65 research outputs found
Self-consistent calculation of nuclear photoabsorption cross section: Finite amplitude method with Skyrme functionals in the three-dimensional real space
The finite amplitude method (FAM), which we have recently proposed (T.
Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)),
simplifies significantly the fully self-consistent RPA calculation. Employing
the FAM, we are conducting systematic, fully self-consistent response
calculations for a wide mass region. This paper is intended to present a
computational scheme to be used in the systematic investigation and to show the
performance of the FAM for a realistic Skyrme energy functional. We implemented
the method in the mixed representation in which the forward and backward RPA
amplitudes are represented by indices of single-particle orbitals for occupied
states and the spatial grid points for unoccupied states. We solve the linear
response equation for a given frequency. The equation is a linear algebraic
problem with a sparse non-hermitian matrix, which is solved with an iterative
method. We show results of the dipole response for selected spherical and
deformed nuclei. The peak energies of the giant dipole resonance agree well
with measurements for heavy nuclei, while they are systematically
underestimated for light nuclei. We also discuss the width of the giant dipole
resonance in the fully self-consistent RPA calculation.Comment: 11 pages, 10 figure
Systems of Hess-Appel'rot Type and Zhukovskii Property
We start with a review of a class of systems with invariant relations, so
called {\it systems of Hess--Appel'rot type} that generalizes the classical
Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an
interesting combination of both integrable and non-integrable properties.
Further, following integrable line, we study partial reductions and systems
having what we call the {\it Zhukovskii property}: these are Hamiltonian
systems with invariant relations, such that partially reduced systems are
completely integrable. We prove that the Zhukovskii property is a quite general
characteristic of systems of Hess-Appel'rote type. The partial reduction
neglects the most interesting and challenging part of the dynamics of the
systems of Hess-Appel'rot type - the non-integrable part, some analysis of
which may be seen as a reconstruction problem. We show that an integrable
system, the magnetic pendulum on the oriented Grassmannian has
natural interpretation within Zhukovskii property and it is equivalent to a
partial reduction of certain system of Hess-Appel'rot type. We perform a
classical and an algebro-geometric integration of the system, as an example of
an isoholomorphic system. The paper presents a lot of examples of systems of
Hess-Appel'rot type, giving an additional argument in favor of further study of
this class of systems.Comment: 42 page
Forming studentspersonal competences of technical university in the field of life safety
Сформульовані особистісні компетенції студентів в області безпеки життєдіяльності.Personal competencies of students are formulated in the field of life safety
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