Critical charge in a superstrong magnetic field

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system I. Vacuum charge density

“…Upon integration over the arcs, the leading terms in the asymptotics (27,28) give (i/r)(−2i R 0 ) for the contribution from C 1 + C 2 and (i/r)(+2i R 0 ) from C 3 + C 4 , which cancel each other. At the same time, the integration of the next-to-leading terms in (27,28) contains always inverse powers of R 0 in the answer, hence, their contribution vanishes for R 0 → ∞. So there follows from (27) and (28), that the integration along the contours P (R 0 ) and E(R 0 ) ( Fig.1) in (15) could be reduced to the imaginary axis, whence one obtains the final expression for the vacuum charge density…”

Vacuum energy of one-dimensional supercritical Dirac–Coulomb system

“…Meanwhile, in Refs. [14]- [20], it was shown that in superstrong homogeneous magnetic fields the effective relativistic dynamics of the electronic component in H-like atoms turns out to be quasi-one-dimensional, while the first critical charge Z cr,1 could be less than 170 in absence of the field [17][18][19][20].…”

Mesons in ultra-intense magnetic field: an evaded collapse

“…1, the color Coulomb collapse is really evaded. We remind that in superstrong MF radiative corrections screen the Coulomb potential in the hydrogen atom thus leading to the freezing of the ground state energy at the value E 0 = −1.7 KeV [11,12]. It is interesting to note that asymptotically at eB → ∞ the matrix element ψ 0 |V OGE |ψ 0 vanishes.…”