105 research outputs found
Comparison of numerical methods for the calculation of cold atom collisions
Three different numerical techniques for solving a coupled channel
Schroedinger equation are compared. This benchmark equation, which describes
the collision between two ultracold atoms, consists of two channels, each
containing the same diagonal Lennard-Jones potential, one of positive and the
other of negative energy. The coupling potential is of an exponential form. The
methods are i) a recently developed spectral type integral equation method
based on Chebyshev expansions, ii) a finite element expansion, and iii) a
combination of an improved Numerov finite difference method and a Gordon
method. The computing time and the accuracy of the resulting phase shift is
found to be comparable for methods i) and ii), achieving an accuracy of ten
significant figures with a double precision calculation. Method iii) achieves
seven significant figures. The scattering length and effective range are also
obtained.Comment: 22 pages, 3 figures, submitted to J. Comput. Phys. documentstyle
[thmsa,sw20aip]{article} in .te
Inclusion of virtual nuclear excitations in the formulation of the (e,e'N)
A wave-function framework for the theory of the (e,e'N) reaction is presented
in order to justify the use of coupled channel equations in the usual Feynman
matrix element. The overall wave function containing the electron and nucleon
coordinates is expanded in a basis set of eigenstates of the nuclear
Hamiltonian, which contain both bound states as well as continuum states.. The
latter have an ingoing nucleon with a variable momentum Q incident on the
daughter nucleus as a target, with as many outgoing channels as desirable. The
Dirac Eqs. for the electron part of the wave function acquire inhomogeneous
terms, and require the use of distorted electron Green's functions for their
solutions. The condition that the asymptotic wave function contain only the
appropriate momentum Q_k for the outgoing nucleon, which corresponds to the
electron momentum k through energy conservation, is achieved through the use of
the steepest descent saddle point method, commonly used in three-body
calculations.Comment: 30 page
Complex Conjugate Pairs in Stationary Sturmians
Sturmian eigenstates specified by stationary scattering boundary conditions
are particularly useful in contexts such as forming simple separable two
nucleon t matrices, and are determined via solution of generalised eigenvalue
equation using real and symmetric matrices. In general, the spectrum of such an
equation may contain complex eigenvalues. But to each complex eigenvalue there
is a corresponding conjugate partner. In studies using realistic
nucleon--nucleon potentials, and in certain positive energy intervals, these
complex conjugated pairs indeed appear in the Sturmian spectrum. However, as we
demonstrate herein, it is possible to recombine the complex conjugate pairs and
corresponding states into a new, sign--definite pair of real quantities with
which to effect separable expansions of the (real) nucleon--nucleon reactance
matrices.Comment: (REVTEX) 8 Pages, Padova DFPD 93/TH/78 and University of Melbourn
The pion-three-nucleon problem with two-cluster connected-kernel equations
It is found that the coupled piNNN-NNN system breaks into fragments in a
nontrivial way. Assuming the particles as distinguishable, there are indeed
four modes of fragmentation into two clusters, while in the standard three-body
problem there are three possible two-cluster partitions and conversely the
four-body problem has seven different possibilities. It is shown how to
formulate the pion-three-nucleon collision problem through the
integral-equation approach by taking into account the proper fragmentation of
the system. The final result does not depend on the assumption of separability
of the two-body t-matrices. Then, the quasiparticle method a' la
Grassberger-Sandhas is applied and effective two-cluster connected-kernel
equations are obtained. The corresponding bound-state problem is also
formulated, and the resulting homogeneous equation provides a new approach
which generalizes the commonly used techniques to describe the three-nucleon
bound-state problem, where the meson degrees of freedom are usually suppressed.Comment: 20 pages, REVTeX, with 3 COLOR figures (PostScript
Low temperature scattering with the R-matrix method: the Morse potential
Experiments are starting to probe collisions and chemical reactions between
atoms and molecules at ultra-low temperatures. We have developed a new
theoretical procedure for studying these collisions using the R-matrix method.
Here this method is tested for the atom -- atom collisions described by a Morse
potential. Analytic solutions for continuum states of the Morse potential are
derived and compared with numerical results computed using an R-matrix method
where the inner region wavefunctions are obtained using a standard nuclear
motion algorithm. Results are given for eigenphases and scattering lengths.
Excellent agreement is obtained in all cases. Progress in developing a general
procedure for treating ultra-low energy reactive and non-reactive collisions is
discussed.Comment: 18 pages, 6 figures, 3 tables, conferenc
New Discrete Basis for Nuclear Structure Studies
A complete discrete set of spherical single-particle wave functions for
studies of weakly-bound many-body systems is proposed. The new basis is
obtained by means of a local-scale point transformation of the spherical
harmonic oscillator wave functions. Unlike the harmonic oscillator states, the
new wave functions decay exponentially at large distances. Using the new basis,
characteristics of weakly-bound orbitals are analyzed and the ground state
properties of some spherical doubly-magic nuclei are studied. The basis of the
transformed harmonic oscillator is a significant improvement over the harmonic
oscillator basis, especially in studies of exotic nuclei where the coupling to
the particle continuum is important.Comment: 13 pages, RevTex, 6 p.s. figures, submitted to Phys. Rev.
Improved +He potentials by inversion, the tensor force and validity of the double folding model
Improved potential solutions are presented for the inverse scattering problem
for +He data. The input for the inversions includes both the data of
recent phase shift analyses and phase shifts from RGM coupled-channel
calculations based on the NN Minnesota force. The combined calculations provide
a more reliable estimate of the odd-even splitting of the potentials than
previously found, suggesting a rather moderate role for this splitting in
deuteron-nucleus scattering generally. The approximate parity-independence of
the deuteron optical potentials is shown to arise from the nontrivial
interference between antisymmetrization and channel coupling to the deuteron
breakup channels. A further comparison of the empirical potentials established
here and the double folding potential derived from the M3Y effective NN force
(with the appropriate normalisation factor) reveals strong similarities. This
result supports the application of the double folding model, combined with a
small Majorana component, to the description even of such a loosely bound
projectile as the deuteron. In turn, support is given for the application of
iterative-perturbative inversion in combination with the double folding model
to study fine details of the nucleus-nucleus potential. A -He tensor
potential is also derived to reproduce correctly the negative Li quadrupole
moment and the D-state asymptotic constant.Comment: 22 pages, 12 figures, in Revte
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
Quaiselastic scattering from relativistic bound nucleons: Transverse-Longitudinal response
Predictions for electron induced proton knockout from the and
shells in O are presented using various approximations for the
relativistic nucleonic current. Results for the differential cross section,
transverse-longitudinal response () and left-right asymmetry
are compared at (GeV/c) corresponding to TJNAF experiment
89-003. We show that there are important dynamical and kinematical relativistic
effects which can be tested by experiment.Comment: 10 pages, including 2 figures. Removed preliminary experimental data
from the figure
Relativistic mean field approximation to the analysis of 16O(e,e'p)15N data at |Q^2|\leq 0.4 (GeV/c)^2
We use the relativistic distorted wave impulse approximation to analyze data
on 16O(e,e'p)15N at |Q^2|\leq 0.4 (GeV/c)^2 that were obtained by different
groups and seemed controversial. Results for differential cross-sections,
response functions and A_TL asymmetry are discussed and compared to different
sets of experimental data for proton knockout from p_{1/2} and p_{3/2} shells
in 16O. We compare with a nonrelativistic approach to better identify
relativistic effects. The present relativistic approach is found to accommodate
most of the discrepancy between data from different groups, smoothing a long
standing controversy.Comment: 28 pages, 7 figures (eps). Major revision made. New figures added. To
be published in Phys. Rev.
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