Microscopic derivation of a complex heavy ion potential

The energy dependence of a complex heavy ion optical potential is derived in Brueckner Hartree Fock using a local density approximation and a selfconsistent single particle spectrum. The two ions are described by an antisymmetrized cluster model wavefunction. Both real and imaginary part are found to increase with energy. Results are given for the elastic scattering of ⁴⁰Ca+¹⁶O.     

Density of states of the binary alloy in the coherent potential approximation

The density of states of an electron in a binary alloy in the tight binding model is calculated in the single site coherent potential approximation (CPA) as a function of the concentration and the site energy difference. The fluctuations in the site energies due to the random environment is taken into account approximately by giving width to the site energy probability distribution function, which is normally a sum of two delta functions with proper weight factor.     

The scattering of line radiation—III. The source function

After discussing the problems encountered in any attempt to interpret frequency-dependent source functions in terms of the population numbers, a method is developed for doing this to a certain class of frequency-dependent source functions. It is pointed out that, unlike the frequency-independent source functions, an analysis of this nature on the frequency-dependent source functions is not generally practicable and can be done in this case only by virtue of the particular form assumed for the absorption coefficient. Solutions in the form of source functions are presented and discussed for a semi-infinite uniform atmosphere for five different forms of frequency redistribution during the scattering event. The function ∫^∞₀S(ν)φ(ν) dν is then calculated and subsequently is used to obtain the departure parameters of the populations of the energy states. The different population distributions through the atmosphere, that can be deduced from these quantities, are compared for the different cases of frequency redistribution used. Because of the nature of the results obtained, the feasibility of setting up iterative schemes to obtain frequency-dependent source functions for more complex problems is also considered.     

CPA treatment of the s-d model at high temperatures

The coherent potential approximation (CPA) is applied to spin-disorder scattering in systems described by the s-d model such as moderately doped magnetic semiconductors. The possibility of a split conduction band at zero temperature is shown to persist also at high temperatures. Band-narrowing is described and conclusions are drawn regarding optical ‘red-shifts’, the Born-approximation, and the paramagnetic spin polaron in narrow energy bands.     

Atom scattering as a probe of the surface electron-phonon interaction at conducting surfaces

An atomic projectile colliding with a surface at kinetic energies in the thermal or hyperthermal range interacts with and is reflected by the electronic density well in front of the first layer of target atoms, and it is generally accepted that the repulsive interaction potential is proportional to the density of electrons extending outside the surface. This review develops a complete treatment of the elastic and inelastic scattering of atoms from a conducting surface in which the interaction with the electron density and its vibrations is treated using electron-phonon coupling theory. Starting from the basic principles of formal scattering theory, the elastic and inelastic scattering intensities are developed in a manner that identifies the small overlap region in the surface electron density where the projectile atom is repelled. The effective vibrational displacements of the electron gas, which lead to energy transfer through excitation of phonons, are directly related to the vibrational displacements of the atomic cores in the target crystal via electron-phonon coupling. The effective Debye-Waller factor for atom-surface scattering is developed and related to the mean square displacements of the atomic cores. The complex dependence of the Debye-Waller factor on momentum and energy of the projectile, including the effects of the attractive adsorption well in the interaction potential, are clearly defined. Applying the standard approximations of electron-phonon coupling theory for metals to the distorted wave Born approximation leads to expressions which relate the elastic and inelastic scattering intensities, as well as the Debye-Waller factor, to the well known electron-phonon coupling constant λ. This treatment reproduces the previously obtained result that the intensities for single phonon inelastic peaks in the scattered spectra are proportional to the mode specific mass correction components λ_Q,ν defined by the relationship λ = 〈λ_Q,ν〉. The intensities of elastic diffraction peaks are shown to be a weighted sum over the λ_Q,ν, and the Debye-Waller factor can also be expressed in terms of a similar weighted summation. In the simplest case the Debye-Waller exponent is shown to be proportional to λ and for simple metals, metal overlayers, and other kinds of conducting surfaces values of λ are extracted from available experimental data. This dependence of the elastic and inelastic scattering, and that of the Debye-Waller factor, on the electron-phonon coupling constant λ shows that measurements of elastic and inelastic spectra of atomic scattering are capable of revealing detailed information about the electron-phonon coupling mechanism in the surface electron density.     

