Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron-rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density-dependent relativistic mean-field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.     

Assignment of terahertz vibrational modes of L-glutamine using density functional theory within generalized-gradient approximation

The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation(GGA), Perdew–Burke–Ernzerhof(PBE), PBE for solids(PBEsol), PBE with Wu–Cohen exchange(WC), and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.     

Generalized routhian calculations within the Skyrme-Hartree-Fock approximation

We consider here variational solutions in the Hartree-Fock approximation upon breaking time reversal and axial symmetries. When decomposed on axial harmonic oscillator functions, the corresponding single particle triaxial eigenstates as functions of the usual cylindrical coordinates (r, θ, z) are evaluated on a mesh in r and z to be integrated within Gauss-Hermite and Gauss-Laguerre approaches and as Fourier decompositions in the angular variable θ. Using an effective interaction of the Skyrme type, the Hartree-Fock Hamiltonian is also obtained as a Fourier series allowing a two-dimensional calculation of its matrix elements. This particular choice is shown to lead in most cases to shorter computation times compared to the usual decomposition on triaxial harmonic oscillator states. We apply this method to the case of the semi-quantal approach of large amplitude collective motion corresponding to a generalized routhian formalism and present results in the A = 150 superdeformed region for the coupling of global rotation and intrinsic vortical modes in what is known after Chandrasekhar as the S-ellipsoid coupling case.     

Use of the momentum approximation in classical scattering calculations

Abstract

The validity range of the momentum approximation in binary collisions : s investigated. It is shown that at high energies, E ? 10 · Z ₁ Z ₂ e ²/a _TF, the approximation is even applicable to scattering angles ? as large as 60 degrees. An empirical formula for the evaluation of the momentum approximation employing the Thomas-Fermi-Moliére potential is given. It reduces the computer time to calculate ? to ～⊥₁₀ of the time consumed in using the standard algebraic functions appearing in the momentum approximation.     

Magneto-optical activity: Gauge-invariant calculations in the random-phase approximation

The use of London's gauge-invariant orbitals in the calculation of magnetic rotational strengths is investigated. Self-consistent molecular orbitals at non-zero magnetic field strengths have been determined in the Pariser-Parr-Pople model and these have been employed in the calculation of excitation energies and transition moments according to the mono-excited configuration interaction and the random phase approximations. Applications to the magneto-optical activity of aniline, phenol, and benzonitrile are reported. The results are origin-independent and compare well with experimental values.     

Bragg optical solitons beyond the coupled mode approximation

Properties of conservative and dissipative Bragg solitons formed in single-mode optical fibers with induced longitudinal modulation of the refractive index are analyzed beyond the standard approximation of coupled modes, or of slowly varying amplitudes. It is shown that, if the initial velocity of a Bragg soliton is smaller than a critical value, the soliton stops in the process of propagation.     

Comparison of the semiclassical coupled channel theory of particle transfer with exact calculations

Making use of numerical techniques recently developed, inelastic and transfer processes associated with the collision of two systems have been exactly solved in a one-dimensional model. Comparisons are carried out with a coupled channel treatment and perturbation theory. The results are used to estimate the validity of the different approximations for the case of collisions between heavy ions.     

Unitary pole approximation andt-matrix perturbation theory in triton calculations

We find that the quality of the fits of the UPAt-matrix to the exactt-matrix for a given potential do not depend strongly on specific features, such as locality or inclusion of spin orbit forces in the potential. The accuracy of the UPA fits suggests the employment oft-matrix perturbation theory in triton ground state calculations. The accuracy of first ordert-matrix perturbation theory is satisfactory for the rank two separable tensor Tabakin potential.     

A fast,approximation method for LEED intensity calculations

A perturbation series method for obtaining LEED intensities from the transfer matrix method is reported. This approach is based on simple physical considerations and is adaptable to a variety of surface structures. The intensities obtained from this approximation are of comparable accuracy with those obtained by the complete procedure but the computation times are considerably reduced. The method holds promise for intensity calculations on crystals with surface layers of adsorbed atoms.     

Self-consistent calculations within the quasiparticle time blocking approximation with exact account taken of the single-particle continuum

A self-consistent version of the model based on the method of Green’s functions which takes into account conventional phonons of the random phase approximation, complex configurations like 2 quasiparticles?phonon ones, and exact single-particle continuum is used to describe many discrete natural-parity states and giant resonances in the ¹²³Sn and ²⁰⁸Pb nuclei. The quasiparticle-phonon interaction is shown to be important not only for low-lying and high-lying collective states but also for low-lying noncollective states.     

Biot-Savart approximation in calculations of the magnetic fields of polarized ellipsoids

Equations are deduced for calculating the magnetic field of currents in uniformly polarized ellipsoids; a template is presented for calculating the current density in such ellipsoids; the use of the formulas and the template is illustrated by the example of the assumed magnetic effect of a Tashkent earthquake; it is concluded that the theory for the calculation of such phenomena must be improved.     

Tunnelling splitting of coupled rotors in Hartree approximation

The orientational order of the methyl groups in Sn(CH₃)₂F₂ at low temperatures is determined by a Bloch wave ansatz. Starting from this order, coupling effects on the rotational tunnelling spectrum are calculated in Hartree approximation. The line broadening due to coupling is in good agreement with experiment.     

Ion core approximation in calculations of excited atomic states

A one-configuration approximation is used to analyze the possibility of employing the frozen ion core model to calculate excited states with low-lying configurations of the same symmetry when the wave functions of the excited states are orthogonal to the function of the ground state. The nonorthogonality of the wave functions of different excited configurations is then weak. A calculation is made for certain Isns¹S and 1s²2sns¹S terms of two-and four-electron ions, respectively, and the relaxation effects in the core are investigated for these excited states. This approximation is employed to obtain a variational equation for virtual orbitals allowing for the core relaxation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 71–77, June, 1980.     

Application of the rational function approximation to Wiener-Hopf calculations for fluid-loaded plates

This paper discusses the Wiener-Hopf analysis for the solution of fluid-loaded plate problems when the planar acoustic impedance is represented by a rational function approximation. With such a formulation, the factorization of the integrand kernel can immediately be written once the system poles are determined. The approach is applied to several representative problems, and the approximate results are shown to be in agreement with those of exact solutions.     

A distributed mean spherical approximation for the strongly coupled one-component plasma

The static properties of the strongly coupled one-component plasma are determined from a self-consistent method based on the mean spherical approximation.     

All-electron GW approximation with the mixed basis expansion based on the full-potential LMTO method

We present a new all-electron, augmented-wave implementation of the GW approximation using eigenfunctions generated by a recent variant of the full-potential LMTO method. The dynamically screened Coulomb interaction W is expanded in a mixed basis set which consists of two contributions, local atom-centered functions confined to muffin-tin spheres, and plane waves with the overlap to the local functions projected out. The former can include any of the core states; thus the core and valence states can be treated on an equal footing. Systematic studies of semiconductors and insulators show that the GW fundamental bandgaps consistently fall low in comparison to experiment. Also the quasi-particle (QP) levels differ significantly from other, approximate methods, in particular those that approximate the core with a pseudopotential, or those that include valence states only.     

Mean field approximation for noisy delay coupled excitable neurons

Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by N?1 stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.