A small-parameter approach for few-body problems

A procedure to solve few-body problems is developed which is based on an expansion over a small parameter. The parameter is the ratio of potential energy to kinetic energy for states having not small hyperspherical quantum numbers, K>K ₀. Dynamic equations are reduced perturbatively to equations in the finite-dimension subspace with K ⩽ K ₀. Contributions from states with K>K ₀ are taken into account in a closed form, i.e., without an expansion over basis functions. Estimates concerning the efficiency of the approach are presented. The text was submitted by the author in English.     

A simple chiral Lagrangian approach toK→πππ decays andε′+0−

We analyse theK→πππ decays in the framework of a chiral Lagrangian supplemented by the 1/N expansion (N being the number of colors). The measuredK _L →π⁺π⁰π⁺ Dalitz plot is very well reproduced. Contrary to a recent claim, the Li-Wolfenstein relation between the CP impurities associated with theK→πππ(ε′_+0?) and theK→ππ(ε′) decay amplitudes is rather stable against isospin-breaking effects and higher-order (in the chiral expansion) weak operator corrections. We also predict a branching ratio of 2.1 10^?7 for the CP-conservingK _S →π⁺π⁰π⁺ decay.     

A study of the decay KL0 → π±e∓νe

In a study of charged K_L⁰ three-body decays a sample of 6668 K_L⁰ → π^±e^?ν candidates has been obtained. The Dalitz plot distribution is in agreement with V ? A theory, and limits are presented for scalar and tensot contributions to the weak current. Using a conventional expansion for the form factor f₊ we find λ₊ = 0.055 ± 0.010 with systematic effects estimated at ± 0.01.     

A phenomenological equation of state for isospin asymmetric nuclear matter

A phenomenological momentum-independent(MID) model is constructed to describe the equation of state(EOS) for isospin asymmetric nuclear matter,especially the density dependence of the nuclear symmetry energy Esym(ρ).This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach.We find that there exists a nicely linear correlation betwee...     

Correlations of pions and kaons as a measure for delayed expansion due to the QCD phase transition

We study pion and kaon correlations in ultra-relativistic heavy ion collisions in a hydrodynamical model with transverse cylindrical and boost-invariant longitudinal symmetry. As a function of the initial energy density ε₀, the ratioR _out/R _side of the inverse widths of the two-particle correlation function in out- and side-direction reflects the behaviour of the lifetime of the system. The ratio shows an enhancement in the case of a delayed expansion caused by the QCD phase transition. We discuss how this time-delay signal depends on the average transverse momentum of the pair, and show that it appears particularly strong for pairs with large average transverse momentum,K _⊥～1 GeV and for initial energy densities ε₀ ? 10 ? 20 GeVfm^?3 GeVfm^?3, corresponding to nuclear collisions at RHIC.     

Analysis of the microwave spectrum of hydrazine

Microwave measurements in the interval from 6 to 133 GHz, consisting of 444 rotational transitions in the vibrational ground state of hydrazine with J ≤ 31 and K_a ≤ 6 were fit to an effective rotational Hamiltonian containing 9 asymmetric rotor constants, 14 NH₂ inversion parameters, and 1 internal rotation parameter, with an overall standard deviation of the fit of 0.40 MHz. This set of parameters contains: (i) the three rotational constants; (ii) tunneling splitting constants for NH₂ inversion at one end of the molecule, for NH₂ inversion at both ends of the molecule, and for internal rotation through the trans barrier; (iii) two K-type doubling constants affecting the K = 1 levels; (iv) an a-type Coriolis interaction with matrix elements linear in K; and (v) various centrifugal distortion corrections to the above parameters. A consistent group theoretical formalism was used to label the energy levels and to select terms in the phenomenological rotational Hamiltonian. The Hamiltonian matrix, which is set up in a tunneling basis set, is of dimension 16×16 and contains only ΔK_a = 0 matrix elements, asymmetric rotor effects being taken into account on the diagonal by terms from a Polo expansion in bⁿ. Hyperfine splittings and barrier heights are not discussed.     

A simple relation between bulk and surface properties of nuclear matter

Starting from a previously derived relation between the derivatives of the bulk nucleon energy e(n_c) and the surface tension σ(n_c) with respect to the central density n_c we obtain a simple model-independent relation between the values of n_c, σ(n_c), the surface parameter t and the bulk modulus K_∞ at saturation. This relation is checked for values obtained in ETF calculations. K_∞=230 MeV is calculated from the well-known experimental values of n₀, σ₀ and t₀.     

