Symbolic-Numeric Algorithm for Calculations in Geometric Collective Model of Atomic Nuclei

• Published in: Computer Algebra in Scientific Computing Vol. 13366; pp. 103 - 123
• Main Authors: Deveikis, Algirdas, Gusev, Alexander A., Vinitsky, Sergue I., Blinkov, Yuri A., Góźdź, Andrzej, Pȩdrak, Aleksandra, Hess, Peter O.
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2022; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Atomic nuclei; Geometric Collective Model; Gram-Schmidt orthonormalization; Groups; Irreducible representations; Orthonormal non-canonical basis; Spectral characteristic
• ISBN: 9783031147876; 3031147871
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-031-14788-3_7

We developed a symbolic–numeric algorithm involving a set of effective symbolic and numerical procedures for calculations of low lying energy spectra and eigenfunctions of atomic nuclei. The eigenfunctions are expanded over the orthonormal noncanonical U(5)⊃O(5)⊃O(3) $$U(5) {\supset } O(5) {\supset } O(3)$$ basis in Geometric Collective Model. We give implementation of the algorithm and procedures in Wolfram Mathematica. We present benchmark calculations of energy spectrum, quadrupole moment and the reduced upwards transition probability B(E2) for the nucleus 186 $$^{186}$$ Os.