337,916 research outputs found
Effective shell model Hamiltonians from density functional theory: quadrupolar and pairing correlations
We describe a procedure for mapping a self-consistent mean-field theory (also
known as density functional theory) into a shell model Hamiltonian that
includes quadrupole-quadrupole and monopole pairing interactions in a truncated
space. We test our method in the deformed N=Z sd-shell nuclei Ne-20, Mg-24 and
Ar-36, starting from the Hartree-Fock plus BCS approximation of the USD shell
model interaction. A similar procedure is then followed using the SLy4 Skyrme
energy density functional in the particle-hole channel plus a zero-range
density-dependent force in the pairing channel. Using the ground-state solution
of this density functional theory at the Hartree-Fock plus BCS level, an
effective shell model Hamiltonian is constructed. We use this mapped
Hamiltonian to extract quadrupolar and pairing correlation energies beyond the
mean field approximation. The rescaling of the mass quadrupole operator in the
truncated shell model space is found to be almost independent of the coupling
strength used in the pairing channel of the underlying mean-field theory.Comment: 15 pages, 5 figure
Navier-Stokes equations interacting with a nonlinear elastic fluid shell
We study a moving boundary value problem consisting of a viscous
incompressible fluid moving and interacting with a nonlinear elastic fluid
shell. The fluid motion is governed by the Navier-Stokes equations, while the
fluid shell is modeled by a bending energy which extremizes the Willmore
functional and a membrane energy that extremizes the surface area of the shell.
The fluid flow and shell deformation are coupled together by continuity of
displacements and tractions (stresses) along the moving material interface. We
prove existence and uniqueness of solutions in Sobolev spaces.Comment: 56 pages, 1 figur
Spin in Density-Functional Theory
The accurate description of open-shell molecules, in particular of transition
metal complexes and clusters, is still an important challenge for quantum
chemistry. While density-functional theory (DFT) is widely applied in this
area, the sometimes severe limitations of its currently available approximate
realizations often preclude its application as a predictive theory. Here, we
review the foundations of DFT applied to open-shell systems, both within the
nonrelativistic and the relativistic framework. In particular, we provide an
in-depth discussion of the exact theory, with a focus on the role of the spin
density and possibilities for targeting specific spin states. It turns out that
different options exist for setting up Kohn-Sham DFT schemes for open-shell
systems, which imply different definitions of the exchange-correlation energy
functional and lead to different exact conditions on this functional. Finally,
we suggest some possible directions for future developments
Density-functional calculation of ionization energies of current-carrying atomic states
Current-density-functional theory is used to calculate ionization energies of
current-carrying atomic states. A perturbative approximation to full
current-density-functional theory is implemented for the first time, and found
to be numerically feasible. Different parametrizations for the
current-dependence of the density functional are critically compared. Orbital
currents in open-shell atoms turn out to produce a small shift in the
ionization energies. We find that modern density functionals have reached an
accuracy at which small current-related terms appearing in open-shell
configurations are not negligible anymore compared to the remaining difference
to experiment.Comment: 7 pages, 2 tables, accepted by Phys. Rev.
Constitutive relations, off shell duality rotations and the hypergeometric form of Born-Infeld theory
We review equivalent formulations of nonlinear and higher derivatives
theories of electromagnetism exhibiting electric-magnetic duality rotations
symmetry. We study in particular on shell and off shell formulations of this
symmetry, at the level of action functionals as well as of equations of motion.
We prove the conjecture that the action functional leading to Born-Infeld
nonlinear electromagnetism, that is duality rotation invariant off shell and
that is known to be a root of an algebraic equation of fourth order, is a
hypergeometric function.Comment: 20 pages. Contribution to the proceedings of the conference BUDS2013,
Frascat
Classical Many-particle Clusters in Two Dimensions
We report on a study of a classical, finite system of confined particles in
two dimensions with a two-body repulsive interaction. We first develop a simple
analytical method to obtain equilibrium configurations and energies for few
particles. When the confinement is harmonic, we prove that the first transition
from a single shell occurs when the number of particles changes from five to
six. The shell structure in the case of an arbitrary number of particles is
shown to be independent of the strength of the interaction but dependent only
on its functional form. It is also independent of the magnetic field strength
when included. We further study the effect of the functional form of the
confinement potential on the shell structure. Finally we report some
interesting results when a three-body interaction is included, albeit in a
particular model.Comment: Minor corrections, a few references added. To appear in J. Phys:
Condensed Matte
Quasiparticle-vibration coupling in relativistic framework: shell structure of Z=120 isotopes
For the first time, the shell structure of open-shell nuclei is described in
a fully self-consistent extension of the covariant energy density functional
theory. The approach implies quasiparticle-vibration coupling for superfluid
systems. One-body Dyson equation formulated in the doubled quasiparticle space
of Dirac spinors is solved for nucleonic propagators in tin isotopes which
represent the reference case: the obtained energies of the single-quasiparticle
levels and their spectroscopic amplitudes are in agreement with data. The model
is applied to describe the shell evolution in a chain of superheavy isotopes
120 and finds a rather stable proton spherical shell
closure at Z = 120. An interplay of the pairing correlations and the
quasiparticle-phonon coupling gives rise for a smooth evolution of the neutron
shell gap between N = 172 and N = 184 neutron numbers. Vibrational corrections
to the alpha decay energies reach several hundred keV and can be either
positive and negative, thus also smearing the shell effects.Comment: 10 pages, 3 figure
Influence of ligand shape and steric hindrance on the composition of the nanocrystal ligand shell
Organic ligands play a key role in the synthesis of colloidal semiconductor nanocrystals or quantum dots. Generally they consist of a functional group and an aliphatic chain, with carboxylic acids, thiols and phosphonic acids as typical examples. The functional group ensures the binding to the nanocrystal surface, while the stability of the dispersion strongly depends on the interactions between the organic chains of the adjacent ligands. A number of studies already addressed the binding strength and the type of binding between the nanocrystal surface and the ligand yet none discuss the effect of the organic chain on the ligand exchange.
By means of NMR spectroscopy, we examine the ligand shell composition of CdSe nanocrystals originally capped with oleic acid (OA), when exposed to a linear carboxylic acid. Regardless of chain length, we see a one-to-one exchange between the carboxylic acids. The composition of the ligand shell closely matches that of the ligand mixture in solution, indicating that the ligand shell can be seen as an ideal mixture of both ligands. As a consequence, a mixed ligand shell can easily be prepared by adding a ligand mixture with desired composition to the nanocrystal dispersion.
On the other hand, when the CdSe nanocrystals are exposed to a branched carboxylic acid with two long aliphatic chains, like 2-hexyldecanoic acid, the ligand shell mainly consists of OA moieties. We interpret these results using an exchange process where the incoming ligand not only displaces oleic acid but also occupies additional space in the ligand shell to accommodate both aliphatic chains. Hence, given a one-for-one exchange reaction, steric hindrance in a fully packed ligand shell will prevent complete ligand exchange. These results can be very useful in view of producing nanocrystals with lower ligand densities by means of synthesis with these branched carboxylic acids
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