509 research outputs found
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
Supersymmetric transformations for coupled channels with threshold differences
The asymptotic behaviour of the superpotential of general SUSY
transformations for a coupled-channel Hamiltonian with different thresholds is
analyzed. It is shown that asymptotically the superpotential can tend to a
diagonal matrix with an arbitrary number of positive and negative entries
depending on the choice of the factorization solution. The transformation of
the Jost matrix is generalized to "non-conservative" SUSY transformations
introduced in Sparenberg et al (2006 J. Phys. A: Math. Gen. 39 L639). Applied
to the zero initial potential the method permits to construct superpartners
with a nontrivially coupled Jost-matrix. Illustrations are given for two- and
three-channel cases.Comment: 17 pages, 3 explicit examples and figures adde
Correlation energies by the generator coordinate method: computational aspects for quadrupolar deformations
We investigate truncation schemes to reduce the computational cost of
calculating correlations by the generator coordinate method based on mean-field
wave functions. As our test nuclei, we take examples for which accurate
calculations are available. These include a strongly deformed nucleus, 156Sm, a
nucleus with strong pairing, 120Sn, the krypton isotope chain which contains
examples of soft deformations, and the lead isotope chain which includes the
doubly magic 208Pb. We find that the Gaussian overlap approximation for angular
momentum projection is effective and reduces the computational cost by an order
of magnitude. Cost savings in the deformation degrees of freedom are harder to
realize. A straightforward Gaussian overlap approximation can be applied rather
reliably to angular-momentum projected states based on configuration sets
having the same sign deformation (prolate or oblate), but matrix elements
between prolate and oblate deformations must be treated with more care. We
propose a two-dimensional GOA using a triangulation procedure to treat the
general case with both kinds of deformation. With the computational gains from
these approximations, it should be feasible to carry out a systematic
calculation of correlation energies for the nuclear mass table.Comment: 11 pages revtex, 9 eps figure
Eigenphase preserving two-channel SUSY transformations
We propose a new kind of supersymmetric (SUSY) transformation in the case of
the two-channel scattering problem with equal thresholds, for partial waves of
the same parity. This two-fold transformation is based on two imaginary
factorization energies with opposite signs and with mutually conjugated
factorization solutions. We call it an eigenphase preserving SUSY
transformation as it relates two Hamiltonians, the scattering matrices of which
have identical eigenphase shifts. In contrast to known phase-equivalent
transformations, the mixing parameter is modified by the eigenphase preserving
transformation.Comment: 16 pages, 1 figur
Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States
We consider the multi-channel inverse scattering problem in one-dimension in
the presence of thresholds and bound states for a potential of finite support.
Utilizing the Levin representation, we derive the general Marchenko integral
equation for N-coupled channels and show that, unlike to the case of the radial
inverse scattering problem, the information on the bound state energies and
asymptotic normalization constants can be inferred from the reflection
coefficient matrix alone. Thus, given this matrix, the Marchenko inverse
scattering procedure can provide us with a unique multi-channel potential. The
relationship to supersymmetric partner potentials as well as possible
applications are discussed. The integral equation has been implemented
numerically and applied to several schematic examples showing the
characteristic features of multi-channel systems. A possible application of the
formalism to technological problems is briefly discussed.Comment: 19 pages, 5 figure
Coupling between scattering channels with SUSY transformations for equal thresholds
Supersymmetric (SUSY) transformations of the multi-channel Schr\"odinger
equation with equal thresholds and arbitrary partial waves in all channels are
studied. The structures of the transformation function and the superpotential
are analyzed. Relations between Jost and scattering matrices of superpartner
potentials are obtained. In particular, we show that a special type of SUSY
transformation allows us to introduce a coupling between scattering channels
starting from a potential with an uncoupled scattering matrix. The possibility
for this coupling to be trivial is discussed. We show that the transformation
introduces bound and virtual states with a definite degeneracy at the
factorization energy. A detailed study of the potential and scattering matrices
is given for the case. The possibility of inverting coupled-channel
scattering data by such a SUSY transformation is demonstrated by several
examples (, and partial waves)
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/
Variational collocation for systems of coupled anharmonic oscillators
We have applied a collocation approach to obtain the numerical solution to
the stationary Schr\"odinger equation for systems of coupled oscillators. The
dependence of the discretized Hamiltonian on scale and angle parameters is
exploited to obtain optimal convergence to the exact results. A careful
comparison with results taken from the literature is performed, showing the
advantages of the present approach.Comment: 14 pages, 10 table
Breakup reaction models for two- and three-cluster projectiles
Breakup reactions are one of the main tools for the study of exotic nuclei,
and in particular of their continuum. In order to get valuable information from
measurements, a precise reaction model coupled to a fair description of the
projectile is needed. We assume that the projectile initially possesses a
cluster structure, which is revealed by the dissociation process. This
structure is described by a few-body Hamiltonian involving effective forces
between the clusters. Within this assumption, we review various reaction
models. In semiclassical models, the projectile-target relative motion is
described by a classical trajectory and the reaction properties are deduced by
solving a time-dependent Schroedinger equation. We then describe the principle
and variants of the eikonal approximation: the dynamical eikonal approximation,
the standard eikonal approximation, and a corrected version avoiding Coulomb
divergence. Finally, we present the continuum-discretized coupled-channel
method (CDCC), in which the Schroedinger equation is solved with the projectile
continuum approximated by square-integrable states. These models are first
illustrated by applications to two-cluster projectiles for studies of nuclei
far from stability and of reactions useful in astrophysics. Recent extensions
to three-cluster projectiles, like two-neutron halo nuclei, are then presented
and discussed. We end this review with some views of the future in
breakup-reaction theory.Comment: Will constitute a chapter of "Clusters in Nuclei - Vol.2." to be
published as a volume of "Lecture Notes in Physics" (Springer
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