  New techniques in core-electron spectroscopy are necessary to resolve the
structures of oxides of $f$-elements and other strongly correlated materials
that are present only as powders and not as single crystals. Thus, accurate
quantum chemical methods need to be developed to calculate core spectroscopic
properties in such materials. In this contribution, we present an important
development in this direction, extending our fully adaptive real-space
multiwavelet basis framework to tackle the 4-component Dirac-Coulomb-Breit
Hamiltonian. We show that Multiwavelets are able to reproduce one-dimensional
grid-based approaches. They are however a fully three-dimensional approach
which can later on be extended to molecules and materials. Our Multiwavelet
implementation attained precise results irrespective of the chosen nuclear
model, provided that the error threshold is tight enough and the chosen
polynomial basis is sufficiently large. Furthermore, our results confirmed that
in two-electron species, the magnetic and Gauge contributions from $s$-orbitals
are identical in magnitude and can account for the experimental evidence from
$K$ and $L$ edges.
