Abstract
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.
Highlights
Introduction and MotivationUtilization of several important physical models is limited to specialists in the field and broad-scope programs are not generally available to a larger pool of scientists
Hamiltonian [1,2] has been extended to a more complete model and it is known with a few different names: often called the Bohr–Mottelson model from the name of the two Nobel prize winning proposers, or it is called Geometric Collective Model (GCM) with reference to the fact that macroscopic variables are used to parameterize the geometric shape of a drop of quantum fluid and to describe the normal modes of vibrations of its surface, or it is called Roto-Vibrational model with reference to the ability of the model to describe on the same footing the quantum vibrational and rotational spectra that are observed at low excitation energy of even-even nuclei
These names merge with the so-called Generalized Collective Model of Gneuss and Greiner (Frankfurt model) [3,4] that used the simplest possible potential energy form built out of invariant operators that has anyway the property of giving all the relevant configurations: spherical, axially
Summary
Utilization of several important physical models is limited to specialists in the field and broad-scope programs are not generally available to a larger pool of scientists. Computation 2018, 6, 48 deformed (prolate or oblate), triaxial and γ-unstable All these naming schemes usually refer to the model limited to the quadrupole degree of freedom, which is by far the most important, except in very high mass nuclei, but other types of motion (octupole, hexadecupole, etc.) have been studied with generalized versions of this model. This model has the virtue of catching the essence of low-energy nuclear excitations and provides a convenient language for classifying important spectroscopic data in terms of β- and γ-bands and a convenient mathematical formalism for further calculations (quadrupole moments, electromagnetic transitions, etc.).
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