Higher order field equations II; Limit properties of green's functions

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions G^M_R(x) and G^M_A(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions G^M_R(x) and G^M_A(x) approach the Green's functions Δ_R(x) and Δ_A(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of G^M_A(x) and G^M_A(x) is the same as of Δ_R(x) and Δ_A(x) - and also the same as for D_R(x) and D_A(x) for t→ ± ∞, where D_R and D_A are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.     

Applications of photoelectron spectroscopy to molecular propertles: XVIII. The vertlcal ionization potentials of diphosphene as calculated by perturbation corrections to koopmans' theorem

The vertlcal ionization potentials (VIP's) of dimethyl diphosphene have been computed using perturbation corrections to Koopmans' theorem. These corrections allow an estimate of the effects of polarization and correlation, and show for this molecule an important contribution of the specific correlation of the ion for the ²A_g and ²B_u states. The results predict for the first three VIP's the ordering ²A_g, ²A_u, ²B_u, in agreement with our previous assignment.     

Operator equivalents in general

We show that recent criticism of a formula for diagonal operator equivalents (OE's) is unfounded. We generalise this formula to derive off-diagonal OE's ^jT_l^m, as a finite polynomial in J_Z, and claim that this is a definitive formula for the ^jT_l^m.     

Correlations between two large transverse momentum πO mesons at the CERN ISR

The correlations between two π^O's of high transverse momentum were studied at the CERN ISR at a centre-of-mass energy $\text{s}\text{= 52.7}\text{GeV}$. Results are presented for two π^O's detected with an azimuthal separation near 180° and also near 0°. Angular and p_⊥ correlations are discussed, as well as invariant mass plots. The observations are compared with some theoretical models of high p_⊥ phenomena. The most striking feature of the data is a strong correlation in the transverse momentum of the two π^O's.     

Semi-empirical analysis of magnetic moments of single-particle (or-hole) states around the 208Pb core

Magnetic moments of single-particle (or-hole) states around the ²⁰⁸Pb core were fitted by three state-independent parameters δg_l^(p), δg_l⁽ⁿ⁾ and α, where α is a parameter that is connected closely with δg_S and g_p. The analysis was performed under the assumptions that (i) the state-dependence of radial integral I((nl)²(n'l')²) involved in δg_s and g_p is calculated by the harmonic-oscillator potential, and (ii) δg_s is taken as being equal to ?4g_p, as expected from the δ-force type core polarization. An excellent fit was obtained when δg_l^(p) = 0.10(2), δg_l⁽ⁿ⁾ = ?0.05(1) and α = 1.2(1), which show that the main contributor to δg_s is the M1 core polarization and δg_l⁽ⁿ⁾ is certainly smaller than 0. B(M1)'s for allowed transitions calculated with the use of the same parameters as above are smaller than the observed B(M1)'s whereas α = 1.01(1) explains well the observed B(M1)'s.     

Axion search in a monochromatic γ-transition: A new lower limit for the axion mass

A search for axion emission in ¹³⁷Ba¹ was performed, looking for the decay of the a₀'s in two photons. The existence of a₀'s with m_a?160 (200) keV can be excluded with rather mild assumptions.     

Indirect exciton dispersion in III–V semiconductors: “Camel's back” in GaP

A new perturbation approach to exciton dispersion in indirect gap semiconductors is developed. For GaP and AlSb existence of the “camel's back” in exciton dispersion is confirmed, and a precise value of the “camel's back” parameter for X^c₁-minima in GaP is reported: E(X^c₁)?E_min(Δ^c₁)=3.5±0.3 meV. At the X-point the 21.44 and 19.48 meV exciton binding energies in GaP are obtained. The corresponding valley-anisotropy splitting is 1.96 meV.     

Comparative study of the VMI model expressions for the fitting of the rotational spectrum of a single intrinsic wave function

Skyrme's method is used to introduce a correlation coefficient which tells us which of the VMI model expressions should be considered better in the calculation of the projected energies E_J when one uses a single intrinsic wave function for a set of good J-states. As an application of the correlation coefficient, we have shown that out of several VMI model expressions for the energy which have the same overlap with the Hamiltonian, the one having minimum dispersion should be considered to be the best choice. A remark is passed that the Holmberg-Lipas model can also be derived using Bohr and Mottelson's conditions. Numerical calculations are carried out for the nuclei ²⁸Si and ³⁶Ar using Ripka's Hartree-Fock wave functions to compare Holmberg-Lipas model with the one in which one directly expands the energy E_J in powers of J(J + 1), where J is the total angular momentum.     

