Pair Production in an Intense Laser Pulse: The Effect of Pulse Length

Production of positron-electron (e⁺e⁻) pairs in an intense laser pulse is investigated by solving the Dirac equation with analytical and numerical methods. We observe that the probability of the pair production will firstly decrease slowly as the pulse length τ becomes shortened. Then it will increase until τ is reduced to the Compton time τ_c=ħ/(m_ec)≈1.29×10⁻²¹ s and finally decrease exponentially to zero. Hence, for a prominent pair production, we not only require that the electric field strength should be higher than the the Schwinger critical value E_cr=m²c³/(eħ)≈1.32×10¹⁶ V/cm, but also that the pulse duration τ should be larger than τ_c. The latter is shown to be related to momentum requirement for the transition. For fields with different pulse lengths, the phase and chirp influences upon the pair production are also explored.