An extended approach for computing the critical properties in the two-and three-dimensional lattices within the effective-field renormalization group method

In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.     

An intuitive approach to a generalized parton picture for high-energy lepton-hadron scattering

A generalized parton picture is developed, based on the impulse approximation. A parton is allowed to have non-point-like elastic form factors; inelastic current-parton scattering is taken into account explicitly. The amplitude of any exclusive channel of lepton-induced reactions is written down, with the parts containing the long-distance and the short-distance behavior of interaction dynamics clearly separated. Scaling violation is a natural feature of this picture. The inelastic structure functions, W₁ and νW₂, are studied in this scheme using various different theories; perturbative QCD, the scale-invariant parton model, the hadron bootstrap picture, and a phenomenological stripped-down hadron-parton model. The application of this picture to elastic lepton-hadron scattering and the problem of the selection of an infinite momentum frame are also discussed.     

Vector correlations in the F + HD reaction

A theoretical study of the orientation of product rotational angular momenta for two chemical reaction channels: F + HD(ν _r = 0, j _r = 0) → HF(ν, j) + D and F + HD(ν _r = 0, j _r = 0) → DF(ν, j) + H at a E _coll = 78.54 meV collision energy was performed. Angular momentum orientation was described on the basis of irreducible tensor operators (state multipoles) expressed through anisotropy transfer coefficients, which contained quantum-mechanical scattering T matrices determined on the basis of exact solutions to quantum scattering equations obtained using the hyperquantization algorithm. The possibility of the existence of substantial orientation of the angular momentum of reaction products j in the direction perpendicular to the scattering plane was demonstrated. The dependences of differential reaction cross sections and state multi-poles on the ν and j quantum numbers were calculated and analyzed. A experimental scheme based on the multiphoton ionization method was suggested. The scheme can be used to detect predicted reaction product angular momentum orientation.     

Light scattering by Gaussian random ellipsoid particles: First results with discrete-dipole approximation

We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a?b?c. The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles.     

Many-body theory of π electron systems

Many-body perturbation theory is developed within the dielectric function method presented in a preceding paper [15]. We have explicitly considered the local field corrections (which are disregarded in the random phase approximation) to the self consistent field. These corrections are of second order in the density-density correlation function x and are evaluated exactly in the framework of the adopted approximation scheme because all the integrals which appear in the expressions can be evaluated analytically. Here the method is applied to π electron systems within the zero differential overlap approximation ; explicit calculations of the excitation energies of the benzene molecule using different parametrizations are presented. Comparison is made with results obtained in the RPA and other schemes.     

Influence of dilution on magnetization properties of geometrically frustrated magnetic systems: Effective-field theory cluster approximations on kagome lattice

The influence of the site dilution on the magnetization properties of the antiferromagnetic spin-1/2 Ising model on the kagome lattice is systematically investigated using various n-site cluster effective-field theory approximations up to the cluster size $n=12$. It is shown that, regardless of the cluster approximation, the site dilution of the system leads, in addition to the existence of the standard saturated ground state, to the formation of four nontrivial plateau ground states together with five single-point ground states that separate them in the zero temperature limit. It is also shown that, while magnetization properties of the saturated ground state and two single-point ground states are stable with respect to the used cluster approximation, the magnetization properties of all four nontrivial plateau ground states and three single-point ground states that separate them strongly depend on the used approximation and have tendency to approach each other with increasing of the cluster approximation.     

