1,225 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
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.
Variational collocation on finite intervals
In this paper we study a new family of sinc--like functions, defined on an
interval of finite width. These functions, which we call ``little sinc'', are
orthogonal and share many of the properties of the sinc functions. We show that
the little sinc functions supplemented with a variational approach enable one
to obtain accurate results for a variety of problems. We apply them to the
interpolation of functions on finite domain and to the solution of the
Schr\"odinger equation, and compare the performance of present approach with
others.Comment: 12 pages, 8 figures, 1 tabl
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