The central and tensor force matrix elements for arbitrary average and two-body potentials

A general method is described for computing central as well as tensor force matrix elements for shell-model states. The method consists of expanding the two-body potential into free multipole fields. The advantages of the method are that

(i) arbitrary forms of the average and two-body potential can be chosen; (ii) even in the case of a finite-range force, double integrals are eliminated, and the radial integrals are independent of the shape and parameters of the two-body force; and (iii) the central and the tensor forces are treated on the same footing.

FORTRAN codes employing this method are available for the computation of the two-body force matrix elements for an arbitrary nucleus.     

Construction and classification of indecomposable finite-dimensional representations of the homogeneous Galilei group

We discuss finite-dimensional representations of the homogeneous Galilei group which, when restricted to its subgroup SO(3), are decomposed to spin 0, 1/2 and 1 representations. In particular we explain how these representations were obtained in our paper (M. de Montigny et al.: J. Phys. A39 (2006) 9365) via reduction of the classification problem to a matrix one admitting exact solutions, and via contraction of the corresponding representations of the Lorentz group. Finally, for discussed representations we derive all functional invariants.     

Can the eigenstates of a many-body Hamiltonian be represented exactly using a general two-body cluster expansion?

It is proved that a recent conjecture that the exact ground-state wave function of an arbitrary many-fermion system with one- and two-body interactions may be represented by an exponential cluster expansion employing finite two-body operators, starting from any reference function sufficiently close to the exact eigenfunction, is not valid. We show that the space of initial reference functions which lead to the exact ground state is of dimension equal to the number of two-body operators. If the dimension of the multiparticle space is greater than the number of two-body operators, then the space of good reference functions is of measure zero in it.     

H2Se(X1A1)分子的解析势能函数

使用密度泛函B3LYP方法和 6-311++G**基组,在优化H2Se(X1A1)基态结构,确定其正确离解极限,计算所有两体项和三体项参数基础上,建立了H2Se(X1A1)的多体项展式解析势能函数。其中对处于激发态两体项HSe(A2∑+)的计算,则使用SAC-CI方法。H2Se(X1A1)的等值势能图准确地表现了其结构和势能面的特征。     

Exactness of the general two-body cluster expansion in many-body quantum theory

We show that the exact ground-state wave function for an arbitrary two-body Hamiltonian in second-quantized, finite basis set, form cannot generally be represented by a generalized coupled-cluster operator with real finite matrix elements acting on an arbitrary initial trial function.     

Similarities between the lattice gas model and some other models of nuclear multifragmentation

We continue our development of the nuclear lattice gas model by exploring links and similarities with other theoretical approaches to nuclear multifragmentation: the percolation model and the statistical multifragmentation model. It is shown that there exists a limit where the lattice gas model reduces to the percolation model. The similarity between the lattice gas model and the statistical multifragmentation model is more indirect and we utilize the equations of state in the two models. By using the law of partial pressures we obtain P-ϱ diagrams for the statistical multifragmentation model and find that these are remarkably similar to those obtained in the lattice gas model via an exact evaluation of the nuclear partition function on the lattice. For completeness, we also compute the P-ϱ diagram for a system obeying pure classical molecular dynamics with a simple two-body force.     

Construction of the two-electron contribution to the Fock matrix by numerical integration

A novel method to numerically calculate the Fock matrix is presented. The Coulomb operator is re-expressed as an integral identity, which is discretized. The discretization of the auxiliary t dimension separates the x, y, and z dependencies transforming the two-electron Coulomb integrals of Gaussian-type orbitals (GTO) to a linear sum of products of two-dimensional integrals. The s-type integrals are calculated analytically and integrals of the higher angular-momentum functions are obtained using recursion formulae. The contributions to the two-body Coulomb integrals obtained for each discrete t value can be evaluated independently. The two-body Fock matrix elements can be integrated numerically, using common sets of quadrature points and weights. The aim is to calculate Fock matrices of enough accuracy for electronic structure calculations. Preliminary calculations indicate that it is possible to achieve an overall accuracy of at least 10^?12 E _h using the numerical approach.     

