High-precision evaluation of Wigner's d-matrix by exact diagonalization

Abstract

The precise calculations of the Wigner's d-matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using the Wigner's formula suffer from loss of precision. We present a simple method to avoid this problem by expanding the d-matrix into a complex Fourier series and calculate the Fourier coefficients by exactly diagonalizing the angular-momentum operator $J_y$ in the eigenbasis of $J_z$. This method allows us to compute the d-matrix and its various derivatives for spins up to a few thousand. The precision of the d-matrix from our method is about $10^{-14}$ for spins up to $100$.

Comments: 4 pages, 3 figures; a Fortran90 code is included; resubmitted to Phys. Rev. E