Geometric Collective Model of Atomic Nuclei: Finite Element Method Implementations

The piecewise polynomial functions constructed from the multivariate Hermitian interpolation polynomials that are continuous together with derivatives on the boundaries of finite elements are used in implementations of the high-accuracy finite element method (FEM). The efficiency of our finite element schemes, algorithms and program GCMFEM implemented in Maple and Mathematica are demonstrated by reference calculations of the boundary value problems (BVPs) for the Geometric Collective Model (GSM) of atomic nuclei. The BVP for GSM is reduced also to the BVP for a system of ordinary differential equations, which is solved by program KANTBP 5M implemented in Maple and compared with solution of algebraic eigenvalue problem in representation of the basis functions associated within irreducible representations of the \(U(5) \supset O(5) \supset O(3)\) chain of groups.