Supercritical Dirac resonance parameters from extrapolated analytic continuation methods

TL;DR

This paper compares complex scaling, exterior scaling, and absorbing potential methods for calculating supercritical Dirac resonances, demonstrating the effectiveness of extrapolation techniques and analyzing higher-order potential effects.

Contribution

It introduces an extrapolation approach using Pade approximants to achieve parameter-independent resonance energies in supercritical systems.

Findings

Extrapolated results from SES and CAP are highly consistent.

Dipole and quadrupole terms cause broadening of resonance widths near contact.

Resonance energies become independent of stabilization parameters through extrapolation.

Abstract

The analytic continuation methods of complex scaling (CS), smooth exterior scaling (SES), and complex absorbing potential (CAP) are investigated for the supercritical quasimolecular ground state in the U(92+)-Cf(98+) system at an internuclear separation of R=20 fm. Pade approximants to the complex-energy trajectories are used to perform an extrapolation of the resonance energies, which, thus, become independent of the respective stabilization parameter. Within the monopole approximation to the two-center potential is demonstrated that the extrapolated results from SES and CAP are consistent to a high degree of accuracy. Extrapolated CAP calculations are extended to include dipole and quadrupole terms of the potential for a large range of internuclear separations R. These terms cause a broadening of the widths at the permille level when the nuclei are almost in contact, and at the % level for R values where the ground state enters the negative continuum.