# Simple model to study pair production for many-centre systems (here, the two-centre system is shown)

**Figure 2.** Simple model to study pair production for many-centre systems (here, the two-centre system is shown). The electric field has a finite extent in space. The pair production rate calculation reduces to a transmission–reflection problem: the incoming, reflected and transmitted wavefunctions are given in the figure. In blue is the Klein region where it is possible to have a transition from a negative to a positive energy state.

**Abstract**

Electron–positron pair production is considered for many-centre systems with multiple bare nuclei immersed in a constant electric field. It is shown that there are two distinct regimes where the pair production rate is enhanced. At small interatomic distance, the effective charge of the nuclei approaches the critical charge where the ground state dives into the negative continuum. This facilitates the transition from the negative to the positive energy states, which in turn increases the pair production rate. At larger atomic distance, the enhancement is due to the crossing of resonances and the pair production proceeds by the resonantly enhanced pair production mechanism. These processes are studied within a simple one-dimensional model. A numerical method is developed to evaluate the transmission coefficient in relativistic quantum mechanics, which is required in the calculation of the pair production rate. The latter is evaluated for systems with many (up to five) nuclei. It is shown that the production rate for many-centre systems can reach a few orders of magnitude above Schwinger's tunnelling result in a static field.