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.
Highlights
The density functional theory (DFT) in its nonrelativistic [2] and relativistic [3] realizations is a standard tool of modern nuclear structure studies
Providing global description of atomic nuclei, it still suffers from the fact that many channels of effective interaction are not uniquely defined: this is a reason for a large variety of the DFT parametrizations, the quality of many of which is poorly known
The results obtained in Refs. [1, 10] within the TS-method show that the Skyrme density functional theory (SDFT) provides better description of spin-orbit splittings than the RMF: it was suggested in Ref. [1] that only 5% reduction in isoscalar ls strength is needed in the SDFT approach in order to reproduce experimental data
Summary
The density functional theory (DFT) in its nonrelativistic [2] and relativistic [3] realizations is a standard tool of modern nuclear structure studies. [1] that the set of terminating states in the N = Z, A ∼ 44 mass region provides unique and reliable constraints on time-odd mean fields and the strength of spin-orbit interaction in Skyrme density functional theory (SDFT), see Refs. [1, 10] within the TS-method show that the SDFT provides better description of spin-orbit splittings than the RMF: it was suggested in Ref.
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