Simple analytical representation for Delbrück scattering amplitudes at high energies

We use a new representation for the semiclassical Green’s function of the Dirac equation in the Coulomb field to find an exact (in the parameter Zα) expression for the amplitudes of small-angle Delbru ck scattering of high-energy photons. The values of these amplitudes agree with those obtained in earlier calculations, but the structure of the expressions is much simpler than that of previously known representations, which makes numerical calculations much easier. Zh. éksp. Teor. Fiz. 116, 78–84 (July 1999)     

Morphing the shell model into an effective theory

We describe a strategy for attacking the canonical nuclear structure problem-bound-state properties of a system of point nucleons interacting via a two-body potential-which involves an expansion in the number of particles scattering at high momenta, but is otherwise exact. The required self-consistent solutions of the Bloch-Horowitz equation for effective interactions and operators are obtained by an efficient Green's function method based on the Lanczos algorithm. We carry out this program for the simplest nuclei, d and 3He, in order to explore the consequences of reformulating the shell model as a controlled effective theory.     

Simple separable expansions for calculating matrix elements of two-body local interactions with harmonic oscillator functions

A simple method is proposed to calculate the matrix elements of two-body local interactions using a harmonic oscillator basis (HOF). Using the properties of HOF, it is shown that any local potential can be replaced by a simple series for the purpose of calculating matrix elements. This series can be reduced to a finite sum when evaluating a matrix element. Its terms are separable functions of the coordinates of the two particles; hence the advantage of the method. In the present article we treat the most important components of the two-body interaction, namely central, two-body spin-orbit, and tensor forces. As a representation we have chosen spherical harmonic oscillator functions expressed with spherical coordinates. This technique appears to be very well adapted to and efficient for Hartree-Fock calculations in any representation of the HOF. A very interesting feature of this formulation is that it can be easily extended to calculations employing generalized HOF as defined by Wong.     

Features of the electronic structure of the intermetallic Co3Ti in an atomically disordered state

Using a method based on incorporating statistics into the theory of multiple scattering via the distribution function of atoms on lattices, the electronic structure of the intermetallic Co₃Ti is calculated for both complete atomic order and complete disorder. An unusual feature of the electronic structure of this intermetallic when it is disordered in the solid state is identified. Possible consequences of this behavior are analyzed. Fiz. Tverd. Tela (St. Petersburg) 39, 809–810 (May 1996)     

The potential harmonic expansion method

Various properties of the hyperspherical potential basis are investigated. The expansion of any two-body function, in particular the two-body potential, is given. The matrix elements with two and three potential harmonics needed for the construction of the potential matrix are calculated. Useful recurrence formulae are derived. The concept of potential basis is extended to systems with any number of fermions. A method for improving the accuracy of the expansion of the wavefunction by taking into account more than the two-body correlations is suggested.     

Theory of quasimagnetic impurity in a metal: An exactly soluble model of interacting electrons

We study an impurity atom, on which two-body forces are important, dissolved in a metal, where they are negligible. With the aid of the well-known boson excitation spectrum of the electronic Fermi sea, we predict the low-energy effects of one- and two-body potentials on the impurity, in the nonmagnetic regime. We obtain for the first time exact expressions for the cutoff independent contributions to the specific heat and paramagnetic susceptibility, the spectral amplitudes or one-electron density of states on the impurity, and the scattering cross-section. The entire spectrum of manybody eigenstates is explicitly obtained. The onset of a local magnetic moment appears as a sudden breakdown of the model Hamiltonian, and occurs when the two-body potential exceeds a critical value U_c which is O(E_F) in magnitude. A study of the renormalization of the interaction parameters terminates the paper.     

