A relativistic model of the composite π meson

The pion is treated as a fermion-antifermion composite state, described by the Euclidean Bethe-Salpeter equation. The kernel of the equation is a local potential having an exponentially infinite spectral function, connected with the empirical mass spectrum of resonances. For the simplest potential U(r) = f²(r²?a²)^?1 the equation for the massless pion is solved by using WKBJ method, and the parameters f, a and the fermion mass M are estimated.     

Lattice energy of alkali halide crystals

A new repulsive term in the ionic interaction potential ψ(r) = Ar^?ne^?r/gl, is suggested and the three unknown parameters A, λ and n are evaluated. Lattice energies of alkali halide crystals are calculated using this form. The results agree fairly well with the experimental values.     

On the path integral for the potential V = ar−2 + br2

A simple, alternative path integral formulation for the potential V = ar^?2 + br², r ? 0, is presented. This is achieved by mapping the problem to a two-dimensional oscillator and using the method of image paths.     

Indirect interaction of Mössbauer nuclei

An expression is deduced for the operator of the indirect interaction of nuclei via the electromagnetic field. The properties of Mössbauer nuclei are described within the pseudospin formalism, which is usually used in the theory of optical two-level systems. The indirect interaction of pseudospins is derived by a method adopted from the theory of superconductivity. It is found that the potentials of this interaction involve terms decreasing as r ^?3, r ^?2, and r ^?1. The estimates demonstrate that the two-particle interaction can contribute significantly to the width of the resonance line, for example, in crystals whose cells contain thulium nuclei.     

Energy eigenvalues from a modified operator method

Large-order perturbation calculation of energy eigenvalues of confining potential models of the V = ?r^?1 + λr^k, k = 1, 2,..., using a modified operator method is discussed. Very accurate results are obtained for positive and negative λ values when k = 1 and k = 2.     

Long Range Potential Component in the NN Force

The Fourier transform of the Born term of the AGS equation in the NNπ-system generates an energy-dependent Yukawa-type local NN-quasi-potential. An appropriate average with respect to energy suggests a variety of local NN-potentials with different ranges: 1/r(r + a) ^m?1 (for 2 ≤ m) where in the long range region it becomes 1/r ^m , while in the short range region the Yukawa-type potential e ^?(m?1)r/a /r results. Therefore, one finds that the Yukawa potential is automatically accompanied by an additional longer range interaction 1/r ^m . For m = 2, the potential 1/r ² produces Efimov-like bound states in the deuteron spectra. The m = 6, 7 cases lead to the Van der Waals potential.     

Freezing of Energy of a Soliton in an External Potential

In this paper we study the dynamics of a soliton in the generalized NLS with a small external potential ?V of Schwartz class. We prove that there exists an effective mechanical system describing the dynamics of the soliton and that, for any positive integer r, the energy of such a mechanical system is almost conserved up to times of order ?^?r. In the rotational invariant case we deduce that the true orbit of the soliton remains close to the mechanical one up to times of order ?^?r.     

Franck-Condon factors and R-centroids for the A1∑+-X1∑+ and B3Π(0+)−X1∑+ band system of 63Cu1H and 63Cu2H

The recently reported new RKR potential energy curves for the X¹∑⁺, A¹∑⁺, and B³Π(0⁺) electronic states of ⁶³Cu¹H and ⁶³Cu²H are used to calculate Franck-Condon factors and r-centroids for the A?X and B?X band systems for 0≤v″≤20, 0≤v′≤10 and J = 0, 30, 40. The r-centroid approximation is verified and a physical interpretation of the r-centroid is discussed.     

