141 research outputs found
Universal Equation for Efimov States
Efimov states are a sequence of shallow 3-body bound states that arise when
the 2-body scattering length is large. Efimov showed that the binding energies
of these states can be calculated in terms of the scattering length and a
3-body parameter by solving a transcendental equation involving a universal
function of one variable. We calculate this universal function using effective
field theory and use it to describe the three-body system of 4He atoms. We also
extend Efimov's theory to include the effects of deep 2-body bound states,
which give widths to the Efimov states.Comment: 8 pages, revtex4, 2 ps figures, table with numerical values of
universal function adde
Universality in the Three-Body Problem for 4He Atoms
The two-body scattering length a for 4He atoms is much larger than their
effective range r_s. As a consequence, low-energy few-body observables have
universal characteristics that are independent of the interaction potential.
Universality implies that, up to corrections suppressed by r_s/a, all
low-energy three-body observables are determined by a and a three-body
parameter \Lambda_*. We give simple expressions in terms of a and \Lambda_* for
the trimer binding energy equation, the atom-dimer scattering phase shifts, and
the rate for three-body recombination at threshold. We determine \Lambda_* for
several 4He potentials from the calculated binding energy of the excited state
of the trimer and use it to obtain the universality predictions for the other
low-energy observables. We also use the calculated values for one potential to
estimate the effective range corrections for the other potentials.Comment: 23 pages, revtex4, 6 ps figures, references added, universal
expressions update
Three-body problem in Fermi gases with short-range interparticle interaction
We discuss 3-body processes in ultracold two-component Fermi gases with
short-range intercomponent interaction characterized by a large and positive
scattering length . It is found that in most cases the probability of 3-body
recombination is a universal function of the mass ratio and , and is
independent of short-range physics. We also calculate the scattering length
corresponding to the atom-dimer interaction.Comment: 4 pages, 2 figure
More on the infrared renormalization group limit cycle in QCD
We present a detailed study of the recently conjectured infrared
renormalization group limit cycle in QCD using chiral effective field theory.
It was conjectured that small increases in the up and down quark masses can
move QCD to the critical trajectory for an infrared limit cycle in the
three-nucleon system. At the critical quark masses, the binding energies of the
deuteron and its spin-singlet partner are tuned to zero and the triton has
infinitely many excited states with an accumulation point at the three-nucleon
threshold. We exemplify three parameter sets where this effect occurs at
next-to-leading order in the chiral counting. For one of them, we study the
structure of the three-nucleon system in detail using both chiral and contact
effective field theories. Furthermore, we investigate the matching of the
chiral and contact theories in the critical region and calculate the influence
of the limit cycle on three-nucleon scattering observables.Comment: 17 pages, 7 figures, discussion improved, results unchanged, version
to appear in EPJ
Weakly-Bound Three-Body Systems with No Bound Subsystems
We investigate the domain of coupling constants which achieve binding for a
3-body system, while none of the 2-body subsystems is bound. We derive some
general properties of the shape of the domain, and rigorous upper bounds on its
size, using a Hall--Post decomposition of the Hamiltonian. Numerical
illustrations are provided in the case of a Yukawa potential, using a simple
variational method.Comment: gzipped ps with 11 figures included. To appear in Phys. Rev.
Unusual condensates in quark and atomic systems
In these lectures we discuss condensates which are formed in quark matter
when it is squeezed and in a gas of fermionic atoms when it is cooled. The
behavior of these two seemingly very different systems reveals striking
similarities. In particular, in both systems the Bose-Einstein condensate to
Bardeen--Cooper-Schrieffer (BEC-BCS) crossover takes place.Comment: Lectures delivered at 8th Moscow school of Physics (33rd ITEP Winter
School of Physics
Singular potentials and annihilation
We discuss the regularization of attractive singular potentials , by infinitesimal imaginary addition to interaction
constant . Such a procedure enables unique
definition of scattering observables and is equal to an absorption (creation)
of particles in the origin. It is shown, that suggested regularization is an
analytical continuation of the scattering amplitudes of repulsive singular
potential in interaction constant . The nearthreshold properties of
regularized in a mentioned way singular potential are examined. We obtain
expressions for the scattering lengths, which turn to be complex even for
infinitesimal imaginary part of interaction constant. The problem of
perturbation of nearthreshold states of regular potential by a singular one is
treated, the expressions for level shifts and widths are obtained. We show,
that the physical sense of suggested regularization is that the scattering
observables are insensitive to any details of the short range modification of
singular potential, if there exists sufficiently strong inelastic short range
interaction. In this case the scattering observables are determined by
solutions of Schrodinger equation with regularized potential . We point out that the developed formalism can be applied for the
description of systems with short range annihilation, in particular low energy
nucleon-antinucleon scattering.Comment: 10 page
Singular Potentials and Limit Cycles
We show that a central singular potential (with ) is
renormalized by a one-parameter square-well counterterm; low-energy observables
are made independent of the square-well width by adjusting the square-well
strength. We find a closed form expression for the renormalization-group
evolution of the square-well counterterm.Comment: 15 pages LaTex, 5 eps figures, error in figures and text correcte
Confinement and Chiral Symmetry Breaking via Domain-Like Structures in the QCD Vacuum
A qualitative mechanism for the emergence of domain structured background
gluon fields due to singularities in gauge field configurations is considered,
and a model displaying a type of mean field approximation to the QCD partition
function based on this mechanism is formulated. Estimation of the vacuum
parameters (gluon condensate, topological susceptibility, string constant and
quark condensate) indicates that domain-like structures lead to an area law for
the Wilson loop, nonzero topological susceptibility and spontaneous breakdown
of chiral symmetry. Gluon and ghost propagators in the presence of domains are
calculated explicitly and their analytical properties are discussed. The
Fourier transforms of the propagators are entire functions and thus describe
confined dynamical fields.Comment: RevTeX, 48 pages (32 pages + Appendices A-E), new references added
[1,2,4,5] and minor formulae corrected for typographical error
A Model Study of Discrete Scale Invariance and Long-Range Interactions
We investigate the modification of discrete scale invariance in the bound
state spectrum by long-range interactions. This problem is relevant for
effective field theory descriptions of nuclear cluster states and
manifestations of the Efimov effect in nuclei. As a model system, we choose a
one dimensional inverse square potential supplemented with a long-range Coulomb
interaction. We study the renormalization and bound-state spectrum of the
system as a function of the Coulomb interaction strength. Our results indicate,
that the counterterm required to renormalize the inverse square potential alone
is sufficient to renormalize the full problem. However, the breaking of the
discrete scale invariance through the Coulomb interaction leads to a modified
bound state spectrum. The shallow bound states are strongly influenced by the
Coulomb interaction while the deep bound states are dominated by the inverse
square potential.Comment: 8 pages, 6 figures, EPJ style, published versio
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