The reduced transition probability \( B \) is defined in terms of reduced matrix elements of a one-body operator by $$ B(i \rightarrow f)= \frac{\langle J_{f}||{\cal O}(\lambda )||J_{i}\rangle^{2}}{(2J_{i}+1)}. $$ With our definition of the reduced matrix element, $$ \langle J_{f}||{\cal O}(\lambda )||J_{i}\rangle^{2} =\langle J_{i}||{\cal O}(\lambda )||J_{f}\rangle^{2}, $$ the transition probability \( B \) depends upon the direction of the transition by the factor of \( (2J_{i}+1) \). For electromagnetic transitions \( J_{i} \) is that for the higher-energy initial state. But in Coulomb excitation the initial state is usually taken as the ground state, and it is normal to use the notation \( B(\uparrow) \) for transitions from the ground state.