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

TL;DR

This paper introduces a novel finite basis method using cubic Hermite splines for solving the time-dependent Dirac equation, enabling relativistic calculations of ion collisions with improved accuracy and insights into negative-energy spectrum effects.

Contribution

The paper develops a new spline-based finite basis approach for relativistic two-center Dirac equations, enhancing computational methods for ion collision studies.

Findings

Relativistic excitation and charge-transfer probabilities calculated for U91+ and U92+ collisions.

Comparison shows improved results over previous Dirac-Sturm basis set methods.

Investigation of negative-energy Dirac spectrum effects within the monopole approximation.

Abstract

A new method for solving the time-dependent two-center Dirac equation is developed. The approach is based on the using of the finite basis of cubic Hermite splines on a three-dimensional lattice in the coordinate space. The relativistic calculations of the excitation and charge-transfer probabilities in the U91+(1s)-U92+ collisions in two and three dimensional approaches are performed. The obtained results are compared with our previous calculations employing the Dirac-Sturm basis sets [I.I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)]. The role of the negative-energy Dirac spectrum is investigated within the monopole approximation.