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

TL;DR

This paper compares asymptotic formulas and numerical calculations for photon splitting rates in strong magnetic fields, confirming some approximations and correcting errors in previous analytical results.

Contribution

It provides accurate numerical results for photon splitting rates in supercritical magnetic fields and refines existing asymptotic formulas, correcting prior numerical errors.

Findings

Asymptotic approximations are confirmed in their respective regimes.

Numerical calculations match asymptotic formulas in low and high-field limits.

Previous analytical formulas contained numerical errors that are corrected in this work.

Abstract

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 that, although the analytical formula is correct, the splitting rates calculated there are wrong due to an error in the numerical calculations.