24,595 research outputs found

### The stability of the spectator, Dirac, and Salpeter equations for mesons

Mesons are made of quark-antiquark pairs held together by the strong force.
The one channel spectator, Dirac, and Salpeter equations can each be used to
model this pairing. We look at cases where the relativistic kernel of these
equations corresponds to a time-like vector exchange, a scalar exchange, or a
linear combination of the two. Since the model used in this paper describes
mesons which cannot decay physically, the equations must describe stable
states. We find that this requirement is not always satisfied, and give a
complete discussion of the conditions under which the various equations give
unphysical, unstable solutions

### Two-pion exchange potential and the $\pi N$ amplitude

We discuss the two-pion exchange potential which emerges from a box diagram
with one nucleon (the spectator) restricted to its mass shell, and the other
nucleon line replaced by a subtracted, covariant $\pi N$ scattering amplitude
which includes $\Delta$, Roper, and $D_{13}$ isobars, as well as contact terms
and off-shell (non-pole) dressed nucleon terms. The $\pi N$ amplitude satisfies
chiral symmetry constraints and fits $\pi N$ data below $\sim$ 700 MeV pion
energy. We find that this TPE potential can be well approximated by the
exchange of an effective sigma and delta meson, with parameters close to the
ones used in one-boson-exchange models that fit $NN$ data below the pion
production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped
tar fil

### Pathway from condensation via fragmentation to fermionization of cold bosonic systems

For small scattering lengths, cold bosonic atoms form a condensate the
density profile of which is smooth. With increasing scattering length, the
density {\it gradually} acquires more and more oscillations. Finally, the
number of oscillations equals the number of bosons and the system becomes {\it
fermionized}. On this pathway from condensation to fermionization intriguing
phenomena occur, depending on the shape of the trap. These include macroscopic
fragmentation and
{\it coexistence} of condensed and fermionized parts that are separated in
space.Comment: 12 pages, 2 figure

### Beyond Mean-Field Theory for Attractive Bosons under Transverse Harmonic Confinement

We study a dilute gas of attractive bosons confined in a harmonic cylinder,
i.e. under cylindric confinement due to a transverse harmonic potential. We
introduce a many-body wave function which extends the Bethe ansatz proposed by
McGuire (J. Math. Phys. {\bf 5}, 622 (1964)) by including a variational
transverse Gaussian shape. We investigate the ground state properties of the
system comparing them with the ones of the one-dimensional (1D) attractive Bose
gas. We find that the gas becomes ultra 1D as a consequence of the attractive
interaction: the transverse width of the Bose gas reduces by increasing the
number of particles up to a critical width below which there is the collapse of
the cloud. In addition, we derive a simple analytical expression for the
simmetry-breaking solitonic density profile of the ground-state, which
generalize the one deduced by Calogero and Degasperis (Phys. Rev. A {\bf 11},
265 (1975)). This bright-soliton analytical solution shows near the collapse
small deviations with respect to the 3D mean-field numerical solution. Finally,
we show that our variational Gauss-McGuire theory is always more accurate than
the McGuire theory. In addition, we prove that for small numbers of particles
the Gauss-McGuire theory is more reliable than the mean-field theory described
by the 3D Gross-Pitaevskii equation.Comment: To be published in J. Phys. B.: At. Mol. Opt. Phy

### Bimodality as a signal of Liquid-Gas phase transition in nuclei?

We use the HIPSE (Heavy-Ion Phase-Space Exploration) Model to discuss the
origin of the bimodality in charge asymmetry observed in nuclear reactions
around the Fermi energy. We show that it may be related to the important
angular momentum (spin) transferred into the quasi-projectile before secondary
decay. As the spin overcomes the critical value, a sudden opening of decay
channels is induced and leads to a bimodal distribution for the charge
asymmetry. In the model, it is not assigned to a liquid-gas phase transition
but to specific instabilities in nuclei with high spin. Therefore, we propose
to use these reactions to study instabilities in rotating nuclear droplets.Comment: 4 pages, 4 figures Accepted to PR

### Rigorous Derivation of the Gross-Pitaevskii Equation

The time dependent Gross-Pitaevskii equation describes the dynamics of
initially trapped Bose-Einstein condensates. We present a rigorous proof of
this fact starting from a many-body bosonic Schroedinger equation with a short
scale repulsive interaction in the dilute limit. Our proof shows the
persistence of an explicit short scale correlation structure in the condensate.Comment: 4 pages, 1 figur

### Solitary wave complexes in two-component mixture condensates

Axisymmetric three-dimensional solitary waves in uniform two-component
mixture Bose-Einstein condensates are obtained as solutions of the coupled
Gross-Pitaevskii equations with equal intracomponent but varying intercomponent
interaction strengths. Several families of solitary wave complexes are found:
(1) vortex rings of various radii in each of the components, (2) a vortex ring
in one component coupled to a rarefaction solitary wave of the other component,
(3) two coupled rarefaction waves, (4) either a vortex ring or a rarefaction
pulse coupled to a localised disturbance of a very low momentum. The continuous
families of such waves are shown in the momentum-energy plane for various
values of the interaction strengths and the relative differences between the
chemical potentials of two components. Solitary wave formation, their stability
and solitary wave complexes in two-dimensions are discussed.Comment: 4 pages, 2 figures, 2 table

### Fragmentation Phase Transition in Atomic Clusters II - Coulomb Explosion of Metal Clusters -

We discuss the role and the treatment of polarization effects in many-body
systems of charged conducting clusters and apply this to the statistical
fragmentation of Na-clusters. We see a first order microcanonical phase
transition in the fragmentation of $Na^{Z+}_{70}$ for Z=0 to 8. We can
distinguish two fragmentation phases, namely evaporation of large particles
from a large residue and a complete decay into small fragments only. Charging
the cluster shifts the transition to lower excitation energies and forces the
transition to disappear for charges higher than Z=8. At very high charges the
fragmentation phase transition no longer occurs because the cluster
Coulomb-explodes into small fragments even at excitation energy $\epsilon^* =
0$.Comment: 19 text pages +18 *.eps figures, my e-mail adress: [email protected]
submitted to Z. Phys.

### N-representability and stationarity in time-dependent density functional theory

To construct an N-representable time-dependent density-functional theory, a
generalization to the time domain of the Levy-Lieb (LL) constrained search
algorithm is required. That the action is only stationary in the Dirac-Frenkel
variational principle eliminates the possibility of basing the search on the
action itself. Instead, we use the norm of the partial functional derivative of
the action in the Hilbert space of the wave functions in place of the energy of
the LL search. The electron densities entering the formalism are
$N$-representable, and the resulting universal action functional has a unique
stationary point in the density at that corresponding to the solution of the
Schr\"{o}dinger equation. The original Runge-Gross (RG) formulation is subsumed
within the new formalism. Concerns in the literature about the meaning of the
functional derivatives and the internal consistency of the RG formulation are
allayed by clarifying the nature of the functional derivatives entering the
formalism.Comment: 9 pages, 0 figures, Phys. Rev. A accepted. Introduction was expanded,
subsections reorganized, appendix and new references adde

- …