Mean-square atomic displacements in f.c.c. crystals

The mean-square displacements of volume atoms, surface atoms and atoms near a vacancy are calculated for f.c.c. metals and rare gas solids, using a simple series expansion of the Wallis formula. We employ a model with rotationally invariant bond bending forces, unlike the de Launay model used by Masri and Dobrzynski. For atoms near a vacancy and for rare gas solids this method has been applied for the first time. The calculations are done to the R⁴ term in the expansion. The inclusion of the R⁴ term together with temperature-dependent elastic constants give results which are in better agreement with experiment. For rare gas solids Lindemann ratios calculated by this method agree closely with the values obtained from elaborate computations as well as those deduced from entropy data. The present calculation also supports the view that the melting of solids is initiated at the crystal surfaces and in the neighbourhood of vacancies.     

Correlation between the optical model potential and matter distribution parameters in heavy-ion elastic scattering

Starting from the analytical expression for the folding model potential for the heavy-ion scattering, a simple relationship between the potential and the nuclear density parameters is obtained. This relationship is consistent with the analysis of the proximity forces and is confirmed around the strong absorption radius through the results of the folding model calculations for¹⁶O projectile incident on a variety of targets ranging from⁴⁰Ca to²⁰⁸Pb. These relations help to deduceR _x the distance where the folding potential has a specific valuex and the densities of the target nuclei. The predictions are found to be in good agreement with the experiment.     

Electronic absorption spectrum of CO+ in an ion beam

The He+He⁺¹ interactions have been studied, as a function of the internuclear separation R, in terms of the electronic forces acting on the nuclei and the change in the charge distribution. The analysis reveals that at large R the atomic densities are polarized inwards, causing an attractive force on each nucleus, while at small R the difference in the nature of the interactions in the ²Σ_u and ²Σ_g systems is noted. It is seen that the He+He⁺¹ (²Σ_u) interaction is less attractive than the He⁺¹+He⁺¹ interaction at lower values of R.     

The casimir effect as a screening effect in quantized field theory

We study the vacuum energy and the vacuum force in a system of quantized scalar fields (massive and massless) in interaction with a given screening medium. Regularization of the energy is studied and the types of determinable forces are clarified. The Casimir effect—the attraction between two conducting plates in a vacuum, and its extension to different geometries —is re-examined in this framework. Instead of the puzzling repulsion for a spherical shell conductor, an attractive force is obtained in our case. As a by-product, we obtain a potential energy between two balls of large screening power and at remote distance R, ?a₁a₂/4πR³, where a_i are the ball radii.     

Theoretical dipole moment function of the X1Σ+ state of HI

Multiconfiguration self-consistent-field calculation has yielded the dipole moment function for the X¹Σ⁺ state of HI, which qualitatively confirms the experimental finding that the dipole derivative at R_e is negative. The calculated dipole moment for the v = 0 vibrational level is 0.665 D for both HI and DI as compared with the experimental values of 0.38 and 0.445 ± 0.02 D, respectively. The calculated potential curve yields values of R_e, D₀, and ΔG_v+1/2, in good agreement with spectroscopic data. A simple valence bond explanation has been provided for the qualitative difference between the dipole moment function of HI and those of the smaller hydrogen halides.     

Calculation of a pair correlation function for the three-dimensional Ising model with long-range exchange forces

A simple difference equation for one type of correlators has been obtained by the method of direct calculation of the correlation functions (CF). It is correct for the Ising model of an arbitrary dimension with the exactness $\text{O}$($\text{1}\text{z}$) (z-number of particles covered by the interaction potential). The equation obtained is used to calculate the pair CF 〈S^z_fS^z_j〉 in the three-dimensional Ising model with long-range forces which are of importance when dealing with the applied magnetic problems. The results of the calculations lead to corrections in the Ornstein-Zernike (OZ) theory.     

s- and p-wave neutron spectroscopy. Xe. Intermediate structure in 90Y and the generalized R-matrix theory

