Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

Abstract

A method for calculating the electronic levels in the compact superheavy nuclear quasi-molecules, based on solving the two-center Dirac equation using the multipole expansion of two-center potential, is developed. For the internuclear distances up to d ∼ 100 fm such technique reveals a quite fast convergence and allows for computing the electronic levels in such systems with accuracy ∼ 10 −6 . The critical distances Rcr between the nuclei for 1σg and 1σu electronic levels in the region Z ≃ 87 − 100 are calculated. By means of the same technique the shifts of electronic levels due to the effective interaction ∆UAMM of the electron's magnetic anomaly with the Coulomb field of the closely spaced heavy nuclei are evaluated as a function of the internuclear distance and the charge of the nuclei, non-perturbatively both in Zα and (partially) in α/π. It is shown, that the levels shifts near the lower continuum decrease with the enlarging size of the system of Coulomb sources both in the absolute units and in units of Z 4 α 5 /πn 3 . The last result is generalized to the whole self-energy contribution to the level shifts and so to the possible behavior of radiative part of QED-effects with virtual photon exchange near the lower continuum in the overcritical region.

Super-critical QED-effects via VP-energy

“…At the same time, before first levels diving the curves of I(l) in all the partial channels reveal an almost quadratical growth. For the last channel with l = 3 this growth takes place during almost the whole interval 0 < Z < 600, since the first level diving in this channel occurs at Z ≃ 578.6, which is very close to Z = 600 and simultaneously large enough 5 With such a choice for a charged ball with Z = 170 the lowest 1s 1/2 -level lies precisely at ǫ 1s = −0.99999. Furthermore, it is quite close to 1.23, which is the most commonly used coefficient in heavy nuclei physics.…”

“…The negative result of early investigations at GSI [35] can be at least partially explained by the last circumstance. Moreover, estimating the self-energy contribution to the radiative part of QED effects due to virtual photon exchange near the lower continuum shows [5] that it is just a perturbative correction to essentially nonlinear VP-effects caused by fermionic loop and so yields only a small increase of Z cr,i and of other VP-quantities under question.…”

“…Nowadays the behavior of QED-vacuum under influence of a supercritical Coulomb source is subject to an active research [1][2][3][4][5][6]. Of the main interest is that in such external fields there should take place a deep vacuum state reconstruction, caused by discrete levels diving into the lower continuum and accompanied by such nontrivial effects as spontaneous positron emission combined with vacuum shells formation (see e.g., Refs.…”

Estimating the radiative part of QED effects in systems with supercritical charge

“…In the first case the total moment of the electron j and the operator k = β( σ l+1) are conserved, and so the upper and the lower components of the electronic wave function will contain the real radial functions f κ , g κ and the spherical spinors X −|κ|,m j ≡ Ω jlm j , X |κ|,m j ≡ ( σ n) Ω jlm j (the definition of spherical harmonics and spinors follows Refs. [8,11])…”

“…All the Coulomb multipole moments U n are evaluated analytically in the model of nucleus charge used (see Ref. [8]). The systems of equations (8) and (10) are solved by numerical methods; in the case of compact quasi-molecules (d = 2a 100 fm) the technique used converges quite fast with growing the cutoff κ max = K in the expansion (7), which allows one to determine the electronic levels energy with an accuracy of 10 −6 ∼ 10 −7 electron mass [8].…”