Molecular structure and centrifugal distortion constants of isocyanic acid from the microwave,millimeter wave,and far-infrared spectra

The pure rotational spectra of HNCO and DNCO were measured in the far-infrared region from 80 to 350 cm^?1 by a Fourier transform spectrometer with a resolution of 0.1 cm^?1. The ^rR_K branches were measured and assigned for HNCO from K = 1 to 6, and for DNCO from K = 3 to 8. The measured transition wavenumbers were analyzed together with the microwave and millimeter wave data reported by Hocking, Gerry, and Winnewisser [Can. J. Phys.53, 1869–1901 (1975)] and with the far-infrared data of Krakow, Lord, and Neely [J. Mol. Spectrosc.27, 148–176 (1968)] in the low-wavenumber region. The microwave and millimeter wave data of H¹⁵NCO, HN¹³CO, and HNC¹⁸O reported by Hocking et al. were reanalyzed assuming several centrifugal distortion constants to be identical with those of the normal species. The molecular structure of HNCO was reevaluated using a modified substitution method from the rotational constants obtained in this work. The molecule has a bent structure in a trans configuration with $\text{r}\text{(NH) = 0.995}\text{A}\text{?}$, $\text{r}\text{(NC) = 1.314}\text{A}\text{?}$, $\text{r}\text{(CO) = 1.668}\text{A}\text{?}$, ∠HNC = 123.9°, and ∠NCO = 172.6°.     

Mass spectrum of the two dimensional λφ4−1/4φ2−μφ quantum field model

It is shown thatr-particle irreducible kernels in the two-dimensional λφ⁴?1/4φ²?μφ quantum field theory have (r+1)-particle decay for |μ|≦λ²?1. As a consequence there is an upper mass gap and, in the subspace of two-particle states, a bound state. The proof extends Spencer's expansion [20] to handle fluctuations between the two wells of the classical potential. A new method for resumming the low temperature cluster expansion is introduced.     

Intermediate asymptotic expressions for high-order spin correlation functions in a two-dimensional classical ferromagnet

Different-point spin correlation functions are calculated for a two-dimensional classical ferromagnet in a pacerturbative range of distances r: a<r?m ^?1, where a is the lattice parameter and m ^?1 is the correlation length. The expressions for the four-and higher-order correlation functions are presented.     

Approximate eigensolutions of Dirac equation for the superposition Hellmann potential under spin and pseudospin symmetries

The Hellmann potential is simply a superposition of an attractive Coulomb potential ?a/r plus a Yukawa potential be^{?δ r} /r. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number κ in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.     

Wavefunctions of helium-like systems in limiting regions

We find an approximate analytic form for the solution ψ(r ₁, r ₂, r ₁₂) of the Schrödinger equation for a system of two electrons bound to a nucleus in the spatial regions r ₁ = r ₂ = 0 and r ₁₂ = 0, which are of great importance for a number of physical processes. The forms are based on the well-known behavior of ψ(r ₁, r ₂, r ₁₂) near the singular triple coalescence point. The approximate functions are compared to the locally exact ones obtained earlier by the correlation function hyperspherical harmonic (CFHH) method for the helium atom, light helium-like ions, and the negative ion of hydrogen H^?. The functions are shown to determine a natural basis for the expansion of CFHH functions in the considered spatial region. We demonstrate how these approximate functions simplify calculations of high-energy ionization processes.     

Calculation method for the continuum states of atomic systems

In the present work, we develop a calculational method of solving the scattering equations for spherically symmetric potentials by expanding the solutions on Coulomb functions. We utilize a multistep integration scheme together with the standard partial wave analysis in a region where the potential term dominates. The method applies to any physical problem expressed as [? ² + V(r) + k ²]ψ(r) = 0, while the extension of the method to more general scattering problems is briefly discussed. At present, we demonstrate a two-step Coulomb-fitted integration scheme by calculating the short-range scattering phase shifts for various potentials V (r).     

Interatomic force constants studies of AMF3perovskite-type crystals (A = K,Rb; M = Mg,Ni, Co,Zn, Mn)

A simple model involving only three force constants allows us to evaluate the short range interactions in perovskite fluorides from the experimental values of the elastic constants and the lattice parameters of these compounds. The results indicate that the A-F bonds are quite central in character whereas the M-F bonds are axially symmetric; thus the short range A-F interactions are assumed to have the Born-Mayer form:ZZZZZBy studying the variations of the force constants with respect to the lattice parameter r, it is determined that ρ = 0·232 , λ = 2·8 × 10^?8 ergs for K⁺-F^?; ρ = 0·232 , λ = 4·1 × 10^?8 ergs for Rb⁺-F^?; λ₂, ρ₂ and ρ₂ are respectively 6·9 × 10^?10 ergs, 0·34 , 0·98for Co²⁺-F^? and 2·9 × 10^?10 ergs, 0·46 , 1·40for Mn²⁺-F^?. Taking into account both the short range repulsive potential and the long range electrostatic potential we can study the variations of the lattice energy as a function of r near the equilibrium position and deduce a theoretical value of the lattice distance. In spite of the simplicity of the model, the discrepancy between the experimental and the theoretical values is less than 10 per cent for all the compounds.     

