733 research outputs found
Analysis of the He decay into the continuum within a three-body model
The beta-decay process of the He halo nucleus into the alpha+d continuum
is studied in a three-body model. The He nucleus is described as an
alpha+n+n system in hyperspherical coordinates on a Lagrange mesh. The
convergence of the Gamow-Teller matrix element requires the knowledge of wave
functions up to about 30 fm and of hypermomentum components up to K=24. The
shape and absolute values of the transition probability per time and energy
units of a recent experiment can be reproduced very well with an appropriate
alpha+d potential. A total transition probability of 1.6E-6 s is
obtained in agreement with that experiment. Halo effects are shown to be very
important because of a strong cancellation between the internal and halo
components of the matrix element, as observed in previous studies. The
forbidden bound state in the alpha+d potential is found essential to reproduce
the order of magnitude of the data. Comments are made on R-matrix fits.Comment: 18 pages, 9 figures. Accepted for publication in Phys.Rev.
A unique decay process: beta delayed emission of a proton and a neutron by the Li halo nucleus
The neutron-rich Li halo nucleus is unique among nuclei with known
separation energies by its ability to emit a proton and a neutron in a
decay process. The branching ratio towards this rare decay mode is evaluated
within a three-body model for the initial bound state and with Coulomb
three-body final scattering states. The branching ratio should be comprised
between two extreme cases, i.e.\ a lower bound obtained
with a pure Coulomb wave and an upper bound obtained with a
plane wave. A simple model with modified Coulomb waves provides plausible
values between between and with
most probable total energies of the proton and neutron between 0.15 and 0.3
MeV.Comment: 15 pages, 3 figure
Phase equivalent potentials for three-body halos
We compare the properties of three-body systems obtained with two-body
potentials with Pauli forbidden states and with the corresponding phase
equivalent two-body potentials. In the first case the forbidden states are
explicitly excluded in the calculation. Differences arise due to the off-shell
properties of these on-shell equivalent potentials. We use the adiabatic
hyperspherical method to formulate a practical prescription to exclude Pauli
forbidden states in three-body calculations. Schematic as well as realistic
potentials are used. Almost indistinguishable results are obtained.Comment: 18 pages, 6 figure
Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for Feshbach resonance
A new type of supersymmetric transformations of the coupled-channel radial
Schroedinger equation is introduced, which do not conserve the vanishing
behavior of solutions at the origin. Contrary to usual transformations, these
``non-conservative'' transformations allow, in the presence of thresholds, the
construction of potentials with coupled scattering matrices from uncoupled
potentials. As an example, an exactly-solvable potential matrix is obtained
which provides a very simple model of Feshbach-resonance phenomenon.Comment: 10 pages, 2 figure
Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation
We construct exact ring soliton-like solutions of the cylindrically symmetric
(i.e., radial) Gross- Pitaevskii equation with a potential, using the
similarity transformation method. Depending on the choice of the allowed free
functions, the solutions can take the form of stationary dark or bright rings
whose time dependence is in the phase dynamics only, or oscillating and
bouncing solutions, related to the second Painlev\'e transcendent. In each case
the potential can be chosen to be time-independent.Comment: 8 pages, 7 figures. Version 2: stability analysis of the dark
solutio
Crossover from one to three dimensions for a gas of hard-core bosons
We develop a variational theory of the crossover from the one-dimensional
(1D) regime to the 3D regime for ultra-cold Bose gases in thin waveguides.
Within the 1D regime we map out the parameter space for fermionization, which
may span the full 1D regime for suitable transverse confinement.Comment: 4 pages, 2 figure
11Li beta decay into 9Li and deuteron within a three-body model
The beta decay process of the 11Li halo nucleus into 9Li and d is studied in
a three-body model. The 11Li nucleus is described as a 9Li+n+n system in
hyperspherical coordinates on a Lagrange mesh. Various 9Li+d potentials are
compared involving a forbidden state, a physical bound state, and a resonance
near 0.25 MeV in the s-wave. With an added surface absorption, they are
compatible with elastic scattering data. The transition probability per time
unit is quite sensitive to the location of the resonance. For a fixed resonance
location, it does not depend much on the potential choice at variance with the
6He delayed deuteron decay. The calculated transition probability per time unit
is larger than the experimental value but the difference can be explained by a
slightly higher resonance location and/or by absorption from the 9Li+d final
channel.Comment: 14 pages, 7 figures, 3 table
- âŠ