Description of the (a) REPP and (b) ECEPP mechanisms for the two-centre system
Figure 1. Description of the (a) REPP and (b) ECEPP mechanisms for the two-centre system. The dark grey regions are the positions of resonances which have a high density of state, while the light grey regions correspond to accessible energies which have a lower density of state. In (a), the interatomic distance is large and the ground and first excited states are quasi-degenerate. These two states are Stark-shifted in the presence of the field. In (b), the interatomic distance is small such that the ground state has low energy, close to −mc2. In that limit, the Stark shift is less important than for large R.
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.