2,245 research outputs found
Atomic Ground-State Energies
It is demonstrated that atomic Hartree–Fock binding energies may be reproduced with great accuracy (within about four parts in a thousand) by a scaled model system in which the electrons are noninteracting, and are bound in a bare Coulomb potential. </jats:p
How harmonic is dipole resonance of metal clusters?
We discuss the degree of anharmonicity of dipole plasmon resonances in metal
clusters. We employ the time-dependent variational principle and show that the
relative shift of the second phonon scales as in energy, being
the number of particles. This scaling property coincides with that for nuclear
giant resonances. Contrary to the previous study based on the boson-expansion
method, the deviation from the harmonic limit is found to be almost negligible
for Na clusters, the result being consistent with the recent experimental
observation.Comment: RevTex, 8 page
Periodic-Orbit Bifurcations and Superdeformed Shell Structure
We have derived a semiclassical trace formula for the level density of the
three-dimensional spheroidal cavity. To overcome the divergences occurring at
bifurcations and in the spherical limit, the trace integrals over the
action-angle variables were performed using an improved stationary phase
method. The resulting semiclassical level density oscillations and
shell-correction energies are in good agreement with quantum-mechanical
results. We find that the bifurcations of some dominant short periodic orbits
lead to an enhancement of the shell structure for "superdeformed" shapes
related to those known from atomic nuclei.Comment: 4 pages including 3 figure
Closed orbits and spatial density oscillations in the circular billiard
We present a case study for the semiclassical calculation of the oscillations
in the particle and kinetic-energy densities for the two-dimensional circular
billiard. For this system, we can give a complete classification of all closed
periodic and non-periodic orbits. We discuss their bifurcations under variation
of the starting point r and derive analytical expressions for their properties
such as actions, stability determinants, momentum mismatches and Morse indices.
We present semiclassical calculations of the spatial density oscillations using
a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev.
Lett. 100 200408], employing standard uniform approximations from perturbation
and bifurcation theory, and test the convergence of the closed-orbit sum.Comment: LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final
version (v3) to be published in J. Phys.
Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap
We derive simple analytical expressions for the particle density
and the kinetic energy density for a system of noninteracting
fermions in a dimensional isotropic harmonic oscillator potential. We test
the Thomas-Fermi (TF, or local-density) approximation for the functional
relation using the exact and show that it locally
reproduces the exact kinetic energy density , {\it including the shell
oscillations,} surprisingly well everywhere except near the classical turning
point. For the special case of two dimensions (2D), we obtain the unexpected
analytical result that the integral of yields the {\it
exact} total kinetic energy.Comment: 4 pages, 4 figures; corrected versio
A semiclassical analysis of the Efimov energy spectrum in the unitary limit
We demonstrate that the (s-wave) geometric spectrum of the Efimov energy
levels in the unitary limit is generated by the radial motion of a primitive
periodic orbit (and its harmonics) of the corresponding classical system. The
action of the primitive orbit depends logarithmically on the energy. It is
shown to be consistent with an inverse-squared radial potential with a lower
cut-off radius. The lowest-order WKB quantization, including the Langer
correction, is shown to reproduce the geometric scaling of the energy spectrum.
The (WKB) mean-squared radii of the Efimov states scale geometrically like the
inverse of their energies. The WKB wavefunctions, regularized near the
classical turning point by Langer's generalized connection formula, are
practically indistinguishable from the exact wave functions even for the lowest
() state, apart from a tiny shift of its zeros that remains constant for
large .Comment: LaTeX (revtex 4), 18pp., 4 Figs., already published in Phys. Rev. A
but here a note with a new referece is added on p. 1
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