Dispersed fluorescence spectroscopy of S0 vibrational levels in formaldehyde-d

High resolution dispersed fluorescence (DF) spectra of excited vibrational levels in S₀ HDCO up to 10 000 cm⁻¹ energy were recorded in a free-jet expansion. Excitation to the 0₀₀ rotational level in 4⁰ and 4¹ S₁ HDCO yielded pure vibrational spectra that are free from rotational congestion. The 162 transitions (133 unique vibrational levels) assigned in these spectra have been fit to a multiresonant Hamiltonian model, which includes harmonic frequencies , anharmonic constants (x_ij), and resonance constants (K). The assigned vibrational states were fit to the model with a standard deviation of 4.02 cm⁻¹. Extensive vibrational mixing is observed throughout the spectra. Six harmonic constants, eight anharmonic constants, and four resonance constants (K_44,1, K_66,1, K_44,66, and K_33,5) were determined experimentally. The 18 experimentally determined spectroscopic constants, with the exception of and K_66,1, were found to agree within 6 cm⁻¹ of ab initio calculated values.     

Nuclear rotation for low and high spin values

It is shown that a rigorous application of the Peierls-Yoccoz angular momentum projection method leads, in the case ofK=0 rotational bands, to a simple exact expression for the projected energyE _I , which may be especially suitable for numerical calculations. On the basis of this energy law and without making any assumption for the overlapsn(Β) andh(Β), a finite expansion ofE _I in powers ofI( _I +1) is obtained and discussed. Using this finite series a microscopical variable moment of inertia model is presented.     

Inclusive cross sections in the central region and the supercritical pomeron

Using the double-Regge formalism and a supercritical pomeron with α_P(0)=1+Δ, we analyse the energy dependence of inclusive cross sections for negatively charged particles (c⁻) and K_s⁰ at CM rapidity y=0 in the CERN PS-Sp̄pS collider energy range. The values of Δ(c⁻)=0.170±0.008 and Δ(K_s⁰)=0.167±0.024 are found to be very close to each other and compatible with estimates of Δ derived from the total cross sections.     

Structure and high pressure behaviour of organic crystals based on aromatically substituted 1,3,4-oxadiazoles

The crystalline structure of a new compound containing the 1,3,4-oxadiazole moiety, 4-(5-methyl-1,3,4-oxadiazole-2yl-)-N,N′-dimethyl-phenylamine (MODPA) was determined. It shows a monoclinic structure with space group P2₁/c and lattice parameters: a=1.02997(6), b=0.64840(4), c=1.58117(10) nm and β=99.4820(10)°. To study the intermolecular interactions in oxadiazole containing organic crystals, X-ray studies on MODPA and 2,5-diphenyl-1,3,4-oxadiazole (DPO) were performed up to 5 GPa at room temperature. The Murnaghan equation of state is used to describe the compression behaviour of both substances. From these results, the bulk modulus and its pressure derivative were determined. The values obtained are: K₀=6.3 GPa and K′₀=6.8 for MODPA and K₀=7.3 GPa and K′₀=6.7 for DPO. Additionally, measurements under increasing temperature at ambient pressure were carried out to evaluate the thermal expansion coefficient: α=1.8×10⁻⁴ K⁻¹ for MODPA and α=1.9×10⁻⁴ K⁻¹ for DPO.     

K0 production in e+e− annihilations at 30 GeV center of mass energy

Inclusive K⁰-production has been measured in e⁺e^- annihilation at a center of mass energy of about W = 30 GeV. The ratio of K⁰ + K⁰ production to μ⁺μ^- production is R_K0 = 5.6 ± 1.1 (statist. error) ± 0.8 (system.error) This value is about a factor of three higher than R_K0 at W = 7 GeV. The cross sections (s/β) dσ/dx is consistent with a scaling behaviour.     

The torsion-rotation spectrum of perchloric acid, HClO4

The rotational spectrum of HClO₄ has been observed in selected regions between 51.7 and 870 GHz. The molecule is a near spherical rotor with a moderately low barrier to internal rotation. The spectrum is characterized by strong μ_a, R-branch groupings with B + C = 5276.78 MHz. Although there are no E torsional states, the R-branches show three distinct groups of lines. There is a relatively tight cluster of symmetric rotor like transitions with K = 3n, a rather regular progression of transitions with K = 3n + 2 to high frequency and a less regular group of transitions with K = 3n + 1 to low frequency. Because the molecule is nearly spherical, the energy as a function of K is dominated by the K dependent solutions of the Mathieu equation. This unusual energy level distribution gives rise to numerous anomalous splittings and shifts due to avoided crossings within the K stacks as well as widely scattered μ_b transitions. The fitting procedure will be described and the effective parameters will be presented. Rotational transitions of excited torsional states at and above the top of the barrier and the v_t = 2-0 far infrared spectrum have been assigned. The dipole moment and the quadrupole coupling constants have been determined. Structural implications will be discussed.     

