  The magnetic hyperfine field and electric-field gradient at isolated
lanthanide impurities in an Fe host lattice are calculated from first
principles, allowing for the first time a qualitative and quantitative
understanding of an experimental data set collected over the past 40 years. It
is demonstrated that the common Local Density Approximation leads to
quantitatively and qualitatively wrong results, while the LDA+U method performs
much better. In order to avoid pitfalls inherent to the LDA+U method, a careful
strategy had to be used, which will be described in detail. The lanthanide 4f
spin moment is found to couple antiferromagnetically to the magnetization of
the Fe lattice, in agreement with the model of Campbell and Brooks. There is
strong evidence for a delocalization/localization transition that is shifted
from Ce to at least Pr and maybe further up to Sm. This shift is interpreted in
terms of the effective pressure felt by lanthanides in Fe. Implications for
resolving ambiguities in the determination of delocalization in pure lanthanide
metals under pressure are discussed. For the localized lanthanides, Yb is shown
to be divalent in this host lattice, while all others are trivalent (including
Eu, the case of Tm is undecided). The completely filled and well-bound 5p shell
of the lanthanides is shown to have a major and unexpected influence on the
dipolar hyperfine field and on the electric-field gradient, a feature that can
be explained by their 1/r^3 dependence. An extrapolation to actinides suggests
that the same is true for the actinide 6p shell. The case of free lanthanide
atoms is discussed as well.
