37 research outputs found
One-dimensional Bose chemistry: effects of non-integrability
Three-body collisions of ultracold identical Bose atoms under tight
cylindrical confinement are analyzed. A Feshbach resonance in two-body
collisions is described by a two-channel zero-range interaction. Elimination of
the closed channel in the three-body problem reduces the interaction to a
one-channel zero-range one with an energy dependent strength. The related
problem with an energy independent strength (the Lieb-Liniger-McGuire model)
has an exact solution and forbids all chemical processes, such as three-atom
association and diatom dissociation, as well as reflection in atom-diatom
collisions. The resonant case is analyzed by a numerical solution of the
Faddeev-Lovelace equations. The results demonstrate that as the internal
symmetry of the Lieb-Liniger-McGuire model is lifted, the reflection and
chemical reactions become allowed and may be observed in experiments.Comment: 5 pages, 4 figure
Quantum Transparency of Barriers for Structure Particles
Penetration of two coupled particles through a repulsive barrier is
considered. A simple mechanism of the appearance of barrier resonances is
demonstrated that makes the barrier anomalously transparent as compared to the
probability of penetration of structureless objects. It is indicated that the
probabilities of tunnelling of two interacting particles from a false vacuum
can be considerably larger than it was assumed earlier.Comment: Revtex, 4 pages, 4 figure
The explanation of unexpected temperature dependence of the muon catalysis in solid deuterium
It is shown that due to the smallness of the inelastic cross-section of the
-atoms scattering in the crystal lattice at sufficiently low temperatures
the -mesomolecules formation from the upper state of the hyperfine
structure starts earlier than the mesoatoms thermolization. It
explains an approximate constancy of the -mesomolecule formation rate in
solid deuterium.Comment: 6 pages, 2 jpeg-figure
New representation of orbital motion with arbitrary angular momenta
A new formulation is presented for a variational calculation of -body
systems on a correlated Gaussian basis with arbitrary angular momenta. The
rotational motion of the system is described with a single spherical harmonic
of the total angular momentum , and thereby needs no explicit coupling of
partial waves between particles. A simple generating function for the
correlated Gaussian is exploited to derive the matrix elements. The formulation
is applied to various Coulomb three-body systems such as , and up to in order to show its usefulness and
versatility. A stochastic selection of the basis functions gives good results
for various angular momentum states.Comment: Revte
Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field
A countable set of asymptotic space -- localized solutions is constructed by
the complex germ method in the adiabatic approximation for 3D Hartree type
equations with a quadratic potential. The asymptotic parameter is 1/T, where
is the adiabatic evolution time.
A generalization of the Berry phase of the linear Schr\"odinger equation is
formulated for the Hartree type equation. For the solutions constructed, the
Berry phases are found in explicit form.Comment: 15 pages, no figure
Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
A countable set of asymptotic space -- localized solutions is constructed by
the complex germ method in the adiabatic approximation for the nonstationary
Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic
potential. The asymptotic parameter is 1/T, where is the adiabatic
evolution time.
A generalization of the Berry phase of the linear Schr\"odinger equation is
formulated for the Gross-Pitaevskii equation. For the solutions constructed,
the Berry phases are found in explicit form.Comment: 13 pages, no figure
Three-body halos. V. Computations of continuum spectra for Borromean nuclei
We solve the coordinate space Faddeev equations in the continuum. We employ
hyperspherical coordinates and provide analytical expressions allowing easy
computation of the effective potentials at distances much larger than the
ranges of the interactions where only s-waves in the different Jacobi
coordinates couple. Realistic computations are carried out for the Borromean
halo nuclei 6He (n+n+\alpha) for J\pi = 0+-, 1+-, 2+- and 11Li (n+n+9Li) for
(1/2)+-, (3/2)+-, (5/2)+-. Ground state properties, strength functions, Coulomb
dissociation cross sections, phase shifts, complex S-matrix poles are computed
and compared to available experimental data. We find enhancements of the
strength functions at low energies and a number of low-lying S-matrix poles.Comment: 35 pages, 14 figure