Pair production by photons in the field of the nucleus

Electron positron pair cascades can be started by accelerated ions in thermal photon fields. A photon can decay into an electron positron pair in the Coloumb field of a nucleus when the center of momentum frame energy exceeds the rest mass of the nucleus plus two electrons, that is

where is the mass of the nucleus. This condition can be satisfied for soft photons from the polar cap in the presence of accelerated ions. We can estimate the mean free path of an ion before producing an average one pair. If we believe one pair per primary particle is enough to short out the electric field, this mean free path length, represented by , can be identified as the gap length (Figures 3 and 4).

  
Figure 3: Pair production due to ion colliding with soft photon from polar cap emission above the polar cap with . Beside ions, the outflowing charges may include positrons.

  
Figure 4: Plots of cumulative number of pairs produced per ion as a function of distance. Solid, dashed and dotted curves correspond respectively to for the whole star's surface, for the polar cap (but the star's surface has ), and for the polar cap (but the star's surface has ). The thick and thin curves are calculated using the potentials (2) and (3), respectively. We assume , .

Numerical evaluation of the mean free path for an accelerated ion traversing an isotropic thermal photon field was given by Protheroe (1984), and Protheroe & Johnson (1996). The injection rate of pairs for a given energy of iron nuclei was numerically calculated by Bednarek & Karakula (1995) for an anisotropic photon field from the polar cap. We calculate number of pairs produced by iron nuclei accelerated along open field lines by the potentials given by Eqs. (2) and (3), and the mean free path corresponds to the average distance at which one pair is produced per ion nucleus. The mean cumulative number of pairs produced in the radiation field of the polar cap (or whole neutron star) at temperature T by a nucleus of energy E traveling along the neutron star magnetic axis from the pole to distance above the polar cap surface is given by,

where is the differential photon number density of photons of energy in black body radiation at temperature T, and is the total cross section for pair production (Protheroe 1997) by a the nucleus at center of momentum (CM) frame energy squared, s, given by

where is the angle between the directions of the nucleus and photon. Note that is determined by the threshold condition (5). Plots of accumulative number of pairs produced per ion through interaction with thermal photons as a function of distance from the polar cap are shown in Figure 4. for and . Compared to RICS, in this case we have . Although we use a high B, the process strongly depends on P and T.

© Copyright Astronomical Society of Australia 1997