propagator of vector currents. A set of sum rules reminiscent of the generalized first Weinberg sum rules but involving certain unknown parameters are derived. These parameters are fixed from the leptonic decay modes of ?, ω, ?. The sum rules are used to calculate the ω-? mixing angle and thereby predict $\text{Γ(?→}\text{K}\text{K}\text{) = 3.24±0.34}\text{MeV}$, in agreement with experiment. Simple mass mixing or current mixing model for the vector mesons seem to be inconsistent with data. The total cross section for e⁺e^?→hadrons is calculated in the scaling region. If scaling is achieved at $\text{s ? 9–16}\text{GeV}{}^2$ then it is argued that about 22% of the events in this energy region will include strange particles.     

Hemispheroidal quantum harmonic oscillator

A deformed single-particle shell model is derived for a hemispheroidal potential well. Only the negative parity states of the Z(z) component of the wave function are allowed, so new magic numbers are obtained. The influence of a term proportional to l² in the Hamiltonian is investigated. The maximum degeneracy is reached at a superdeformed hemispheroidal prolate shape whose magic numbers are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator. This remarkable property suggests an increased stability of such a distorted shape of deposited clusters when the planar surface remains opaque.     

A scaling law for molecular orbital X Rays

Absolute molecular-orbital thick-target x-ray yields have been measured for a wide variety of targets using 1.4-MeV/amu⁵⁰Ti,⁵⁸Ni, and⁸⁶Kr and 2.4-MeV/amu⁸⁴Kr beams. A scaling law for calculating two-collision molecular-orbital x-ray yields is derived which fits the shape of the measured yields very well in all collision systems examined, and the intensity within a factor of two for near symmetric ion-atom encounters.     

Structure of 72,74Se at high spin

Lifetimes of high spin states up to { }=22⁺ in the yrast positive parity bands have been measured to investigate the shape evolution with increasing spin in ^{72, 74}Se. The Q _t values derived from these measurements indicate that prolate shape stabilizes for ⁷²Se, while a triaxial shape develops for ⁷⁴Se at higher spins. Comparison of the observed trend in Q _t with spin for ^{72, 74}Se with that of the corresponding kryptones isotones emphasizes the stability provided by N=38 prolate shell gap even at high rotational frequency.     

The quadrupole moment of the 40 ps fission isomer in 236Pu

A quadrupole moment of 37_?8⁺¹⁴ b has been deduced for the 40 ps shape isomer in ²³⁶Pu. The value has been derived from a measured delayed fission fragment angular distribution with an anisotropy of 1.48 ± 0.15 for the isomeric decays at 30°. The deformation of the second minimum expressed by the axes ratio of a spheroid is found to be 2.0 ± 0.3.     

QCD sum rules for heavy quark systems

In this paper we present in a detailed and coherent fashion our work on QCD sum rules for equal mass heavy quark meson states. We discuss the technical procedures used to calculate the perturbative and non-perturbative contributions to the vacuum polarization, which have been calculated for all currents up to and including spin 2⁺⁺. Using dispersion relations, sum rules are derived. Extensive applications are made to the lowest lying states of the charmonium and upsilon systems. The masses of the S- and P-wave charmonium levels are reproduced to a high degree of accuracy, and the mass of the ¹P₁ level is predicted at 3.51 GeV. For the upsilon system it only appears to be possible to predict the γ-η_b splitting which gives 60 MeV. Very accurate values are given for the current quark masses at p² = ?m_q²: m_c = 1.28 GeV and m_b = 4.25 GeV.