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross section measurements in the range of 0.3 to 1.2 MeV incident energy was investigated using the generalized R-matrix theory of nuclear reactions and the doorway interpretation of intermediate structure. The energies and wave functions of the doorway resonances were calculated in a 2-particle and 3p-1h basis of the shell model. The model space and the parameters of the model calculation chosen were consistent with other shell model calculations in the mass-90 region. Several strong p-wave doorways with J^π = 0⁺, 1⁺, and 2⁺ were predicted by the model in the energy range studied. This is due to proximity of p-wave giant resonance. The escape widths Γ^↑ and the spreading widths Γ^↓ for these states were evaluated using the model wave functions and the R-matrix formalism. The calculated energy dependence of the total cross section shows that most of the predicted doorways are in general agreement with the observed anamolies with similar relative strength. More significantly, the underlying p-wave gross structure representing a grand average is of very similar shape in both theory and experiment. As expected in the mass 90-region, the s- and d-wave doorways contribute less significantly to the calculated resonance structure.     

Microscopic calculation of friction in heavy ion reaction using linear response theory

We present a realistic calculation of the frictional coefficients for²⁸Si+²⁰Ne system using the two-center shell model on the basis of the linear response theory. Adopting the center separationR and the deformationδ as collective variables we study the dependence of frictional coefficients γ _RR , γ _Rδ and γ_δδ on those variables, for various values of the neck parameter?, the temperatureT and the smearing widthΓ. The direct application of the linear response theory to the two-center potential gives non-vanishing friction for the simple translational motion of the two fragments even when they are far apart. A method to avoid this energy dissipation is proposed and is used in the calculation. Results show that the form factor of the frictional force is surface-peaked and the peak becomes lower as the prolate deformation or neck formation increases. Temperature dependence is mild, but is not negligible. We compare our γ _RR and γ_δδ with other models.     

Electronic-excitation transfer collisions in flames—VI. Interpretation of the temperature dependence of alkali-quenching by N2 and general conclusions about the energy transfer mechanism

The experimental temperature dependence of alkali-N₂ quenching cross sections is explained semi-quantitatively by a simple theoretical model, based on an ionic intermediate state, in which attractive van-der-Waals forces play an essential role. Using this model, quenching experiments are compared with Na(3²P)-N₂ excitation measurements in molecular beams. From this comparison it is concluded that the distribution of relative cross sections for specific vibrational transitions during the quenching process can be described by a distribution calculated by Fisher,⁽⁸⁾ whereas the distribution given by Bjerre⁽¹⁸⁾ has to be rejected. Resonant vibrational-electronic energy transfer is not important.     

Strong radiative corrections to annihilations of quarkonia in QCD

The significance of the lowest-order QCD prediction for the annihilations of heavy quark-antiquark bound states is analyzed. The calculation of the leading strong radiative corrections to the hadronic versus electromagnetic annihilation rate ratio R of pseudoscalar quarkonium is presented. In terms of the coupling constant α_s, as defined in the minimal subtraction scheme, we find R = R⁽⁰⁾(1 + 22.14α_s/π). The physical significance of this result is discussed by comparing it with the calculation of the non-leading effects in α_s on the scaling violations in deep inelastic scattering. A bad convergence of the relative perturbative expansion is found, demanding for its safe application a value of the relevant momentum definitely higher than that of charmonium physics.     

Ground state properties of the two impurity Anderson model in a 1/N expansion

The intersite contribution to the ground state energy for the two impurity Anderson model is calculated to first order in 1/N. The dependence of this contribution on the interimpurity separation has an R^?1 or R^?3 envelope for distances smaller or larger than a length ν_F/T_A ranges from a value equal to the bare ?-level position (in the weak valent regime) to the Kondo temperature (in the local moment limit).     

The PbPb collision

The reaction ²⁰⁸Pb on ²⁰⁸Pb was studied at bombarding energies of 7.0 and 7.57 MeV/u. One-particle inclusive measurements using a large-area position-sensitive ionisation chamber delivered the kinetic energy, charge and scattering angle of the reaction products. A precise calibration of the stopping power for very heavy ions in the detector gas was performed. The measured Wilczynski diagrams show, for increasing loss of kinetic energy, an increase of the mean scattering angle. It is attributed to the dominance of the repulsive Coulomb forces with respect to the attractive nuclear forces. The element distribution for the ²⁰⁸Pb on ²³⁸U reaction at 7.5 MeV/u was also measured and compared to the PbPb and UU reactions. Fission probabilities are derived as a function of charge and total kinetic energy loss. The most striking result is seen in the σ_z² versus TKEL correlation: the average rate of energy loss per nucleon exchange is abnormally large. It is shown that this behaviour is associated with the double magic closed shell character of the colliding nuclei. Nuclear structure information is extracted through a simple parametrisation.     

