31,887 research outputs found
Benchmark calculation for proton-deuteron elastic scattering observables including Coulomb
Two independent calculations of proton-deuteron elastic scattering
observables including Coulomb repulsion between the two protons are compared in
the proton lab energy region between 3 MeV and 65 MeV. The hadron dynamics is
based on the purely nucleonic charge-dependent AV18 potential. Calculations are
done both in coordinate space and momentum space. The coordinate-space
calculations are based on a variational solution of the three-body
Schr\"odinger equation using a correlated hyperspherical expansion for the wave
function. The momentum-space calculations proceed via the solution of the
Alt-Grassberger-Sandhas equation using the screened Coulomb potential and the
renormalization approach. Both methods agree within 1% on all observables,
showing the reliability of both numerical techniques in that energy domain. At
energies below three-body breakup threshold the coordinate-space method remains
favored whereas at energies higher than 65 MeV the momentum-space approach
seems to be more efficient.Comment: Submitted to Phys. Rev.
P-matrix and J-matrix approaches. Coulomb asymptotics in the harmonic oscillator representation of scattering theory
The relation between the R- and P-matrix approaches and the harmonic
oscillator representation of the quantum scattering theory (J-matrix method) is
discussed. We construct a discrete analogue of the P-matrix that is shown to be
equivalent to the usual P-matrix in the quasiclassical limit. A definition of
the natural channel radius is introduced. As a result, it is shown to be
possible to use well-developed technique of R- and P-matrix theory for
calculation of resonant states characteristics, scattering phase shifts, etc.,
in the approaches based on harmonic oscillator expansions, e.g., in nuclear
shell-model calculations. P-matrix is used also for formulation of the method
of treating Coulomb asymptotics in the scattering theory in oscillator
representation.Comment: Revtex, 57 pages including 15 figures; to be published in Annals of
Physic
Long-range correlation energy calculated from coupled atomic response functions
An accurate determination of the electron correlation energy is essential for
describing the structure, stability, and function in a wide variety of systems,
ranging from gas-phase molecular assemblies to condensed matter and
organic/inorganic interfaces. Even small errors in the correlation energy can
have a large impact on the description of chemical and physical properties in
the systems of interest. In this context, the development of efficient
approaches for the accurate calculation of the long-range correlation energy
(and hence dispersion) is the main challenge. In the last years a number of
methods have been developed to augment density functional approximations via
dispersion energy corrections, but most of these approaches ignore the
intrinsic many-body nature of correlation effects, leading to inconsistent and
sometimes even qualitatively incorrect predictions. Here we build upon the
recent many-body dispersion (MBD) framework, which is intimately linked to the
random-phase approximation for the correlation energy. We separate the
correlation energy into short-range contributions that are modeled by
semi-local functionals and long-range contributions that are calculated by
mapping the complex all-electron problem onto a set of atomic response
functions coupled in the dipole approximation. We propose an effective
range-separation of the coupling between the atomic response functions that
extends the already broad applicability of the MBD method to non-metallic
materials with highly anisotropic responses, such as layered nanostructures.
Application to a variety of high-quality benchmark datasets illustrates the
accuracy and applicability of the improved MBD approach, which offers the
prospect of first-principles modeling of large structurally complex systems
with an accurate description of the long-range correlation energy.Comment: 15 pages, 3 figure
Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets
Calculating highly accurate thermochemical properties of condensed matter via
wave function-based approaches (such as e.g. Hartree-Fock or hybrid
functionals) has recently attracted much interest. We here present two
strategies providing accurate Hartree-Fock energies for solid LiH in a large
Gaussian basis set and applying periodic boundary conditions. The total
energies were obtained using two different approaches, namely a supercell
evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an
extrapolation toward the full-range Hartree-Fock limit of a Pad\'e fit to a
series of short-range screened Hartree-Fock calculations. These two techniques
agreed to significant precision. We also present the Hartree-Fock cohesive
energy of LiH (converged to within sub-meV) at the experimental equilibrium
volume as well as the Hartree-Fock equilibrium lattice constant and bulk
modulus.Comment: 7.5 pages, 2 figures, submitted to Phys. Rev. B; v2: typos removed,
References adde
Analysis of corrections to the eikonal approximation
Various corrections to the eikonal approximations are studied for two- and
three-body nuclear collisions with the goal to extend the range of validity of
this approximation to beam energies of 10 MeV/nucleon. Wallace's correction
does not improve much the elastic-scattering cross sections obtained at the
usual eikonal approximation. On the contrary, a semiclassical approximation
that substitutes the impact parameter by a complex distance of closest approach
computed with the projectile-target optical potential efficiently corrects the
eikonal approximation. This opens the possibility to analyze data measured down
to 10 MeV/nucleon within eikonal-like reaction models.Comment: 10 pages, 8 figure
Interatomic Methods for the Dispersion Energy Derived from the Adiabatic Connection Fluctuation-Dissipation Theorem
Interatomic pairwise methods are currently among the most popular and
accurate ways to include dispersion energy in density functional theory (DFT)
calculations. However, when applied to more than two atoms, these methods are
still frequently perceived to be based on \textit{ad hoc} assumptions, rather
than a rigorous derivation from quantum mechanics. Starting from the adiabatic
connection fluctuation-dissipation (ACFD) theorem, an exact expression for the
electronic exchange-correlation energy, we demonstrate that the pairwise
interatomic dispersion energy for an arbitrary collection of isotropic
polarizable dipoles emerges from the second-order expansion of the ACFD
formula. Moreover, for a system of quantum harmonic oscillators coupled through
a dipole--dipole potential, we prove the equivalence between the full
interaction energy obtained from the Hamiltonian diagonalization and the ACFD
correlation energy in the random-phase approximation. This property makes the
Hamiltonian diagonalization an efficient method for the calculation of the
many-body dispersion energy. In addition, we show that the switching function
used to damp the dispersion interaction at short distances arises from a
short-range screened Coulomb potential, whose role is to account for the
spatial spread of the individual atomic dipole moments. By using the ACFD
formula we gain a deeper understanding of the approximations made in the
interatomic pairwise approaches, providing a powerful formalism for further
development of accurate and efficient methods for the calculation of the
dispersion energy
Singular Short Range Potentials in the J-Matrix Approach
We use the tools of the J-matrix method to evaluate the S-matrix and then
deduce the bound and resonance states energies for singular screened Coulomb
potentials, both analytic and piecewise differentiable. The J-matrix approach
allows us to absorb the 1/r singularity of the potential in the reference
Hamiltonian, which is then handled analytically. The calculation is performed
using an infinite square integrable basis that supports a tridiagonal matrix
representation for the reference Hamiltonian. The remaining part of the
potential, which is bound and regular everywhere, is treated by an efficient
numerical scheme in a suitable basis using Gauss quadrature approximation. To
exhibit the power of our approach we have considered the most delicate region
close to the bound-unbound transition and compared our results favorably with
available numerical data.Comment: 14 pages, 5 tables, 2 figure
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