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Title

Progress in the symbolic computing of the two-intrinsic-phonon extended EPM
Author

O. Lahde
Journal / Anthology

Innovation in Mathematics: Proceedings of the Second International Mathematica Symposium
Year: 1997
Page range: 323-330
Description

The extension of Extended Phonon Projection Model [1] is so the called Multi-Band-Phonon-Projection-Model. This model includes two-intrinsic-phonon excited bands. The model is a so called geometric collective model, which is a phenomenological model for the description of the low-energy collective properties of even-even nuclei. In all collective models the most important collective degrees of freedom are the quadrupole and octupole vibrations and rotations of statically deformed nuclear shapes. The physical picture behind the model is that these nuclei behave like incompressible liquid drops, especially for higher mass number. Thus, the model neglects single particle properties and determines the physical properties of the nucleus by its shape. From this point of view it is clear that the excitations of the nucleus within this model are vibrations and rotations. Our computer code allows computation of energy spectra of given collective Hamiltonians. Mathematica offers very powerful tools to computer the elements of the energy matrix. We computer the elements, which include integrals by using pattern-matching capabilities built into Mathematica. The pattern-matching is a very powerful and basic ingredient of rule-based programming. When writing the code we employed dynamic (recursive) programming. In the dynamic programming Mathematica will remember the values that it has already calculated, and hence it does not have to recalculate them each time it goes through such a recursive procedure.
Subject

*Science > Physics > Quantum Physics