Calculation of supercritical Dirac resonance parameters for heavy-ion systems from a coupled-differential-equation approach

Abstract

Previous work [E. Ackad and M. Horbatsch, Phys. Rev. A 78, 062711 (2008)] on supercritical Dirac resonance parameters from extrapolated analytic continuation, obtained with a Fourier grid method, is generalized by numerically solving the coupled Dirac radial equations to a high precision. The equations, which contain the multipole decomposition of the two-center potential, are augmented by a complex absorbing potential and truncated at various orders in the partial wave expansion to demonstrate convergence of the resonance parameters in the limit of vanishing absorber. The convergence of the partial-wave spinor and of the multipole potential expansions is demonstrated in the supercritical regime. The comparison of critical distances with literature values shows that the work provides benchmark results for future two-center calculations without multipole expansion.

Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

“…To conclude we have shown that the approach, based on the multipole expansions (12), (15) for solving the two-center DE, can be successfully applied for the compact nuclear quasi-molecules (d 100 fm), and allows to investigate the process of diving of discrete levels into the lower continuum in heavy ions collisions not only qualitatively (what could be performed within the monopole approximation), but also quantitatively. Calculated critical distances R cr for the levels 1σ g and 1σ u are in a good agreement with other computations [20,32,33,36,38,39,45]. Moreover, the results R cr for the 1σ u level significantly improve the most relevant values, which have been obtained early within the monopole approximation [39].…”

“…In the Ref. [45] the critical distances have been calculated via the multipole expansion of the Coulomb potential only up to order l max = 4 and the same truncation κ max = 4 in the WF expansion, which, as it follows from the Sec. 4 and Tabs.…”

“…[33] c From Ref. [45] reproduces the behavior of the whole self-energy contribution for the lowest electronic levels [9][10][11]. Another valuable characteristics of QED-effects is their growth rate as a function of Z.…”

Contribution of higher multipole terms of Coulomb interaction to ionization in low-energy heavy-ion collisions

“…In the 1970s a formation of the charged vacuum in such collisions, provided that the total nuclear charge is larger than the critical one Z c = 173, has been predicted, and the following appropriate calculations were mostly carried out in the monopole approximation of the interaction [1]. In the 2010s interest to this problem has been renewed, and the results obtained beyond this approximation were reported [2,3,4]. In this contribution we implement the multipole expansion of the two-center potential to study the angular distribution of ionized electrons in the U 91+ (1s)-U 92+ collision.…”

Relativistic calculations of the U91+(1s)–U92+ collision using the finite basis set of cubic Hermite splines on a lattice in coordinate space

“…The monopole approximation was found to be very useful for studying processes at short internuclear distances [25]. Unfortunately, this approach as well as its one-center extensions beyond the monopole approximation [26,27] can not be applied to calculations of charge-transfer processes.…”