A new treatment of singular potentials

For a broad class of strongly singular potentials, the effective (finite-dimensional) forms of the hamiltonian H are constructed by its “smooth” algebraic truncation in a large model space. The method is based on an asymptotic factorization of H into a product of matrices. Its efficiency (acceleration of convergence of the energies) is illustrated on the singularly anharmonic potential V(r) = r² + hr^?4.     

Theoretical study of the spin-orbit coupling in the X2Π state of OH

The spin-orbit coupling constant, A(r), as a function of internuclear distance (r) was computed for the X²Π state of OH, using the microscopic spin-orbit Hamiltonian, extended basis sets, and extensive configuration-interaction wavefunctions. Our best theoretical results are in excellent agreement with the “experimental” A(r) functions deduced from an inversion of the observed A_v. Our calculated first-order contributions to A_v, v ≤ 10, obtained by vibrationally averaging our theoretical A(r) function using the X²Π RKR potential, differ from experiment by less than 0.12%. A minimum occurs in the A_v at v = 7 in agreement with experiment, reflecting the local minimum in A(r) near 2.8 bohr. The second-order contributions to A_v are only about 0.1% for v ≤ 10. They arise mainly from the A²Σ⁺ state for the lower vibrational levels, but each of the A²Σ⁺, B²Σ⁺, (1)²Σ^?, (1)⁴Σ^?, and (1)²Δ states contributes significantly for higher vibrational levels. Spin-orbit centrifugal distortion parameters, A_Dv and a_Dv, are reported for v ≤ 6. The theoretical A_Dv are also in excellent agreement with experiment when the “experimental” A(r) function has the same slope at the equilibrium separation as that obtained from the effective spin-rotation constants of OH, OD, and OT.     

Analyticity for one-dimensional systems with long-range superstable interactions

We consider unbounded spin systems and classical continuous particle systems in one dimension. We assume that the interaction is described by a superstable two-body potential with a decay at large distances at least asr ^?2(lnr)^?(2+ε), ε > 0. We prove the analyticity of the free energy and of the correlations as functions of the interaction parameters. This is done by using a “renormalization group technique” to transform the original model into another, physically equivalent, model which is in the high-temperature (small-coupling) region.     

The formation of the superheavy hydrogen isotope <Superscript>6</Superscript>H in the absorption of stopped π<Superscript>−</Superscript>-mesons by nuclei

An experimental search for the superheavy hydrogen isotope ⁶H was conducted through studying the absorption of stopped π^?-mesons by ⁹Be and ¹¹B nuclei. A structure in the missing mass spectrum caused by the resonance states of ⁶H was observed in three reaction channels, namely, ⁹Be(π^?, pd)X, ¹¹B(π^?, d³He)X, and ¹¹B(π^?, p⁴He)X. The parameters of the lowest state E_r=6.6±0.7 MeV and Γ=5.5±2.0 MeV (E_r is the resonance energy with respect to the disintegration into the triton and three neutrons) are evidence that ⁶H is a more weakly bound system than ⁴H and ⁵H. Three excited states of ⁶H were observed. Their resonance levels (E_1r=10.7±0.7 MeV, Γ_1r=4±2 MeV, E_2r=15.3±0.7 MeV, Γ _2r=3±2 MeV, and E_3r=21.3±0.4 MeV, Γ_3r=3.5±1.0 MeV) are energetically capable of disintegrating into six free nucleons.     

Limits on a long range pion nucleon interaction from pionic atom and πN scattering data

Experimental limits are obtained on any non-electromagnetic long range pion nucleon interaction, from accurate π⁺p scattering data and from pionic atom energy levels. Such an interaction is effectively ruled out in the regionr?100 fm unless its potential falls off faster thanr ^?4.