Properties of K0 and Λ inclusive production in charged-current antineutrino-nucleon interactions

In this paper we discuss inclusive spectra of K⁰'s and Λ's produced in charged in charged-current $\text{ν}{}_{\mathrm{\mu }}\text{N}$ interactions in the Fermilab 15 ft bubble chamber filled with a 64% Ne-H₂ mixture. Data presented in terms of the invariant cross section show, when compared with results from experiments with other incident beams, that the behavior of these distributions is approximately the same. The K⁰ and Λ fragmentation functions are presented and the shape of the K⁰ fragmentation function is found to be consistent with the parametrization of Field and Feynman.The average K⁰ and Λ transverse momentum squared as a function of Q², W², x and z is presented. Comparisons for the K⁰'s produced in the current fragmentation region are in qualitative agreement with QCD predictions. The value of the Λ polarization is measured and a positive normal polarization P_N = 0.34±0.18 is found.     

Coulomb excitation of 182, 184, 186W and 166Er with 4He and 16O ions

The Coulomb excitation reaction induced by ⁴He ions selectively excites 2⁺ and 3^? states by direct E2 and E3 Coulomb excitation. In this paper, we present new results from γ-ray spectroscopy with 15 MeV ⁴He ions on a natural abundance target of W. In particular, a 3^? state in each isotope, ^{182, 184, 196}W, was observed by direct E3 excitation. In addition to obtaining B(Eλ, 0 → J = λ) for excitation of each state, information on the reduced transition probabilities for the different decay modes of these states is given. The Coulomb excitation probabilities of the 2'⁺ states at 786 keV in ¹⁶⁶Er and at 737 keV in ¹⁸⁶W were measured with ¹⁶O and ⁴He ions by the backscattered particle-gamma coincidence method in order to determine the static electric quadrupole moment Q_2'. We obtain for ¹⁶⁶Er Q_2' = 2.11 ± 0.37 e· b which is in agreement with (Q_2')_rot and for ¹⁸⁶W Q_2' = 1.17 ± 0.30 e · b which is in agreement with Kumar-Baranger model calculations and is significantly smaller than (Q_2')_rot. This deviation of the measured Q_2' from (Q_2'rot implies in the framework of the Kumar-Baranger calculations a strong coupling between β- and γ-vibrational bands. On the other hand, our observed upper limit for B(E2,2″ → 2′) does not confirm this implication.     

Generalized dielectric function and the plasmon-phonon coupling in GaAs and CdTe

Far infrared (12–235 cm^-1 reflectivity data for GaAs and CdTe have been fitted equally well with the usual two-oscillator dielectric function and Kukharskii's generalized form ?_K. Kukharskii's extended Lyddane—Sachs—Teller relation was confirmed and the quantities appearing in ?_K agreed fairly well with other determinations. ?_K was used to analyze the damped plasmon-phonon modes.     

An analytical model of the heat of chemisorption: A perturbation LCAO MO approach

An analytical LCAO MO perturbation model has been developed for treating the heat of chemisorption Q of an adsorbate A monolayer on a transition metal M film. The model combines parameters of the metal band (the Fermi level E_F, band width W = W^occ + W^vac, the d occupancy N_d, density of states n(?), etc.) with those of the local A-M interactions (the adorbital energy ?_A, off-diagonal matrix elements β_AM, etc.). The major cases of A's having lone pair, singly occupied, and vacant adorbitals have been considered, and the analytical expressions for Q as well as some numerical estimations are presented. The relative values of Q seem to be crucially dependent on the ratio β/(?_A ? E_F). The Q vs. N_d plots for the donor and radical A's are rather flat, typically Q decreasing monotonically as N_d increases, but for the acceptor A's the plots are very parameter dependent and show a variety of trends. The results obtained agree with straightforward computations and (scarce) experimental data.     

A comparison of direct photon, π0 in pp and pp interactions at the CERN ISR

We have measured the production of direct photons, π⁰'s, and η's in p$\text{p}$ and pp collisions at √s=53 GeV in the range 2≈p_T≈6 GeV/c for the central rapidity region |y| 0.4. No statistically significant difference between pp? and pp interactions is observed.     

