Photons splitting in strong magnetic fields: asymptotic approximation formulae vs. accurate numerical results

We present the results of a numerical calculation of the photon splitting rate below the electron-pair creation threshold ($\omega \le 2m$) in magnetic fields $B ~{> \atop \sim}~ B_{\rm cr} = m^2 /e = 4.414 \times 10^{9}$ T. Our results confirm asymptotic approximations derived in the low-field ($B < B_{\rm cr}$) and high-field ($B \gg B_{\rm cr}$) limit, and allow interpolating between the two asymptotic regions. Our expression for the photon splitting rate is a simplified version of a formula given by Mentzel et al. We also point out an error in their numerical calculations.