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The real part of resonances is shown in (a)

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posted on 2013-08-07, 00:00 authored by François Fillion-Gourdeau, Emmanuel Lorin, André D Bandrauk

Figure 3. The real part of resonances is shown in (a). The ground state crosses at the blue circles with resonances coming from the negative energy states (channel 1). The excited state follows the grey line and goes through a series of avoided crossings with the resonances coming from the positive energy states (channel 2). The resonances from both continua cross at the red circle (channel 3). The particle spectrum d〈n〉/dE dt as a function of the internucleus distance is shown in (b). There is clearly an enhancement of pair production at the resonance crossings. Finally, in (c), the total rate d〈n〉/dt is shown. There are peaks in the pair production rate when the ground state crosses with negative energy continuum resonances. The parameters are chosen as g = 0.8 (corresponding to U91 +), F = 0.2 × ES and L = 38 pm. Also, for this figure only, R is the semi-internucleus distance.


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.