Comment on “photon Splitting in Strongly Magnetized Objects Revisited”

I point out that the results stated in the recent articles on photon splitting by Wunner, Sang, and Berg and by Wentzel, Berg, & Wunner directly contradict an earlier analytic and numerical calculation that I performed of the same process using Schwinger’s proper time method, for strong magnetic fields and general energies below the pair production threshold. The results of Wunner et al. and Wentzel et al. do not show the expected low frequency behavior, nor have they been able to reproduce the expected small magnetic field behavior, suggesting that their calculations may not be gauge invariant. In a recent letter in this journal, Wunner, Sang, & Berg (1995) have argued, on the basis of a detailed calculation of the photon splitting rate or absorption coefficient in an external magnetic field by Wentzel, Berg, & Wunner (1994), that the photon splitting process has a much larger rate than was previously believed. Their article suggests that the large splitting rate results from inclusion of effects associated with magnetic fields B of order B cr = 4.4× 10G, and photon energies of order the electron mass m, which they state had not been done in earlier calculations. Wunner et al. correctly emphasize that their calculations, if correct, have important implications for cosmic γ and x–ray sources. I am writing this note to point out serious problems with the results of Wunner et al. which suggest that their numerical calculations may be in error (or may not be gauge invariant). I begin by noting that Wunner et al. have made significant misstatements of fact in their references to the earlier literature, when they state that “the astrophysical implications of magnetic photon splitting had to rely on simple analytical expressions derived by Adler (1971) and Papanyan & Ritus (1972) valid only in the weak-field limit B << B cr ...”. This statement in fact applies only to the earlier letter by Adler, Bahcall, Callan, & Rosenbluth (1970) and not to the follow–up article of Adler (1971). In the Adler et al. letter, the authors showed that gauge invariance implies that the leading contribution to photon