Pair creation by a photon in a strong magnetic field

The process of pair creation by a photon in a strong magnetic field is investigated based on the polarization operator in the field. The total probability of the process is calculated in a relatively simple form using an adequate method. The new results are obtained in the scope of the quasiclassical approach in the case when the magnetic field $B\ll B_0$ ($B_0$ is the critical field). This is the new formulation of the approach which extends its validity to the case when the created particles are not ultrarelativistic. The correction to the standard quasiclassical approximation is found as well, showing the range of applicability of the approach at high photon energy. The very important conclusion is that, for both cases $B\ll B_0$ and $B\ge B_0$, the results of the quasiclassical calculation are very close to averaged probabilities of exact theory in a very wide range of photon energies. The quasiclassical approximation is valid also for the energy distribution if the electron and the positron are created on high enough levels even for $B\ge B_0$.

Figure 1

The pair creation probability for an unpolarized photon at $\mu =0.1$ as a function of $r$. The probability in sawtooth form is calculated according to Eq. (2.12). The dashed line is the result of averaging over the interval ($-\mu /2+r$, $\mu /2+r$). The solid line is calculated according to Eq. (3.4).

Figure 2

The ratio of probabilities $W^{(\mathrm{th})}/W^{(\mathrm{SQA})}$. Curves 2 and 3 are for the polarized photons, curve $t$ is for the probability averaged over the photon polarizations [see Eqs. (3.4, 3.7)].

Figure 3

The pair creation by a photon probability at $\mu =3$ in the quasiclassical approximation. The upper curve is the probability in SQA [Eq. (3.7)]. The lower curve is the sum $W^{(\mathrm{SQA})}+W^{(1)}$ [Eq. (3.1)].

Figure 4

The probability of pair creation at $\mu =3$. The probability in sawtooth form is calculated according to Eq. (2.12). The result of averaging over the interval ($-\mu /2+r$, $\mu /2+r$) is given by the dashed line. The solid curve, which is the quasiclassical approximation, is calculated according to Eqs. (3.1, 3.7).

Figure 5

The spectrum of created particles for $\mu =3$, $r=110(n_m=66)$ vs $n$ [see Eq. (4.2)]. The spectrum in sawtooth form is calculated according to Eq. (2.12). The dashed curve is the spectrum averaged over the interval ($-2\mu +r$, $2\mu +r$). The solid curve is calculated according to Eq. (4.3).

Figure 6

The energy distribution of the created electron (positron) at $\mu =3$ for different $r$: $r=30$, $n_m=16$ (the upper curve), $r=110$, $n_m=66$ (the middle curve), $r=500$, $n_m=318$ (the lower curve), calculated according to Eq. (4.3) (the solid curve) and according to Eq. (4.6) (the dashed curve).