Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: History and Physics of the Klein Paradox   The early papers by Klein, Sauter and Hund which investigate scattering off a
high step potential in the context of the Dirac equation are discussed to
derive the 'paradox' first obtained by Klein. The explanation of this effect in
terms of electron-positron production is reassessed. It is shown that a
potential well or barrier in the Dirac equation can become supercritical and
emit positrons or electrons spontaneously if the potential is strong enough. If
the well or barrier is wide enough, a seemingly constant current is emitted.
This phenomenon is transient whereas the tunnelling first calculated by Klein
is time-independent. It is shown that tunnelling without exponential
suppression occurs when an electron is incident on a high barrier, even when
the barrier is not high enough to radiate. Klein tunnelling is therefore a
property of relativistic wave equations and is not necessarily connected to
particle emission. The Coulomb potential is investigated and it is shown that a
heavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly,
as $Z$ increases the Coulomb barrier should become increasingly transparent to
positrons. This is an example of Klein tunnelling. Phenomena akin to
supercritical positron emission may be studied experimentally in superfluid
$^3$He

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc