Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-07-06
Phys.Rev.D78:025011,2008
Physics
High Energy Physics
High Energy Physics - Theory
33 pages and 9 figures. to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.78.025011
Treating the production of electron and positron pairs by a strong electric field from the vacuum as a quantum tunneling process we derive, in semiclassical approximation, a general expression for the pair production rate in a $z$-dependent electric field $E(z)$ pointing in the $z$-direction. We also allow for a smoothly varying magnetic field parallel to $E(z)$. The result is applied to a confined field $E(z)\not=0$ for $|z|\lesssim \ell $, a semi-confined field $E(z)\not=0$ for $ z\gtrsim 0 $, and a linearly increasing field $E(z)\sim z$. The boundary effects of the confined fields on pair-production rates are exhibited. A simple variable change in all formulas leads to results for electric fields depending on time rather than space. In addition, we discuss tunneling processes in which empty atomic bound states are spontaneously filled by negative-energy electrons from the vacuum under positron emission. In particular, we calculate the rate at which the atomic levels of a bare nucleus of finite size $r_{\rm n}$ and large $Z\gg 1$ are filled by spontaneous pair creation.
Kleinert Hagen
Ruffini Remo
Xue She-Sheng
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