2,002 research outputs found
The Fermionic Density-functional at Feshbach Resonance
We consider a dilute gas of neutral unpolarized fermionic atoms at zero
temperature.The atoms interact via a short range (tunable) attractive
interaction. We demonstrate analytically a curious property of the gas at
unitarity. Namely, the correlation energy of the gas, evaluated by second order
perturbation theory, has the same density dependence as the first order
exchange energy, and the two almost exactly cancel each other at Feshbach
resonance irrespective of the shape of the potential, provided . Here is the range of the two-body potential, and is
defined through the number density . The implications of this
result for universality is discussed.Comment: Five pages, one table. accepted for publication in PR
Dirac particle in a spherical scalar potential well
In this paper we investigate a solution of the Dirac equation for a
spin- particle in a scalar potential well with full spherical
symmetry. The energy eigenvalues for the quark particle in states
(with ) and states (with ) are calculated. We
also study the continuous Dirac wave function for a quark in such a potential,
which is not necessarily infinite. Our results, at infinite limit, are in good
agreement with the MIT bag model. We make some remarks about the sharpness
value of the wave function on the wall. This model, for finite values of
potential, also could serve as an effective model for the nucleus where
is the effective single particle potential.Comment: 9 pages, 8 figures, revtex4, version to appear in PR
The Continuum Limit and Integral Vacuum Charge
We investigate a commonly used formula which seems to give non-integral
vacuum charge in the continuum limit. We show that the limit is subtle and care
must be taken to get correct results.Comment: 5 pages. Submitted to JETP Letter
Relativistic Harmonic Oscillator with Spin Symmetry
The eigenfunctions and eigenenergies for a Dirac Hamiltonian with equal
scalar and vector harmonic oscillator potentials are derived. Equal scalar and
vector potentials may be applicable to the spectrum of an antinucleion imbedded
in a nucleus. Triaxial, axially deformed, and spherical oscillator potentials
are considered. The spectrum has a spin symmetry for all cases and, for the
spherical harmonic oscillator potential, a higher symmetry analogous to the
SU(3) symmetry of the non-relativistic harmonic oscillator is discussed
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
Solitons in Tonks-Girardeau gas with dipolar interactions
The existence of bright solitons in the model of the Tonks-Girardeau (TG) gas
with dipole-dipole (DD) interactions is reported. The governing equation is
taken as the quintic nonlinear Schr\"{o}dinger equation (NLSE) with the
nonlocal cubic term accounting for the DD attraction. In different regions of
the parameter space (the dipole moment and atom number), matter-wave solitons
feature flat-top or compacton-like shapes. For the flat-top states, the NLSE
with the local cubic-quintic (CQ) nonlinearity is shown to be a good
approximation. Specific dynamical effects are studied assuming that the
strength of the DD interactions is ramped up or drops to zero. Generation of
dark-soliton pairs in the gas shrinking under the action of the intensifying DD
attraction is observed. Dark solitons exhibit the particle-like collision
behavior. Peculiarities of dipole solitons in the TG gas are highlighted by
comparison with the NLSE including the local CQ terms. Collisions between the
solitons are studied too. In many cases, the collisions result in merger of the
solitons into a breather, due to strong attraction between them.Comment: 15 pages, 8 figures, accepted by J. Phys. B: At. Mol. Opt. Phy
Pion-delta sigma-term
We use a configuration space chiral model in order to evaluate nucleon and
delta sigma-terms. Analytic expressions are consistent with chiral counting
rules and give rise to expected non-analytic terms in the chiral limit. We
obtain the results MeV and MeV, which are
very close to values extracted from experiment and produced by other groups.Comment: 18 pages, 4 figure
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