Nonrelativistic expansion of the Dirac equation with spherical scalar and vector potentials by a reconstituted Foldy-Wouthuysen transformation

Abstract

Inspired by the reconstituted similarity renormalization group method, the reconstituted Foldy-Wouthuysen (FW) transformation is proposed. Applied to the Dirac equation in the covariant density functional theory, the reconstituted FW transformation shows a fast convergence of the spectrum of the single-particle energy. The single-particle densities and the single-particle scalar densities obtained by this new method are also investigated. In particular, the relativistic corrections to the densities from the picture-change error between the Schrödinger and Dirac pictures are discussed in detail. Taking these relativistic corrections into account, both the single-particle densities and the single-particle scalar densities are almost identical to their exact values.

Theory of nuclear collective vibrations

“…The study of this open question is in progress. One of the possible ways is to establish a bridge between the relativistic and non-relativistic DFTs, by performing the non-relativistic expansion with fast convergence [159,160,161,162,163].…”

Nuclear density functional theory

“…11. The interested reader may consult Appendix 1 of the review paper [116], or the recent paper [117] and references therein. 12.…”

Effective theories and non-minimal couplings in low-dimensional systems

“…The first one, g J µ F µ , generates an anomalous magnetic dipole moment and similar coupling can also be introduced in other field representations with the correspondent three-current, while g 2 ϕ * ϕ F 2 µ is particular to spin-0 description. In this work, we only analyse the effects of an external electromagnetic field, therefore we do not consider the quartic and sixth self-couplings, (ϕ * ϕ) 2 and (ϕ * ϕ) 3 .…”

“…Even though the main purpose of these initial works was the investigation of the electromagnetic interaction, the method can be applied in other situations. For example, it has been a useful tool to describe fundamental and excited states of atomic nuclei [3], some interactions with gravitational and torsion fields [4][5][6][7][8]. Also, it was considered in scenarios with Lorentz symmetry violation [9][10][11][12], accelerated frames [13,14], topological defects [15,16] and topological insulators [17,18].…”