Distribution of electromagnetic transition amplitudes

In this paper the distribution of electromagnetic transition amplitudes 〈W′∥O∥W〉 is described in terms of fluctuations about a gaussian secular variation (as a function of initial and final energies) according to the Porter-Thomas assumption. Explicit formulas are derived both for the case (i) that∑ _w ′¦〈W′∥O∥W〉¦² is replaced by its local average and (ii) that∑ _W ′¦〈W′∥O∥W〉¦² is treated as a stochastic variable showing a χ _d ² -distribution. The resulting distribution function appears to possess a monomial tail. Comparisons with shell-model results are made.