Numerical and symbolic calculation of the multipole matrix elements in the axial and triaxial harmonic oscillator basis Original Research Article

General expressions for matrix elements of the electric multipole operators in axial and triaxial harmonic oscillator basis are given. In each case we present algorithms which are either well suited for efficient numerical evaluation or for algebraic manipulation, using symbols representing the quantum numbers and the oscillator lengths. A Mathematica program using the symbolic algorithm is also presented. In the axial case, a function which provides the selection rules is implemented, thus being able to generate a full table with all the allowed transitions for a given multipolarity.