Energy, compressibility, and covalence in the carbon family

It is shown that a similarity relationship of the type (K ₀ V ₀/E ₀)?const (where K ₀, V ₀, and E ₀ are the bulk modulus, the volume, and the total energy at P=0) exists for the elements of the carbon family, including C, Si, Ge, Sn, and Pb. This fact rules out the possibility of significant covalent effects on the compressibility of the corresponding substances. The record bulk modulus value of diamond is associated with its extreme atomic density.     

Analyzing in-plane magnetic anisotropy from surface morphology for amorphous films

A method is developed to analyze the in-plane magnetic anisotropy from surface morphology for amorphous films. The lateral sizes along radial direction (R_RD) and tangent direction (R_TD) of rotational substrate, which are extracted from the surface morphology of Co_66.3Zr_33.7 amorphous films, are used to calculate stress anisotropy energy E_σ. It is found that E_σ is consistent with the magnetic anisotropy energy K_μ for the samples deposited on Si (1 0 0) substrate and then a relationship K_μ ∝ 1/R_RD − 1/R_TD can be obtained. This method is sensitive to the initial state of substrate so its application range is discussed.     

Convergence properties of the Brillouin-Wigner type of perturbation expansion

We study the Brillouin-Wigner perturbation expansion of the model-space effective Hamiltonian corresponding to the full Hamiltonian H(x) = H₀ + xH₁, H₀ and H₁ being respectively the unperturbed and the interaction Hamiltonian and x being a strength parameter. The radius of convergence for the perturbation expansion is related to the poles of the energy-dependent effective interaction, and the location of these poles in the complex x-plane is discussed. The situation with poles lying off the real x-axis is examined. In terms of the spectrum of the unperturbed Hamiltonian H₀, some necessary conditions for convergence are derived, and the effects of intruder states are discussed. It is shown that the BW expansion of the ground-state energy can always be made convergent by a shift of the unperturbed energy spectrum.     

A study of some potassium hexachlorometallate complexes using electron spectroscopy

X-ray photoelectron (ESCA) spectra of the core (Cl 2p K 2p and metal 4f, if present) and valence orbitals are reported for K₂ReCl₆, K₂OsCl₆, K₂IrCl₆· 3 H₂O, K₂PtCl₆, K₃MoCl₆, and K₂SnCl₆. The K 2p_{$\text{3}\text{2}$} binding energy was found to be nearly constant (292.7 eV) and that of Cl to increase very slightly with increasing atomic number for the third row transition metals. The chemical shifts of Re(IV), Os(IV), Ir(IV), and Pt(IV) relative to the metals were in qualitative agreement with atomic calculations utilizing configurations obtained from extended Hückel calculations. The valence spectra of the transition metal complexes exhibit a three-band structure. On the basis of MO results and intensity considerations the high binding energy band is assigned as a composite of the a_1g, e_g, 1t_2g MO's. The middle band represents the t_2u, 2t_1g MO's; and the low binding energy band the 2t_2g MO. Calculated nd orbital photoionization cross sections correlate reasonably well with the relative intensifies of the valence manifolds. Comparison of band separations and charge-transfer transition energies suggests that interelectronic repulsion and MO energy separation contribute about equally to the overall charge-transfer energy.     

Study of e+e− → KS0K±π∓ in the 1.4–2.18 GeV energy range: A new observation of an isoscalar vector meson: φ′ (1.65 GeV)

First measurements of the e⁺e^? → K_S⁰K^±π^? reaction in the 1.4–2.18 GeV energy range have been performed with the magnetic detector DM1 at the Orsay storage rings DCI. The cross section is rather large. The production is mainly K¹⁰K⁰ which reveals an interference between isovector and isoscalar amplitudes. These results show again the existence of an isoscalar vector at 1.65 GeV shown to be a φ′ meson.     

A separable approximation to the two-body t-matrix for short-range central local potentials

The S-wave potential in momentum space, V₀(p, p′), corresponding to a local two-body central short-range potential may be expanded in separable form with the help of suitable quadrature formulae. With a two-term separable expansion for a variety of nuclear potentials, the resulting t-matrix is found to be in close agreement with the corresponding result with a six-term expansion for small values of p and p′ which are important in the calculation of the trinucleon binding energy.     

A measurement of Kevγ+ decay

The decay K⁺ → e⁺vγ has been observed. In a counter experiment at CERN, 56 events of this type have been identified by detection of a γ with an energy > 100 MeV and of an e⁺ with an energy between 236 MeV and the maximum e⁺ energy, 247 MeV. The angle between γ and e⁺ was > 120°. Thus, the experiment was sensitive only to the structure decay (SD) term proportional to the squared sum of vector- and axialvector amplitudes, |ν_K + a_K|², corresponding to the emission of right handed γ. We find Δ₊(SD)/Δ(K_e2) = 1.05_?0.30^+0.25 and Δ_(SD) < 85 (90% CL). Δ₊ is in agreement with theoretical predictions.