https://doi.org/10.1140/epjc/s10052-017-5325-4
Regular Article - Theoretical Physics
Resonances in positron scattering on a supercritical nucleus and spontaneous production of 
pairs
1
Alikhanov Institute for Theoretical and Experimental Physics, National Research Centre Kurchatov Institute, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117218, Russia
2
Novosibirsk State University, Novosibirsk, 630090, Russia
3
Sorbonne Universités, LPTHE, Université P. et M. Curie, BP 126, 4, Place Jussieu, 75252, Paris Cedex 05, France
4
CNRS, UMR 7589, LPTHE, 75005, Paris, France
5
National Research University Higher School of Economics, Myasnitskaya str., 20, Moscow, 101978, Russia
* e-mail: sgodunov@itep.ru
Received:
28
July
2017
Accepted:
20
October
2017
Published online:
20
November
2017
We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase 
and its dependence on the energy 
of the diving electronic level, for which we give both exact and approximate formulas. The Coulomb potential 
is rounded to the constant 
for 
. We confirm the resonant behavior of that we investigate in detail. In addition to solving the Dirac equation for an electron, we solve it for a positron, in the field of the same nucleus. This clarifies the interpretation of the resonances. Our results are compared with claims made in previous works.
© The Author(s), 2017
