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Electron-positron pair production by collision of photons is investigated inview of application to pulsar physics. We compute the absorption rate ofindividual gamma-ray photons by an arbitrary anisotropic distribution of softerphotons, and the energy and angular spectrum of the outgoing leptons. We workanalytically within the approximation that 1 mc 2 /E > /E, with E and thegamma-ray and soft-photon maximum energy and mc 2 the electron mass energy. Wegive results at leading order in these small parameters. For practicalpurposes, we provide expressions in the form of Laurent series which givecorrect reaction rates in the isotropic case within an average error of $\sim$7%. We apply this formalism to gamma rays flying downward or upward from a hotneutron star thermally radiating at a uniform temperature of 10 6 K. Othertemperatures can be easily deduced using the relevant scaling laws. We finddifferences in absorption between these two extreme directions of almost twoorders of magnitude, much larger than our error estimate. The magnetosphereappears completely opaque to downward gamma rays while there are up to $\sim$10% chances of absorbing an upward gamma ray. We provide energy and angularspectra for both upward and downward gamma rays. Energy spectra show a typicaldouble peak, with larger separation at larger gamma-ray energies. Angularspectra are very narrow, with an opening angle ranging from 10 --3 to 10 --7radians with increasing gamma-ray energies.

Electron-positron pair production by gamma rays in an anisotropic flux of soft photons, and application to pulsar polar caps