  Momentum distributions (MD) of deep hole proton states in $^{238}$U are
studied paying particular attention to the influence of deformation. Two
essentially different mean-field models, Woods-Saxon (WS) and
Skyrme-Hartree-Fock with the SkM$^*$ force, are used. Noticeable deviations
between the WS and SkM$^*$ results are found. They are mainly due to the
difference in effective nucleon mass. In particular, SkM$^*$ gives much weaker
deformation effects at low momenta than WS. It is shown that, in spite of the
deformation mixing, MD at low momenta can serve for identification of
$K^{\pi}=1/2^+$ hole states originating from $s_{1/2}$ spherical sub-shells.
Moreover, following the WS calculations, the deformation results in additional
$K^{\pi}=1/2^+$ states with strong $l=0$ contributions. A possibility to probe
such states in knock-out experiments is discussed.
