A superstrong magnetic field stimulates the spontaneous production of positrons by naked nuclei by diminishing the value of the critical charge Z cr . The phenomenon of screening of the Coulomb potential by a superstrong magnetic field which has been discovered recently acts in the opposite direction and prevents the nuclei with Z < 52 from becoming critical. For Z > 52 for a nucleus to become critical stronger B are needed than without taking screening into account.

An extension of the Standard Model with an additional Higgs singlet is analyzed. Bounds on singlet admixture for the 125 GeV h boson from electroweak radiative corrections and data on h production and decays are obtained. The possibility of double h production enhancement at 14 TeV LHC due to a heavy Higgs contribution is considered.

We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase δ and its dependence on the energy ε of the diving electronic level, for which we give both exact and approximate formulas. The Coulomb potential Z α/r is rounded to the constant Z α/R for r < R. We confirm the resonant behavior of δ 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.