  The formation of deeply-bound antikaonic $K^-/\bar{K}^0$ nuclear states by
nuclear ($K^-$, $N$) reactions is investigated theoretically within a
distorted-wave impulse approximation (DWIA), considering the isospin properties
of the Fermi-averaged $K^-+ N \to N + \bar{K}$ elementary amplitudes. We
calculate the formation cross sections of the deeply-bound $\bar{K}$ states by
the ($K^-$, $N$) reactions on the nuclear targets, $^{12}$C and $^{28}$Si, at
incident $K^-$ lab momentum $p_{K^-}$ = 1.0 GeV/c and $\theta_{\rm lab} =
0^{\circ}$, introducing a complex effective nucleon number $N_{\rm eff}$ for
unstable bound states in the DWIA. The results show that the deeply-bound
$\bar{K}$ states can be populated dominantly by the ($K^-$, $n$) reaction via
the total isoscalar $\Delta T=0$ transition owing to the isospin nature of the
$K^-+ N \to N + \bar{K}$ amplitudes, and that the cross sections described by
${\rm Re}N_{\rm eff}$ and ${\rm Arg}N_{\rm eff}$ enable to deduce the structure
of the $\bar{K}$ nuclear states; the calculated inclusive nucleon spectra for a
deep $\bar{K}$-nucleus potential do not show distinct peak structure in the
bound region. The few-body $\bar{K}\otimes [NN]$ and $\bar{K}\otimes [NNN]$
states formed in ($K^-$, $N$) reactions on $s$-shell nuclear targets, $^3$He,
$^3$H and $^4$He, are also discussed.
