820 research outputs found
Equivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix methods
Siegert pseudostates are purely outgoing states at some fixed point expanded
over a finite basis. With discretized variables, they provide an accurate
description of scattering in the s wave for short-range potentials with few
basis states. The R-matrix method combined with a Lagrange basis, i.e.
functions which vanish at all points of a mesh but one, leads to simple
mesh-like equations which also allow an accurate description of scattering.
These methods are shown to be exactly equivalent for any basis size, with or
without discretization. The comparison of their assumptions shows how to
accurately derive poles of the scattering matrix in the R-matrix formalism and
suggests how to extend the Siegert-pseudostate method to higher partial waves.
The different concepts are illustrated with the Bargmann potential and with the
centrifugal potential. A simplification of the R-matrix treatment can usefully
be extended to the Siegert-pseudostate method.Comment: 19 pages, 1 figur
One-electron atomic-molecular ions containing Lithium in a strong magnetic field
The one-electron Li-containing Coulomb systems of atomic type and
molecular type , and are studied in
the presence of a strong magnetic field a.u. in the
non-relativistic framework. They are considered at the Born-Oppenheimer
approximation of zero order (infinitely massive centers) within the parallel
configuration (molecular axis parallel to the magnetic field). The variational
and Lagrange-mesh methods are employed in complement to each other. It is
demonstrated that the molecular systems , and
can exist for sufficiently strong magnetic fields a.u. and that can even be stable at
magnetic fields typical of magnetars.Comment: 22 pages, 9 figures, 4 table
Study of the 16O(p,gamma) Reaction at Astrophysical Energies
The Feshbach theory of the optical potential naturally leads to a microscopic
description of scattering in terms of the many-body self-energy. We consider a
recent calculation of this quantity for 16O and study the possibility of
applying it at astrophysical energies. The results obtained for the phase
shifts and the 16O(p,\gamma) capture suggest that such studies are feasible but
the calculations require some improvement geared to this specific task.Comment: 4 pages, 3 figures; Proceedings of Nuclei In The Cosmos VIII, to
appear in Nucl. Phys.
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
Toward a Spin- and Parity-Independent Nucleon-Nucleon Potential
A supersymmetric inversion method is applied to the singlet and
neutron-proton elastic phase shifts. The resulting central potential
has a one-pion-exchange (OPE) long-range behavior and a parity-independent
short-range part; it fits inverted data well. Adding a regularized OPE tensor
term also allows the reproduction of the triplet , and
phase shifts as well as of the deuteron binding energy. The potential is thus
also spin-independent (except for the OPE part) and contains no spin-orbit
term. These important simplifications of the neutron-proton interaction are
shown to be possible only if the potential possesses Pauli forbidden bound
states, as proposed in the Moscow nucleon-nucleon model.Comment: 9 pages, RevTeX, 5 ps figure
A generalized Tullock contest
We construct a generalized Tullock contest under complete information where contingent upon winning or losing, the payoff of a player is a linear function of prizes, own effort, and the effort of the rival. This structure nests a number of existing contests in the literature and can be used to analyze new types of contests. We characterize the unique symmetric equilibrium and show that small parameter modifications may lead to substantially different types of contests and hence different equilibrium effort levels
Microscopic description of the beta delayed deuteron emission from \bbox{^6}He
The beta delayed deuteron emission from He is studied in a dynamical
microscopic cluster model. This model gives a reasonably good description for
all the subsystems of He and Li in a coherent way, without any free
parameter. The beta decay transition probability to the Li ground state is
underestimated by a few percents. The theoretical beta delayed deuteron
spectrum is close to experiment but it is also underestimated by about a factor
1.7. We argue that, in spite of their different magnitudes, both
underestimations might have a common origin. The model confirms that the
neutron halo part of the He wave function plays a crucial role in quenching
the beta decay toward the + d channel.Comment: LATEX with REVTEX, Submitted to Phys. Rev. C, 11 pages, 3 figures
(not included) are available upon request. ATOMKI-93/
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