Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in ...atomic, nuclear and particle physics, astrophysics, quantum chemistry, etc. In recent years, however, an alternative technique based on the semi-spectral methods has focused considerable attention. The purpose of this work is first to provide the necessary tools and subsequently examine the efficiency of this method in quantum mechanical applications. Restricting our interest to time-independent two-body problems, we obtained the continuous and discrete spectrum solutions of the underlying Schrödinger or Lippmann–Schwinger equations in both, the coordinate and momentum space. In all of the numerically studied examples we had no difficulty in achieving the machine accuracy and the semi-spectral method showed exponential convergence combined with excellent numerical stability.
A semi-spectral Chebyshev method for solving numerically singular integral equations is presented and applied in the quarkonium bound-state problem in momentum space. The integrals containing both, ...logarithmic and Cauchy singular kernels, can be evaluated without subtractions by dedicated automatic quadratures. By introducing a Chebyshev mesh and using the Nystrom algorithm the singular integral equation is converted into an algebraic eigenvalue problem that can be solved by standard methods. The proposed scheme is very simple to use, is easy in programming and highly accurate.
Hadronic atoms provide a unique laboratory for studying hadronic interactions essentially at threshold. This text is the first book-form exposition of hadronic atom theory with emphasis on recent ...developments, both theoretical and experimental. Since the underlying Hamiltonian is a non-self-adjoined operator, the theory goes beyond traditional quantum mechanics and this book covers topics that are often glossed over in standard texts on nuclear physics. The material contained here is intended for the advanced student and researcher in nuclear, atomic or elementary-particle physics. A good knowledge of quantum mechanics and familiarity with nuclear physics are presupposed.
The proton–proton and proton–
η
′
invariant mass distributions have been determined for the
pp
→
pp
η
′
reaction at an excess energy of
Q
=
16.4
MeV
. The measurement was carried out using the ...COSY-11 detector setup and the proton beam of the cooler synchrotron COSY. The shapes of the determined invariant mass distributions are similar to those of the
pp
→
pp
η
reaction and reveal an enhancement for large relative proton–proton momenta. This result, together with the fact that the proton–
η interaction is much stronger that the proton–
η
′
interaction, excludes the hypothesis that the observed enhancement is caused by the interaction between the proton and the meson.
Exact expressions are presented for efficient computation of the weights in Gauss–Legendre and Chebyshev quadratures for selected singular integrands. The singularities may be of Cauchy type, ...logarithmic type or algebraic-logarithmic end-point branching points. We provide Fortran 90 routines for computing the weights for both the Gauss–Legendre and the Chebyshev (Fejér-1) meshes whose size can be set by the user.
Program title: SINGQUAD
Catalogue identifier: AEBR_v1_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/AEBR_v1_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 4128
No. of bytes in distributed program, including test data, etc.: 25 815
Distribution format: tar.gz
Programming language: Fortran 90
Computer: Any with a Fortran 90 compiler
Operating system: Linux, Windows, Mac
RAM: Depending on the complexity of the problem
Classification: 4.11
Nature of problem: Program provides Gauss–Legendre and Chebyshev (Fejér-1) weights for various singular integrands.
Solution method: The weights are obtained from the condition that the quadrature of order
N must be exact for a polynomial of
degree
⩽
(
N
−
1
)
. The weights are expressed as moments of the singular kernels associated with Legendre or Chebyshev polynomials. These moments are obtained in analytic form amenable for computation.
Additional comments: If the NAGWare f95 compiler is used, the option, “-kind = byte”, must be included in the compile command lines of the Makefile.
Running time: The test run supplied with the distribution takes a couple of seconds to execute.
Solving a Deconvolution Problem in Photon Spectrometry Aleksandrov, D.; Alme, J.; Basmanov, V. ...
Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment,
2010, Volume:
620, Issue:
2
Journal Article
Peer reviewed
We solve numerically a deconvolution problem to extract the undisturbed spectrum from the measured distribution contaminated by the finite resolution of the measuring device. A problem of this kind ...emerges when one wants to infer the momentum distribution of the neutral pions by detecting the
π
0
decay photons using the photon spectrometer of the ALICE LHC experiment at CERN
1. The underlying integral equation connecting the sought for pion spectrum and the measured gamma spectrum has been discretized and subsequently reduced to a system of linear algebraic equations. The latter system, however, is known to be ill-posed and must be regularized to obtain a stable solution. This task has been accomplished here by means of the Tikhonov regularization scheme combined with the L-curve method. The resulting pion spectrum is in an excellent quantitative agreement with the pion spectrum obtained from a Monte Carlo simulation.
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