Photon splitting in strong magnetic fields: Asymptotic approximation formulas versus accurate numerical results

Abstract

We present the results of a numerical calculation of the photon splitting rate below the electron-pair creation threshold $(\omega <~2m)$ in magnetic fields $B\gtrsim B_{\mathrm{cr}}{=m}^2/e=4.414\mathrm{}\times {10}^9$ T. Our results confirm asymptotic approximations derived in the low-field $(B<\mathrm{}{B}_{\mathrm{cr}})$ and high-field $\left(B\gg B_{\mathrm{cr}}\right)$ 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, Berg, and Wunner. We also point out that, although the analytical formula is correct, the splitting rates calculated there are wrong due to an error in the numerical calculations.