27 research outputs found
Condensates of Strongly-interacting Atoms and Dynamically Generated Dimers
In a system of atoms with large positive scattering length, weakly-bound
diatomic molecules (dimers) are generated dynamically by the strong
interactions between the atoms. If the atoms are modeled by a quantum field
theory with an atom field only, condensates of dimers cannot be described by
the mean-field approximation because there is no field associated with the
dimers. We develop a method for describing dimer condensates in such a model
based on the one-particle-irreducible (1PI) effective action. We construct an
equivalent 1PI effective action that depends not only on the classical atom
field but also on a classical dimer field. The method is illustrated by
applying it to the many-body behavior of bosonic atoms with large scattering
length at zero temperature using an approximation in which the 2-atom amplitude
is treated exactly but irreducible -atom amplitudes for are
neglected. The two 1PI effective actions give identical results for the atom
superfluid phase, but the one with a classical dimer field is much more
convenient for describing the dimer superfluid phase. The results are also
compared with previous work on the Bose gas near a Feshbach resonance.Comment: 10 figure
Resonant Dimer Relaxation in Cold Atoms with a Large Scattering Length
Efimov physics refers to universal phenomena associated with a discrete
scaling symmetry in the 3-body problem with a large scattering length. The
first experimental evidence for Efimov physics was the recent observation of a
resonant peak in the 3-body recombination rate for 133Cs atoms with large
negative scattering length. There can also be resonant peaks in the atom-dimer
relaxation rate for large positive scattering length. We calculate the
atom-dimer relaxation rate as a function of temperature and show how
measurements of the relaxation rate can be used to determine accurately the
parameters that govern Efimov physics.Comment: 4 pages, 2 eps figures, normalization error in figures corrected,
equations unchange
Compact and Loosely Bound Structures in Light Nuclei
A role of different components in the wave function of the weakly bound light
nuclei states was studied within the framework of the cluster model, taking
into account of orbitals "polarization". It was shown that a limited number of
structures associated with the different modes of nucleon motion can be of
great importance for such systems. Examples of simple and quite flexible trial
wave functions are given for the nuclei Be, He. Expressions for the
microscopic wave functions of these nuclei were found and used for the
calculation of basic nuclear characteristics, using well known central-exchange
nucleon-nucleon potentials.Comment: 19 pages, 3 ps figure
Controlling a resonant transmission across the -potential: the inverse problem
Recently, the non-zero transmission of a quantum particle through the
one-dimensional singular potential given in the form of the derivative of
Dirac's delta function, , with , being a
potential strength constant, has been discussed by several authors. The
transmission occurs at certain discrete values of forming a resonance
set . For
this potential has been shown to be a perfectly reflecting wall. However, this
resonant transmission takes place only in the case when the regularization of
the distribution is constructed in a specific way. Otherwise, the
-potential is fully non-transparent. Moreover, when the transmission
is non-zero, the structure of a resonant set depends on a regularizing sequence
that tends to in the sense of
distributions as . Therefore, from a practical point of
view, it would be interesting to have an inverse solution, i.e. for a given
to construct such a regularizing sequence
that the -potential at this value is
transparent. If such a procedure is possible, then this value
has to belong to a corresponding resonance set. The present paper is devoted to
solving this problem and, as a result, the family of regularizing sequences is
constructed by tuning adjustable parameters in the equations that provide a
resonance transmission across the -potential.Comment: 21 pages, 4 figures. Corrections to the published version added;
http://iopscience.iop.org/1751-8121/44/37/37530
Effect of Coulomb Forces on the Position of the Pole in the Scattering Amplitude and on Its Residue
Explicit expressions of the vertex constant for the decay of a nucleus into
two charged particles for an arbitrary orbital momentum are derived for the
standard expansion of the effective-range function , as well as when
the function has a pole. As physical examples, we consider the bound
state of the nucleus and the resonant states of the nuclei
He and He in the s-wave, and those of and
in the p-wave. For the systems and the pole
trajectories are constructed in the complex planes of the momentum and of the
renormalized vertex constant. They correspond to a transition from the
resonance state to the virtual state while the Coulomb forces gradually
decrease to zero.Comment: 17 pages, 5 figure
Description of the two-nucleon system on the basis of the Bargmann representation of the S matrix
For the effective-range function , a pole approximation that
involves a small number of parameters is derived on the basis of the Bargmann
representation of the matrix. The parameters of this representation, which
have a clear physical meaning, are related to the parameters of the Bargmann
matrix by simple equations. By using a polynomial least-squares fit to the
function at low energies, the triplet low-energy parameters of
neutron-proton scattering are obtained for the latest experimental data of
Arndt et al. on phase shifts. The results are fm, fm, and fm. With allowance for the values found for the
low-energy scattering parameters and for the pole parameter, the pole
approximation of the function provides an excellent description
of the triplet phase shift for neutron-proton scattering over a wide energy
range (MeV), substantially improving the
description at low energies as well. For the experimental phase shifts of Arndt
et al., the triplet shape parameters of the effective-range expansion
are obtained by using the pole approximation. The description of the phase
shift by means of the effective-range expansion featuring values found for the
low-energy scattering parameters proves to be fairly accurate over a broad
energy region extending to energy values approximately equal to the energy at
which this phase shift changes sign, this being indicative of a high accuracy
and a considerable value of the effective-range expansion in describing
experimental data on nucleon-nucleon scattering. The properties of the deuteron
that were calculated by using various approximations of the effective-range
function comply well with their experimental values.Comment: 39 pages, 3 figure