266 research outputs found
All coordinates transformations that separate the center of mass kinetic energy, their group structure and geometry
The most general coordinates transformations that allow for the exact
separation of the kinetic energy operator of a quantum many-body system into
total center of mass kinetic energy and internal kinetic energy are found and
discussed. We find i) that the suitable transformations, depending on the
number of particles, have a certain number of free parameters and this allows
for the generalization of the Jacobi coordinates to a much larger class of
coordinates with the same properties and ii) that there is a new, uncommon,
additive group structure hidden in the transformation matrices that is
connected to certain geometric properties of the set of coordinates
Break-up and electromagnetic response of light weakly-bound dicluster systems
This study is focused on the break-up and electromagnetic response of light
weakly-bound dicluster nuclei. The cluster picture in the case of Li is
shown to be a very good approximation and in this framework we calculate
nuclear structure observables. We solve the Schr\"odinger equation for the
relative motion both for discrete and continuum states and this automatically
takes into a proper account the role of resonances. A concentration of strength
in the low energy continuum, solely due to the weakly-bound nature of the bound
states is seen and explained as a favourable matching between the wavelengths
of the initial and final states. Finally preliminary results on form factors
are briefly outlined and their microscopic derivation as well as utilization in
reaction studies is discussed.Comment: Contribution to the "Symposium on Nuclear Clusters:from Light Exotic
to Superheavy Nuclei" 284. WE-Heraeus-Seminar, help in Rauischholzhausen
(near Marburg) Germany, 5--9 August 2002. 2 pages, 1 combined figure,
rauisch.sty use
GCM solver (ver. 3.0): a {\it Mathematica} notebook for diagonalization of the Geometric Collective Model (Bohr hamiltonian) with generalized Gneuss-Greiner potential
The program diagonalizes the Geometric Collective Model (Bohr Hamiltonian) with generalized Gneuss–Greiner potential with terms up to the sixth power in β . In nuclear physics, the Bohr–Mottelson model with later extensions into the rotovibrational Collective model is an important theoretical tool with predictive power and it represents a fundamental step in the education of a nuclear physicist. Nuclear spectroscopists might find it useful for fitting experimental data, reproducing spectra, EM transitions and moments and trying theoretical predictions, while students might find it useful for learning about connections between the nuclear shape and its quantum origin. Matrix elements for the kinetic energy operator and for scalar invariants as β 2 and β 3 cos ( 3 γ ) have been calculated in a truncated five-dimensional harmonic oscillator basis with a different program, checked with three different methods and stored in a matrix library for the lowest values of angular momentum. These matrices are called by the program that uses them to write generalized Hamiltonians as linear combinations of certain simple operators. Energy levels and eigenfunctions are obtained as outputs of the diagonalization of these Hamiltonian operators
Algebraic theory of endohedrally confined diatomic molecules: application to H@C
A simple and yet powerful approach for modeling the structure of endohedrally
confined diatomic molecules is introduced. The theory, based on a u(4)+u(3)
dynamical algebra, combines u(4), the vibron model dynamical algebra, with a
u(3) dynamical algebra that models a spherically symmetric three dimensional
potential. The first algebra encompasses the internal roto-vibrations degrees
of freedom of the molecule, while the second takes into account the confined
molecule center-of-mass degrees of freedom. A resulting subalgebra chain is
connected to the underlying physics and the model is applied to the
prototypical case of H2 caged in a fullerene molecule. The spectrum of the
supramolecular complex H2@C60 is described with a few parameters and
predictions for not yet detected levels are made. Our fits suggest that the
quantum numbers of a few lines should be reassigned to obtain better agreement
with data.Comment: 9 pages, 3 figures plus 4 pages of supplemental material. Accepted
for publication in Physical Review
New analytic solutions of the collective Bohr hamiltonian for a beta-soft, gamma-soft axial rotor
New analytic solutions of the quadrupole collective Bohr hamiltonian are
proposed, exploiting an approximate separation of the beta and gamma variables
to describe gamma-soft prolate axial rotors. The model potential is a sum of
two terms: a beta-dependent term taken either with a Coulomb-like or a
Kratzer-like form, and a gamma-dependent term taken as an harmonic oscillator.
In particular it is possible to give a one parameter paradigm for a beta-soft,
gamma-soft axial rotor that can be applied, with a considerable agreement, to
the spectrum of 234U.Comment: (Dipartimento di Fisica ``G.Galilei'' and INFN, via Marzolo 8,
I-35131 Padova, Italy) 10 pages, 3 figure
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