941 research outputs found

### The R-matrix theory

The different facets of the $R$-matrix method are presented pedagogically in
a general framework. Two variants have been developed over the years: $(i)$ The
"calculable" $R$-matrix method is a calculational tool to derive scattering
properties from the Schr\"odinger equation in a large variety of physical
problems. It was developed rather independently in atomic and nuclear physics
with too little mutual influence. $(ii)$ The "phenomenological" $R$-matrix
method is a technique to parametrize various types of cross sections. It was
mainly (or uniquely) used in nuclear physics. Both directions are explained by
starting from the simple problem of scattering by a potential. They are
illustrated by simple examples in nuclear and atomic physics. In addition to
elastic scattering, the $R$-matrix formalism is applied to transfer and
radiative-capture reactions. We also present more recent and more ambitious
applications of the theory in nuclear physics.Comment: 93 pages, 26 figures. Rep. Prog. Phys., in pres

### 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

### Time-dependent analysis of the nuclear and Coulomb dissociation of 11Be

The breakup of 11Be on carbon and lead targets around 70 MeV/nucleon is
investigated within a semiclassical framework. The role of the 5/2+ resonance
is analyzed in both cases. It induces a narrow peak in the nuclear-induced
breakup cross section, while its effect on Coulomb breakup is small. The
nuclear interactions between the projectile and the target is responsible for
the transition toward this resonant state. The influence of the parametrization
of the 10Be-n potential that simulates 11Be is also addressed. The breakup
calculation is found to be dependent on the potential choice. This leads us to
question the reliability of this technique to extract spectroscopic factors.Comment: 9 pages, 6 figures, to be published in the Proceedings of the Second
Argonne/MSU/JINA/INT RIA Workshop on Reaction Mechanisms for rare Isotope
Beams (2005

### Green's function method for strength function in three-body continuum

Practical methods to compute dipole strengths for a three-body system by
using a discretized continuum are analyzed. New techniques involving Green's
function are developed, either by correcting the tail of the approximate wave
function in a direct calculation of the strength function or by using a
solution of a driven Schroedinger equation in a summed expression of the
strength. They are compared with the complex scaling method and the Lorentz
integral transform, also making use of a discretized continuum. Numerical tests
are performed with a hyperscalar three-body potential in the
hyperspherical-harmonics formalism. They show that the Lorentz integral
transform method is less practical than the other methods because of a
difficult inverse transform. These other methods provide in general comparable
accuracies.Comment: 22 pages, 8 figures, to appear in Progress of Theoretical Physic

### Analysis of the $^6$He $\beta$ decay into the $\alpha+d$ continuum within a three-body model

The beta-decay process of the $^6$He halo nucleus into the alpha+d continuum
is studied in a three-body model. The $^6$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$^{-1}$ 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.

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