  The newly observed isomer and ground-state band in the odd-Z neutron-rich
rare-earth nucleus $^{163}$Eu are investigated by using the cranked shell model
(CSM) with pairing treated by the particle-number conserving (PNC) method. This
is the first time detailed theoretical investigations are performed of the
observed $964(1)$ keV isomer and ground-state rotational band in $^{163}$Eu.
The experimental data are reproduced very well by the theoretical results. The
configuration of the $964(1)$ keV isomer is assigned as the three-particle
state
$\frac{13}{2}^{-}(\nu\frac{7}{2}^{+}[633]\otimes\nu\frac{1}{2}^{-}[521]\otimes\pi\frac{5}{2}^{+}[413]$).
More low-lying multi-particle states are predicted in $^{163}$Eu. Due to its
significant effect on the nuclear mean field, the high-order $\varepsilon_{6}$
deformation plays an important role in the energy and configuration assignment
of the multi-particle states. Compared to its neighboring even-even nuclei
$^{162}$Sm and $^{164}$Gd, there is a $10\%\sim15\%$ increase of $J^{(1)}$ of
the one-particle ground-state band in $^{163}$Eu. This is explained by the
pairing reduction due to the blocking of the nucleon on the proton
$\pi\frac{5}{2}^{+}$[413] orbital in $^{163}$Eu.
