Band terminations in density functional theory

TL;DR

This paper investigates the role of nuclear magnetism and time-odd mean fields in nuclear density functional theory, especially at terminating states, highlighting the complexities in isolating these effects due to multiple contributing factors.

Contribution

It reanalyzes the use of energy differences in terminating states as constraints on time-odd mean fields and shows their dependence on the placement of orbitals and the central potential.

Findings

Nuclear magnetism increases binding at terminating states.

Energy differences are influenced by orbital placement and central potential.

Isolating time-odd effects is more complex than previously suggested.

Abstract

The analysis of the terminating bands has been performed in the relativistic mean field framework. It was shown that nuclear magnetism provides an additional binding to the energies of the specific configuration and this additional binding increases with spin and has its {\it maximum} exactly at the terminating state. This suggests that the terminating states can be an interesting probe of the time-odd mean fields {\it provided that other effects can be reliably isolated.} Unfortunately, a reliable isolation of these effects is not that simple: many terms of the density functional theories contribute into the energies of the terminating states and the deficiencies in the description of those terms affect the result. The recent suggestion \cite{ZSW.05} that the relative energies of the terminating states in the $N \neq Z, A\sim 44$ mass region given by $\Delta E$ {\it provide unique and reliable constraints on time-odd mean fields and the strength of spin-orbit interaction} in density functional theories has been reanalyzed. The current investigation shows that the $\Delta E$ value is affected also by the relative placement of the states with different orbital angular momentum ${\it l}$, namely, the placement of the $d$ (${\it l}=2$) and $f$ (${\it l}=3$) states. This indicates the dependence of the $\Delta E$ value on the properties of the central potential.