On the problem of whether the transition probability plays a role in describing secondary-photon yields

The yields of secondary photons, i.e. photons emitted from sputtered excited states, have been described variously as being proportional to either P(?_i) b_fi or P(?_i) v_fiA_fi. Here P( the function giving the probability of a sputtered particle having excitation energy ?_i, b_fi is the branching ratio, v_fi is the photon frequency, and A_fi is the transition probability. In an attempt to clarify the role of A_fi we have compared experimental yields from bombarded Li, Zn, Cd, Sc, and Ti with tabulated plasma yields and obtained results which suggest that A_fi does not enter, in the case of secondary photons, as a simple multiplier of P(?_i). This is not really surprising, as secondary photons are emitted by isolated atoms whereas the use of the factor A(_fi) assumes thermodynamic equilibrium during decay, as in a plasma. In further experiments, yields were measured versus distance in front of the target. Introducing the decay rate constant, γ_i = ΣA_fi, one finds that for γ_i exceeding 0.4 × 10⁸ s^?1 the signals fall by a factor of 10 within 1.5 mm, for γi of (0.02?0.2) × 10⁸ s^?1 they fall by such a factor within 3–10 mm, and for γi of (0.0004–0.004) × 10⁸ s^?1 significant decay occurs beyond the reach of the detector. This shows that A_fi does indeed play a role in describing photon yields whenever γ_i is sufficiently small, namely in the somewhat complicated relation describing the spatial distribution of the photon emission. Nevertheless, in most situations the use of A_fi is unjustified.