Electromagnetic transitions and moments depend upon the reduced nuclear matrix elements \( \langle f\vert\vert {\cal O}(\lambda )\vert\vert i\rangle \). These can be expressed as a sum over one-body transition densities (OBTD) times single-particle matrix elements $$ \langle f\vert\vert {\cal O}(\lambda )\vert\vert i\rangle =\sum _{k_{\alpha } k_{\beta }}\mathrm{OBTD}(f i k_{\alpha } k_{\beta } \lambda ) \langle k_{\alpha }\vert\vert O(\lambda )\vert\vert k_{\beta }\rangle, $$ where the OBTD is given by $$ \mathrm{OBTD}(f i k_{\alpha} k_{\beta}\lambda)= \frac{\langle f\vert\vert [a^{+}_{k_{\alpha }}\otimes \tilde{a}_{k_{\beta }}]^{\lambda }\vert\vert i\rangle}{\sqrt{(2\lambda +1)}}. $$ The labels \( i \) and \( f \) are a short-hand notation for the initial and final state quantum numbers \( (n \omega _{i}J_{i}) \) and \( (n\omega_{f}J_{f}) \), respectively. Thus the problem is divided into two parts, one involving the nuclear structure dependent one-body transition densities OBTD, and the other involving the reduced single-particle matrix elements (SPME).