Coupled-channel R-matrix method on a Lagrange mesh

The coupled-channel R-matrix method on a Lagrange mesh is a very simple approximation of the R-matrix method with a basis. The mesh points are zeros of shifted Legendre polynomials. Bound-state energies and scattering matrices are easily calculated with small numbers of potential values at mesh points. A test with an exactly solvable two-channel potential provides an excellent accuracy over a broad energy range with only 30 mesh points. The efficiency of the method is illustrated for a single channel on α + α scattering and for two channels on the deuteron ground-state energy and on nucleon-nucleon scattering.     

Variational calculations of ν8 models of nuclear matter

We report variational calculations of ν8 models of nuclear matter which contain central, spin, isospin, tensor and spin-orbit potentials. These semi-realistic models can explain the nucleon-nucleon scattering in 1S0, 3S1?3D1, 1P1 and 3P2?3F2 states up to ～ 300 MeV. The variational wave function has two-body central, spin, isospin, tensor and spin-orbit correlations. The terms in the cluster expansion of the energy expectation value, that do not contain the spin-orbit correlations are summed by chain summation techniques developed for the ν6 models. Of the terms containing spin-orbit correlations, the two-body and three-body-separable ones are calculated, and the magnitude of the rest is estimated. Results for three phase-equivalent ν8 models, which differ significantly in the strength of tensor and spin-orbit potentials, are reported. They suggest that simple ν8 models may not be able to simultaneously explain the binding energy and density of nuclear matter.     

Variational principle for regular and random Ising models on the cactus tree or on the usual lattice in the “cactus approximation”

The distribution functions and the free energy are expressed in terms of the effective fields for the regular and random Ising models of an arbitrary spin S on the generalized cactus tree. The same expressions apply to systems on the usual lattice in the “cactus approximation” in the cluster variation method. For an ensemble of random Ising models of an arbitrary spin S on the generalized cactus tree, the equation for the probability distribution function of the effective fields is set up and the averaged free energy is expressed in terms of the probability distribution. The same expressions apply to the system on the usual lattice in the “cactus approximation”. We discuss the quantities on the usual lattice when the system or the ensemble of random systems has the translational symmetry. Variational properties of the free energy for a system and of the averaged free energy for an ensemble of random systems are noted. The “cactus approximations” are applicable to the Heisenberg model as well as to the Ising model of an arbitrary spin, and to ensembles of random systems of these models.     

Cluster approaches to random alloys: An appraisal

Some of the cluster extensions of the coherent potential approximation (CPA) based on the effective medium theory have been critically studied with respect to the decoupling schemes involved in them. Their computational tractability has been examined and it has been found that theself-consistent calculations in three-dimensional systems are immensely difficult to perform. A self-consistent calculation has been reported for simple cubic lattices with diagonal and off-diagonal disorder using a pair-CPA method. A significant finding of the paper is that it has been shown thatnon-analyticities are a general feature of extensions of CPA within multiple scattering framework. The non-analyticities were reported several times but a general proof of their existence was not noticed. It was also believed that the so-called molecular—CPA is analytic, this has been shown to be wrong here. The density of states results with off-diagonal randomness have been qualitatively understood to yield some information about the influence of off-diagonal randomness on Anderson localisation of an electron.     

Atomic effects in coherent neutrino scattering

The influence of atomic electrons on the coherent elastic scattering of low energy neutrinos is studied. For Q²R_atom²≲1, significant interference occurs between scattering from the electrons and from the nucleus, leading to large differences between ν_e and ν_μ cross sections. In particular, ν_e scattering shows a sharp minimum at Q² ≈ (10 keV)² for ²⁸Si and ⁵⁶Fe. As a consequence, for neutrinos in the 10 keV range, the radiation pressure exerted on a medium is much greater for ν_μ than for ν_e. The exceptional case of hydrogen is discussed also.     

