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Positron Production in Heavy Ion-Atom Collisions

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The question of pair creation in strong electrical fields is a very old problem. Already in 1929, within the framework of the new Dirac theory of the electron1, Klein considered the behaviour of an electron wave with a total energy E = ET + mec2 impinging on a one-dimensional step barrier potential Vo> mec2/e (fig. 1a). If the kinetic energy ET of an electron travelling on the z-axis from left to right is less than eVo, then for z>0 an exponentially damped wave function is expected as a solution of the Schrodinger equation. According to Klein’s calculations with the Dirac equation, this behaviour was also found for eVo-2mec2 <ET<eVo, but for a kinetic energy ET<eVo-2mec2 the wave function starts oscillating again. This means that, in a forbidden region, electrons behave as free particles with negative energy (and also negative momentum). This anomaly was called the Klein paradox.