3,698 research outputs found
On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator
The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis,
has an infinite symmetric tridiagonal form, also known as Jacobi matrix form.
This Jacobi matrix structure involves a continued fraction representation for
the inverse of the Green's matrix. The continued fraction can be transformed to
a ratio of two hypergeometric functions. From this result we find
an exact analytic formula for the matrix elements of the Green's operator of
the Coulomb Hamiltonian.Comment: 8 page
Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal
(Jacobi) matrix form in some discrete Hilbert-space basis representation, then
its Green's operator can be constructed in terms of a continued fraction. As an
illustrative example we discuss the Coulomb Green's operator in
Coulomb-Sturmian basis representation. Based on this representation, a quantum
mechanical approximation method for solving Lippmann-Schwinger integral
equations can be established, which is equally applicable for bound-, resonant-
and scattering-state problems with free and Coulombic asymptotics as well. The
performance of this technique is illustrated with a detailed investigation of a
nuclear potential describing the interaction of two particles.Comment: 7 pages, 4 ps figures, revised versio
The Optimal Rubbling Number of Ladders, Prisms and M\"obius-ladders
A pebbling move on a graph removes two pebbles at a vertex and adds one
pebble at an adjacent vertex. Rubbling is a version of pebbling where an
additional move is allowed. In this new move, one pebble each is removed at
vertices and adjacent to a vertex , and an extra pebble is added at
vertex . A vertex is reachable from a pebble distribution if it is possible
to move a pebble to that vertex using rubbling moves. The optimal rubbling
number is the smallest number needed to guarantee a pebble distribution of
pebbles from which any vertex is reachable. We determine the optimal
rubbling number of ladders (), prisms () and
M\"oblus-ladders
Jets and produced particles in pp collisions from SPS to RHIC energies for nuclear applications
Higher-order pQCD corrections play an important role in the reproduction of
data at high transverse momenta in the energy range 20 GeV GeV. Recent calculations of photon and pion production in collisions
yield detailed information on the next-to-leading order contributions. However,
the application of these results in proton-nucleus and nucleus-nucleus
collisions is not straightforward. The study of nuclear effects requires a
simplified understanding of the output of these computations. Here we summarize
our analysis of recent calculations, aimed at handling the NLO results by
introducing process and energy-dependent factors.Comment: 4 pages with 5 eps figures include
Constructions for the optimal pebbling of grids
In [C. Xue, C. Yerger: Optimal Pebbling on Grids, Graphs and Combinatorics]
the authors conjecture that if every vertex of an infinite square grid is
reachable from a pebble distribution, then the covering ratio of this
distribution is at most . First we present such a distribution with
covering ratio , disproving the conjecture. The authors in the above paper
also claim to prove that the covering ratio of any pebble distribution is at
most . The proof contains some errors. We present a few interesting
pebble distributions that this proof does not seem to cover and highlight some
other difficulties of this topic
APPLICATION OF PLANAR MODELLING OF BAR STRUCTURES DURING THE EXAMINATION OF THE SZÉCHENYI CHAIN BRIDGE
Planar modelling of Széchenyi Chain bridge used in association with the load test after
the renewal in 1987-88 is presented. The computation was devoted to demonstration of
the distribution of the tension forces in the suspension bars. In order to get adequated
results, a second order theory was used. It was necessary to take the 'load history' of the
bridge into consideration. This effect was evaluated by a 'try-and-error' method
Effective Q-Q Interactions in Constituent Quark Models
We study the performance of some recent potential models suggested as
effective interactions between constituent quarks. In particular, we address
constituent quark models for baryons with hybrid Q-Q interactions stemming from
one-gluon plus meson exchanges. Upon recalculating two of such models we find
them to fail in describing the N and \Delta spectra. Our calculations are based
on accurate solutions of the three-quark systems in both a variational
Schr\"odinger and a rigorous Faddeev approach. It is argued that hybrid {Q-Q}
interactions encounter difficulties in describing baryon spectra due to the
specific contributions from one-gluon and pion exchanges together. In contrast,
a chiral constituent quark model with a Q-Q interaction solely derived from
Goldstone-boson exchange is capable of providing a unified description of both
the N and \Delta spectra in good agreement with phenomenology.Comment: 21 pages, LaTe
Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions
A three-body scattering process in the presence of Coulomb interaction can be
decomposed formally into a two-body single channel, a two-body multichannel and
a genuine three-body scattering. The corresponding integral equations are
coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve
them by applying the Coulomb-Sturmian separable expansion method. We present
elastic scattering and reaction cross sections of the system both below
and above the threshold. We found excellent agreements with previous
calculations in most cases.Comment: 12 pages, 3 figure
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