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 $^7$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 H2_2@C60_{60}

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