  The orbital effect on the Fulde-Ferrell (FF) phase is investigated in
superconducting core/shell nanowires subjected to the axial magnetic field. The
confinement in the radial direction results in the quantization of the electron
motion with energies determined by the radial $j$ and orbital $m$ quantum
numbers. In the external magnetic field the twofold degeneracy with respect to
the orbital magnetic quantum number $m$ is lifted which leads to the Fermi wave
vector mismatch between the paired electrons $(k, j,m,\uparrow) \leftrightarrow
(-k, j,-m,\downarrow)$. This mismatch is transfered to the nonzero total
momentum of the Cooper pairs which results in the formation of FF phase
occurring sequentially with increasing magnetic field. By changing the nanowire
radius $R$ and the superconducting shell thickness $d$, we discuss the role of
the orbital effect in the FF phase formation in both the nanowire-like ($R/d
\ll 1$) and nanofilm-like ($R/d \gg 1$) regime. We have found that the
irregular pattern of the FF phase, which appears for the case of the
nanowire-like regime, evolves towards the regular distribution, in which the FF
phase stability regions appear periodically between the BCS state, for the
nanofilm-like geometry. The crossover between these two different phase
diagrams is explained as resulting from the orbital effect and the multigap
character of superconductivity in core/shell nanowires.
