2,127 research outputs found
Dimer-atom scattering between two identical fermions and a third particle
We use the diagrammatic -matrix approach to analyze the three-body
scattering problem between two identical fermions and a third particle (which
could be a different species of fermion or a boson). We calculate the s-wave
dimer-atom scattering length for all mass ratios, and our results exactly match
the results of Petrov. In particular, we list the exact dimer-atom scattering
lengths for all available two-species Fermi-Fermi and Bose-Fermi mixtures. In
addition, unlike that of the equal-mass particles case where the three-body
scattering -matrix decays monotonically as a function of the outgoing
momentum, we show that, after an initial rapid drop, this function changes sign
and becomes negative at large momenta and then decays slowly to zero when the
mass ratio of the fermions to the third particle is higher than a critical
value (around 6.5). As the mass ratio gets higher, modulations of the
-matrix become more apparent with multiple sign changes, related to the
"fall of a particle to the center" phenomenon and to the emergence of
three-body Efimov bound states.Comment: 6 pages, 3 figures, and 2 table
Three-boson problem near a narrow Feshbach resonance
We consider a three-boson system with resonant binary interactions and show
that three-body observables depend only on the resonance width and the
scattering length. The effect of narrow resonances is qualitatively different
from that of wide resonances revealing novel physics of three-body collisions.
We calculate the rate of three-body recombination to a weakly bound level and
the atom-dimer scattering length and discuss implications for experiments on
Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.Comment: published versio
Range Corrections to Three-Body Observables near a Feshbach Resonance
A non-relativistic system of three identical particles will display a rich
set of universal features known as Efimov physics if the scattering length a is
much larger than the range l of the underlying two-body interaction. An
appropriate effective theory facilitates the derivation of both results in the
|a| goes to infinity limit and finite-l/a corrections to observables of
interest. Here we use such an effective-theory treatment to consider the impact
of corrections linear in the two-body effective range, r_s on the three-boson
bound-state spectrum and recombination rate for |a| much greater than |r_s|. We
do this by first deriving results appropriate to the strict limit |a| goes to
infinity in coordinate space. We then extend these results to finite a using
once-subtracted momentum-space integral equations. We also discuss the
implications of our results for experiments that probe three-body recombination
in Bose-Einstein condensates near a Feshbach resonance.Comment: 28 pages, 3 figure
The Four-Boson System with Short-Range Interactions
We consider the non-relativistic four-boson system with short-range forces
and large scattering length in an effective quantum mechanics approach. We
construct the effective interaction potential at leading order in the large
scattering length and compute the four-body binding energies using the
Yakubovsky equations. Cutoff independence of the four-body binding energies
does not require the introduction of a four-body force. This suggests that two-
and three-body interactions are sufficient to renormalize the four-body system.
We apply the equations to 4He atoms and calculate the binding energy of the 4He
tetramer. We observe a correlation between the trimer and tetramer binding
energies similar to the Tjon line in nuclear physics. Over the range of binding
energies relevant to 4He atoms, the correlation is approximately linear.Comment: 23 pages, revtex4, 5 PS figures, discussion expanded, results
unchange
Production of three-body Efimov molecules in an optical lattice
We study the possibility of associating meta-stable Efimov trimers from three
free Bose atoms in a tight trap realised, for instance, via an optical lattice
site or a microchip. The suggested scheme for the production of these molecules
is based on magnetically tunable Feshbach resonances and takes advantage of the
Efimov effect in three-body energy spectra. Our predictions on the energy
levels and wave functions of three pairwise interacting 85Rb atoms rely upon
exact solutions of the Faddeev equations and include the tightly confining
potential of an isotropic harmonic atom trap. The magnetic field dependence of
these energy levels indicates that it is the lowest energetic Efimov trimer
state that can be associated in an adiabatic sweep of the field strength. We
show that the binding energies and spatial extents of the trimer molecules
produced are comparable, in their magnitudes, to those of the associated
diatomic Feshbach molecule. The three-body molecular state follows Efimov's
scenario when the pairwise attraction of the atoms is strengthened by tuning
the magnetic field strength.Comment: 21 pages, 8 figures (final version
Few-body physics in effective field theory
Effective Field Theory (EFT) provides a powerful framework that exploits a
separation of scales in physical systems to perform systematically improvable,
model-independent calculations. Particularly interesting are few-body systems
with short-range interactions and large two-body scattering length. Such
systems display remarkable universal features. In systems with more than two
particles, a three-body force with limit cycle behavior is required for
consistent renormalization already at leading order. We will review this EFT
and some of its applications in the physics of cold atoms and nuclear physics.
In particular, we will discuss the possibility of an infrared limit cycle in
QCD. Recent extensions of the EFT approach to the four-body system and N-boson
droplets in two spatial dimensions will also be addressed.Comment: 10 pages, 5 figures, Proceedings of the INT Workshop on "Nuclear
Forces and the Quantum Many-Body Problem", Oct. 200
Collective Excitations of Strongly Interacting Fermi Gases of Atoms in a Harmonic Trap
The zero-temperature properties of a dilute two-component Fermi gas in the
BCS-BEC crossover are investigated. On the basis of a generalization of the
Hylleraas-Undheim method, we construct rigorous upper bounds to the collective
frequencies for the radial and the axial breathing mode of the Fermi gas under
harmonic confinement in the framework of the hydrodynamic theory. The bounds
are compared to experimental data for trapped vapors of Li6 atoms.Comment: 11 pages, 2 figure
On the correlation between the binding energies of the triton and the alpha-particle
We consider the correlation between the binding energies of the triton and
the alpha-particle which is empirically observed in calculations employing
different phenomenological nucleon-nucleon interactions. Using an effective
quantum mechanics approach for short-range interactions with large scattering
length |a| >> l, where l is the natural low-energy length scale, we construct
the effective interaction potential at leading order in l/|a|. In order to
renormalize the four-nucleon system, it is sufficient to include a
SU(4)-symmetric one-parameter three-nucleon interaction in addition to the
S-wave nucleon-nucleon interactions. The absence of a four-nucleon force at
this order explains the empirically observed correlation between the binding
energies of the triton and the alpha-particle. We calculate this correlation
and obtain a prediction for the alpha-particle binding energy. Corrections to
our results are suppressed by l/|a|.Comment: 4 pages, 1 ps figure, references update
Light baryon magnetic moments and N -> Delta gamma transition in a Lorentz covariant chiral quark approach
We calculate magnetic moments of light baryons and N -> Delta gamma
transition characteristics using a manifestly Lorentz covariant chiral quark
approach for the study of baryons as bound states of constituent quarks dressed
by a cloud of pseudoscalar mesons.Comment: 29 pages, 10 figures, accepted for publication in Phys. Rev.
Three body problem in a dilute Bose-Einstein condensate
We derive the explicit three body contact potential for a dilute condensed
Bose gas from microscopic theory. The three body coupling constant exhibits the
general form predicted by T.T. Wu [Phys. Rev. 113, 1390 (1959)] and is
determined in terms of the amplitudes of two and three body collisions in
vacuum. In the present form the coupling constant becomes accessible to
quantitative studies which should provide the crucial link between few body
collisions and the stability of condensates with attractive two body forces
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