Relativistic calculations of charge transfer probabilities in U92+ - U91+(1s) collisions using the basis set of cubic Hermite splines

TL;DR

This paper introduces a novel computational approach using cubic Hermite splines to solve the time-dependent Dirac equation for heavy-ion collisions, enabling more precise charge transfer probability calculations.

Contribution

The paper presents a new spline-based method for solving the two-center Dirac equation in heavy-ion collisions, improving computational efficiency and accuracy.

Findings

Charge transfer probabilities calculated at various impact parameters.

Comparison shows consistency with previous Dirac-Sturm orbital methods.

Potential for studying quantum electrodynamics effects in supercritical regimes.

Abstract

A new approach for solving the time-dependent two-center Dirac equation is presented. The method is based on using the finite basis set of cubic Hermite splines on a two-dimensional lattice. The Dirac equation is treated in rotating reference frame. The collision of U92+ (as a projectile) and U91+ (as a target) is considered at energy E_lab=6 MeV/u. The charge transfer probabilities are calculated for different values of the impact parameter. The obtained results are compared with the previous calculations [I. I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)], where a method based on atomic-like Dirac-Sturm orbitals was employed. This work can provide a new tool for investigation of quantum electrodynamics effects in heavy-ion collisions near the supercritical regime.