Consequences of minimising pair correlations in fluids for dynamics,thermodynamics and structure

ABSTRACT

Liquid-state theory, computer simulation and numerical optimisation are used to investigate the extent to which positional correlations of a hard-sphere fluid – as characterised by the radial distribution function and the two-particle excess entropy – can be suppressed via the introduction of auxiliary pair interactions. The corresponding effects of such interactions on total excess entropy, density fluctuations and single-particle dynamics are explored. Iso-g processes, whereby hard-sphere-fluid pair structure at a given density is preserved at higher densities via the introduction of a density-dependent, soft repulsive contribution to the pair potential, are considered. Such processes eventually terminate at a singular density, resulting in a state that – while incompressible and hyperuniform – remains unjammed and exhibits fluid-like dynamic properties. The extent to which static pair correlations can be suppressed to maximise pair disorder in a fluid with hard cores, determined via direct functional maximisation of two-body excess entropy, is also considered. Systems approaching a state of maximised two-body entropy display a progressively growing bandwidth of suppressed density fluctuations, pointing to a relation between ‘stealthiness’ and maximal pair disorder in materials.     

Effective interactions and charges in58Ni

The structure of the low-lying states of⁵⁸Ni has been calculated in shell model by assuming an inert⁵⁶Ni core plus two valence nucleons in the p_3/2, f_5/2 and p_1/2 orbitals. The two-body matrix elements are first expressed in terms of seven radial matrix elements and these are then parametrized to give best fit between the computed and the observed energies of the levels below 4 MeV. The wave-functions obtained using these two-body matrix elements are used to study the concept of effective charges. It is found that a single effective charge is not sufficient to predict theB(E2) rates equally well for the thirteen known transitions for which experimental values are available. Assumption of state-dependent effective charges gives a far better agreement. An analysis using wavefunctions obtained with Kuo’s two-body matrix elements also gives a similar result.     

Spectral Study of Some Samarium Complexes in the Region 750–250 cm−1

Abstract

Rare earth β -diketonates and diketo-ester complexes are promising laser materials due to narrow line width of the internal 4fⁿ transitions and weak crystal-field interactions¹. The electronic energy states², spectral intensities^3–5, bonding^6,7 and infrared spectra^8–11 of some of these complexes have been recently reported by the authors. However, little information regarding their structure and strengths of various bonds are available. The infrared spectra of rare earth complexes in the spectral region 4000 – 750 cm^?1 are characteristic of the ligand, while those in the region 750 – 250 cm^?1 characterize the metal-ligand bonding. The present communication reports the values of force constants computed from the observed infrared absorption spectra of four ethyl 1-methyl acetoacetate (EMA) and ethylbenzoylacetate (EBA) complexes of trivalent samarium in the region 750 – 250 cm^?1.     

A normal coordinate treatment of the plane symmetrical XY4 molecule

The secular equations for the various irreducible representations of the plane XY₄ molecule (symmetry point group D _4h) are deduced by means of Wilson's F-G matrix method, using the most general harmonic force field. The equations for the case of the SVFF are also given.     

The Bethe-Goldstone equation with singular interactions: A fully off-shell solution for the boundary condition model

The mutual interaction of a pair of fermions imbedded in a many-body system of identical particles when they are excited out of the filled Fermi sea, is studied via the T-matrix or transition amplitude specified by the Bethe-Goldstone (BG) equation. The role of the bare two-body interaction is emphasised, and in particular the consequences are elucidated of whether the potential is “well-behaved” (nonsingular) or not. The properties of the BG T-matrix, including generalized orthonormality and completeness relations, are derived both for nonsingular potentials and for singular potentials containing an infinite hard core. General analytic properties are exploited to derive relations that express the fully off-shell BG T-matrix purely in terms of the half-shell amplitude (and the properties of any possible bound states in the medium). The general formalism is illustrated by deriving exact analytic expressions for the fully off-shell BG T-matrices for a pair of particles with equal and opposite momenta interacting via either of two singular model interactions; namely, the pure hard-core interaction and the boundary condition model. Results for both models are expressed in terms of the solution to a simple one-dimensional Fredholm integral equation. The analytic properties of the solutions are discussed and exploited to prove both their uniqueness and that they satisfy the various general relations derived. To our knowledge, these results represent the first exact nontrivial solution to the fully off-shell BG equation for any local potential, or singular limiting case thereof.