## Total rate for zero to five nuclei, as a function of internucleus distance *R*, for (a) *F* = 0.2 **×** *E*_{S}, (b) *F* = 0.09 **×** *E*_{S} and (c) *F* = 0.05 **×** *E*_{S}

_{S}

_{S}

_{S}

**Figure 4.** Total rate for zero to five nuclei, as a function of internucleus distance *R*, for (a) *F* = 0.2 **×** *E _{S}*, (b)

*F*= 0.09

**×**

*E*and (c)

_{S}*F*= 0.05

**×**

*E*. The strength of the potential well is set to

_{S}*g*= 0.8 (corresponding to uranium nuclei).

**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.