47 research outputs found
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
Universality in Few-Body Systems
Low-energy universality in atomic few-body systems as a result of a large
two-body scattering length has gained a lot of attention recently. Here, I
discuss recent progress in describing the three-body recombination of cold
atoms in terms of a finite set of universal scaling functions and review
results for the recombination length of cesium-133 atoms obtained with these
functions. Furthermore, I will consider the inclusion of effective range
corrections and the relevance for further calculations in atomic and nuclear
physics.Comment: Plenary talk at 20th European Conference on Few-Body Problems in
Physics (EFB 20), Pisa, Italy, 10-14 Sep 2007, FBS style, 2 figue
Nonuniversal Effects in the Homogeneous Bose Gas
Effective field theory predicts that the leading nonuniversal effects in the
homogeneous Bose gas arise from the effective range for S-wave scattering and
from an effective three-body contact interaction. We calculate the leading
nonuniversal contributions to the energy density and condensate fraction and
compare the predictions with results from diffusion Monte Carlo calculations by
Giorgini, Boronat, and Casulleras. We give a crude determination of the
strength of the three-body contact interaction for various model potentials.
Accurate determinations could be obtained from diffusion Monte Carlo
calculations of the energy density with higher statistics.Comment: 24 pages, RevTex, 5 ps figures, included with epsf.te
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
On the modification of the Efimov spectrum in a finite cubic box
Three particles with large scattering length display a universal spectrum of
three-body bound states called "Efimov trimers''. We calculate the modification
of the Efimov trimers of three identical bosons in a finite cubic box and
compute the dependence of their energies on the box size using effective field
theory. Previous calculations for positive scattering length that were
perturbative in the finite volume energy shift are extended to arbitrarily
large shifts and negative scattering lengths. The renormalization of the
effective field theory in the finite volume is explicitly verified. Moreover,
we investigate the effects of partial wave mixing and study the behavior of
shallow trimers near the dimer energy. Finally, we provide numerical evidence
for universal scaling of the finite volume corrections.Comment: 21 pages, 8 figures, published versio
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
Renormalization of the Three-Body System with Short-Range Interactions
We discuss renormalization of the non-relativistic three-body problem with
short-range forces. The problem becomes non-perturbative at momenta of the
order of the inverse of the two-body scattering length, and an infinite number
of graphs must be summed. This summation leads to a cutoff dependence that does
not appear in any order in perturbation theory. We argue that this cutoff
dependence can be absorbed in a single three-body counterterm and compute the
running of the three-body force with the cutoff. We comment on relevance of
this result for the effective field theory program in nuclear and molecular
physics.Comment: 5 pages, RevTex, 4 PS figures included with epsf.sty, some clarifying
comments added, version to appear in Phys. Rev. Let
The Three-Boson System at Next-To-Next-To-Leading Order
We discuss effective field theory treatments of the problem of three
particles interacting via short-range forces (range R >> a_2, with a_2 the
two-body scattering length). We show that forming a once-subtracted scattering
equation yields a scattering amplitude whose low-momentum part is
renormalization-group invariant up to corrections of O(R^3/a_2^3). Since
corrections of O(R/a_2) and O(R^2/a_2^2) can be straightforwardly included in
the integral equation's kernel, a unique solution for 1+2 scattering phase
shifts and three-body bound-state energies can be obtained up to this accuracy.
We use our equation to calculate the correlation between the binding energies
of Helium-4 trimers and the atom-dimer scattering length. Our results are in
excellent agreement with the recent three-dimensional Faddeev calculations of
Roudnev and collaborators that used phenomenological inter-atomic potentials.Comment: 20 pages, 3 eps figure
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
Strangeness in the nucleon and the ratio of proton-to-neutron neutrino-induced quasi-elastic yield
The electroweak form factors of the nucleon as obtained within a three flavor
pseudoscalar vector meson soliton model are employed to predict the ratio of
the proton and neutron yields from , which are induced by quasi-elastic
neutrino reactions. These predictions are found to vary only moderately in the
parameter space allowed by the model. The antineutrino flux of the up-coming
experiment determining this ratio was previously overestimated. The
corresponding correction is shown to have only a small effect on the predicted
ratio. However, it is found that the experimental result for the ratio
crucially depends on an accurate measurement of the energy of the knocked out
nucleon.Comment: 17 pages, LaTeX, 2 tables, 4 figures, Discussion on shape of strange
form factors added, Z. Phys. A, to be publishe