Strong energy condition and the repulsive character of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The Raychaudhuri equation enables to examine the whole spacetime structure without specific solutions of Einstein’s equations, playing a central role for the understanding of the gravitational interaction in cosmology. In General Relativity, without considering a cosmological constant, a non-positive contribution in the Raychaudhuri equation is usually interpreted as the manifestation of the attractive character of gravity. In this case, particular energy conditions—indeed the strong energy condition—must be assumed in order to guarantee the attractive character. In the context of f(R) gravity, however, even assuming the standard energy conditions one may have a positive contribution to the Raychaudhuri equation. Besides providing a simple way to explain the observed cosmic acceleration, this fact opens the possibility of a repulsive character of this kind of gravity. In order to discuss physical bounds on f(R) models, we address the attractive/non-attractive character of f(R) gravity considering the Raychaudhuri equation and assuming the strong energy condition along with recent estimates of the cosmographic parameters.     

Some characteristics of nuclear densities

We propose a simple expression for nuclear densities, which brings out the following important nuclear properties: (i) shell effects in proton and neutron central densities, (ii) approximate global constancy of neutron central densities, (iii) approximate constancy ofRN ^?1/3 and R_pZ^?1/3 whereR is the nuclear half-density radius andR _p is the rms radius of the proton density, (iv) larger surface thickness and rms radius for neutron density as compared to those for proton density.     

Low and room temperature measurements and calculations of O2-broadening coefficients in the ν3 band of CS2

O₂-broadening coefficients have been measured for 16 lines in the P and R branches of the fundamental ν₃ band of ¹²C³²S₂ at room and low temperatures (298.0, 273.2, 248.2, 223.2, and 198.2 K), using a tunable diode laser spectrometer and a low temperature cell. These lines from P(62) and R(64) are located in the spectral range 1519-1547 cm⁻¹. The collisional half-widths are obtained by fitting each observed profile with the Voigt and Rautian lineshape models. The broadening coefficients have also been calculated at all experimental temperatures using a semiclassical calculation performed by considering in addition to the electrostatic quadrupole-quadrupole interaction, a simple anisotropic contribution. Finally, from all the results, the parameter n of the temperature dependence of the broadening coefficients has been determined both experimentally and theoretically.     

The pair distributions and the osmotic coefficient in anomalous electrolytes up to concentrations c≈ 1 mol/1

The osmotic coefficient of anomalous electrolytes up to concentrations c ≈ 1 mol/l is explained by the pair distributions $\text{n(r) =}\text{exp}\text{[-β(}\text{V}{}_{\mathrm{c}}\text{(r) + V(}{}^{\mathrm{hs}}\text{)(r) + V}{}_1\text{(r))]}$. Here $\text{V}$_c(r) is a screened Coulomb potential, V(^hs)(r) a hard sphere potential and V₁(r) = ?A/r⁶ a short range attractive potential. For the contact distances R₊₊, R_?? and R_+? of the hard sphere potentials between ions with the same sign of their charges (++,??) and ions of opposite charges (+?) the relations R₊₊ = R_?? = R and R_+? = q₁R with 0 < q₁ < 1 are assumed. In contrast to a previous paper the parameter q₁ takes a fixed value q₁ ≈ 0,8. The constant A is determined by the fraction q₂ defined by A/R⁶ = q₂(Z²e²/DR) where the positive integer Z is the charge number of the ions and D the dielectric constant of the solvent. The numerical calculation of the osmotic coefficient of 1-1-valent hydrous electrolytes in the range of temperature 273 K ? T ? 293 K shows that the anomalous electrolytes are described by fractions q₂ in the range 0,25 ? q₂ ? 0,5 if the contact distances R are in the range $\text{3}\text{A}\text{?}\text{? R ? 7}\text{A}\text{?}$.