On the production of a lepton pair in the collision of ultrarelativistic neutral particle with nonzero magnetic moment with nuclei

Explicit formulas which describe muon pair production in reaction γν→μ⁺μ⁻ν through neutrino magnetic moment are obtained and used to derive in the leading approximation cross section of muon pair production in νN-scattering due to neutrino magnetic moment. This cross section appears to be proportional to log⁴E_ν. Comparison with experimental data on tridents production provides an upper bound μ_νμ<4×10⁻⁸μ_B, which is approximately two orders of magnitude weaker than that from ν_μe elastic scattering data.     

Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems

The exp S formalism for the ground state of a many-body system is derived from a variational principle. An energy functional is constructed using certain n-body linked-cluster amplitudes with respect to which the functional is required to be stationary. By using two different sets of amplitudes one either recovers the normal exp S method or obtains a new scheme called the extended exp S method. The same functional can be used also to obtain the average values of any operators as well as the linear response to static perturbations. The theory is extended to treat dynamical phenomena by introducing time dependence to the cluster amplitudes. This allows the calculation of both nonlinear dynamical behaviour and of dynamical linear response and Green's functions. Practical approximation schemes are considered. In a SUB n approximation the m-body amplitudes are restricted to the order $\text{m ? n}$ and the energy functional is a finite-order multinomial in the amplitudes to be variationally determined. It is shown that the solution corresponds to summing well-defined subsets of Goldstone diagrams. These subsets are conveniently specificed in terms of tree structures, the normal or extended generalized time ordering g.t.o. trees. The extended exp S method is in the SUB n approximation able to sum, in addition to the normal SUB n diagrams, a set which contains m-body cluster amplitudes of arbitrarily high order (m > n) in the ordinary sense. The article also discusses how the SUB n truncation schemes must be modified to be able to treat a system with a strong repulsive core in the two-body interaction. The method is formulated for the general cases of Bose and Fermi systems which may or may not conserve total particle number. It is shown that the simplest approximation, SUB 1, in the extended exp S method agrees with the mean field theory, which is the coherent-state approximation in the boson case or the Hartree-Fock approximation in the fermion case. It is argued that the extended exp S method already in low-order approximations can realistically treat a great variety of diverse many-body problems, even including systems which may undergo ground-state phase transitions. A few applications are described in more detail. The Bose liquid is treated in the extended SUB 2 approximation. It is shown that the ground-state results in the uniform limit are exact and agree with the hypernetted-chain approximation. The modifications due to hard-core interactions and the non-linear equations of motion are also discussed in this case. For Fermi systems it is shown that the supercondictive phase transition of the BCS model Hamiltonian and the deformation phase transition of the Lipkin model are properly obtained by the extended exp S method in a low-order approximation.     

Generator coordinate amplitude for scattering

In the generator coordinate method for scattering the proper boundary condition is accomplished by requiring the GC amplitude to satisfy an integral equation of the first kind. Attempts to solve this problem are first reviewed and then an improved approximation is proposed which is applicable to a wider class of scattering problems in addition to the Coulomb scattering.A better approximation is obtained in the asymptotic region, where the generator coordinate, i.e., the distance between two shell-model wells of the fragments, is larger than the touching distance of the colliding nuclei, by deriving partial differential equations of first order for the terms of an asymptotic series in $\text{1}\text{E}$, where E is the scattering energy.Extracting the information on the GC amplitude for small values of the generator parameter from the integral equation of the first kind is an ill-posed problem. It is shown that the method of statistical regularization offers a powerful and controllable procedure to uncover the GC amplitude. The unknown GC amplitude is treated as a random function with an a priori distribution of probability which is based on the assumption that the amplitude is bounded and that the errors in the input are random with zero expectation value. A useful procedure is found for fixing parameters of the a priori distribution. The solution for small values of the GC parameter is expressed in the form of a Dini series.The method is applied to the calculation of the GC amplitude for scattering of two α-particles at 15 MeV c.m. energy. The measure of the accuracy is the difference between the input wave function of relative motion and the result of folding of the GC amplitude with the kernel of the integral equation. The prescribed accuracy is reached with this method on a much larger interval than with any previously proposed method.