A statistical approach to quantum mechanics

A Monte Carlo method is used to evaluate the Euclidean version of Feynman's sum over particle histories. Following Feynman's treatment, individual paths are defined on a discrete (imaginary) time lattice with periodic boundary conditions. On each lattice site, a continuous position variable x_i specifies the spacial location of the particle. Using a modified Metropolis algorithm, the low-lying energy eigenvalues, |ψ₀(x)|², the propagator, and the effective potential for the anharmonic oscillator are computed, in good agreement with theory. For a deep double-well potential, instantons were found in our computer simulations appearing as multi-kink configurations on the lattice.     

Determination of valley splitting in (100) Si inversion layers

An experimental method is presented to determine the valley splitting in n-channel Si inversion layers. The method is an extension of the “tilted field” experiment under conditions, where the valley splitting is resolved at all tilt angles. In the framework of Ohkawa and Uemura's theory, the bare splitting as well as the effective exchange interaction are obtained directly from the angles of coincidence. The bare valley splitting in the samples investigated is 0.15 meV/10¹² cm^-2 ·n_s. Using experimentally determined parameters we have calculated the oscillatory conductivity σ_xx in a simplified version of Ohkawa and Uemura's model. The calculated curves reproduce the detailed structure of the experimental data for the various tilt angles of the experiment.     

Large transverse momentum phenomena in a hadronic bremsstrahlung model

We present a bremsstrahlung model which at large transverse momenta p_T leads to an inverse power law for the pion distribution in pp → π^±0 + X. The model predicts particle yields that increase with energy at fixed p_T (breaking Feynman scaling in a definite way) and provides an understanding of the excess of π⁺'s over π^?'s, and of the increase with p_T of the associated multiplicity in the direction opposite to the observed pion; it also accounts for proton to π⁺ ratios of order 1, but in a parameter-dependent way. The recently observed increase of the mean charged multiplicity in pp → p + MM with the transverse momentum of the projectile is also accounted for.     

Mesures de durees de vie dans le cas de faibles intensites lumineuses

A simple method concerning the possibility of lifetime's measurement in the case of low light level, 20 photons/s, is described. Application to some n¹S₀ and ¹D₂ excited states of the Hg atom is given.     

Theory of cyclotron resonance halfwidth for electrons scattered by impurities and phonons

A general theory of the cyclotron resonance halfwidth for electrons scattered by impurities and phonons is developed on the basis of the proper connected diagram expansion of the current-correlation-function formula for the dynamic conductivity. The theory is applied to the cases of Ge samples at extremely high magnetic fields and different temperatures. The usual form of Matthiessen's rule Γ = Γ₁ + Γ₂ + …, where Γ and Γ_j are the total and component energy-dependent resonance widths, is valid only if the component widths Γ_j computed separately for each cause of scattering depend linearly on the densities of scatterers. The resonance width Γ_I due to the charged impurities at very low electron densities ($\text{\$}\text{?}$10¹² cm^?3) and at very low temperatures is known to vary in proportion to the square-root of the impurity density. Large deviations from the Matthiessen's rule occur in such a case. The theory is in good quantitative agreement with currently available experimental data. In order to test the generalized form of Matthiessen's rule, however, the high-field resonance experiments around 15 K is desirable where both phonon and impurity scatterings contribute in a comparable manner.     

Chemical shifts of the copper and cobalt K absorption discontinuities in some ternary compounds

The present paper reports the chemical shifts of the K X-ray absorption discontinuities of copper and cobalt in ternary compounds. Relationships between the chemical shifts ΔE of the discontinuities and the various bond parameters (C, E_g, and f_i) calculated from Levine's theory have been established. It is found that distinctly separate curves can be drawn for different valencies (Cu¹⁺ and Cu²⁺, Co²⁺ and Co³⁺) of the absorbing ions. Making use of Levine's method for calculating bond charges, the effective charges q on the absorbing ions have been evaluated. The dependence of ΔE on q has been confirmed.     

Some rigorous results for electromagnetic mass splittings in QCD

Written proved recently that m_π⁺m_π⁰. We note that this result is a consequence of the Green's function inequalities generalized to include EM as background fields. We also suggest that all ΔI = 2EM mass splittings can be proved to be positive.