Continuity of the Differential Oscillator Strength through a Dissociation Limit; Application to O2 Schumann—Runge and Herzberg I Systems

Using semiclassical methods it is shown that, if the final molecular state in the photodissociation of diatomics has an attractive potential (with no natural or rotational barrier at large R) deep enough to support bound states, then the differential oscillator strength in the photodissociation continuum ${\mathrm{df/d\nu \equiv \sigma \; m}}_e{c}^2{\mathrm{/\pi \; e}}^2$ (where σ is the photodissociation cross section) may be extrapolated smoothly through the dissociation limit using the continuity relation ${\mathrm{df/d\nu \leftrightarrow f}}_v{\mathrm{\rho (E}}_v)$ , where f_v is the oscillator strength of a transition to vibrational state v and ${\mathrm{\rho \; (E}}_v{\mathrm{)\equiv dv/d\; E}}_v$ is the density of vibrational states at energy E_v. Applied to the Schumann—Runge (B—X) system of O₂, the continuity relation shows that measurements of oscillator strength in the discrete and continuous regions are reasonably consistent; accurate interpolated values of f_v for the 17–0 to 20–0 bands are presented. In the Herzberg I(A—X) system, discrete band oscillator strengths determined by Hasson et al. are more consistent with the continuum measurements of Ditchburn and Young than with more recent measurements by Ogawa and by Shardandard. The implications of the continuity relation for the behavior of the photodissociation cross section at threshold are discussed.