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Combining Symbolic and Numerical Computing in the Multi-Band-Phonon-Projection Model

J. Suhonen
O. Lahde
Journal / Anthology

Mathematics with Vision: Proceedings of the First International Mathematica Symposium
Year: 1995
Page range: 243-250

The new collective model, which is an extension of the Extended Phonon Projection Model [1] includes two-intrinsic-phonon excited bands. The generalized collective model is a phenomenological model for the description of the low energy collective properties of even-even nuclei, i.e. nuclei with even charge and neutron numbers. Physical picture behind the model is that these nuclei behave like incompressible liquid drops, especially for higher mass-numbers. Thus, the model neclets the 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, transition probabilities, etc. of given collective hamiltonians. Mathematica offers very powerful tools to compute the elements of the hamiltonian matrix. The elements, which include integrals, are quite complicated. But now we have for the first time the new opportunity to symbolically compute these integrals. By using the built-in Mathematica functions and numerical facilities of Mathematica, we get high precision values for these integrals. when writing the code we employed rule-based and dynamical (recursive) programming which produced the symbolic expressions for the definite integrals involved.

*Science > Physics > Quantum Physics