  In the sequel of the present study, we have investigated the rotational
motion of triaxially deformed nucleus by using the microscopic framework of
angular-momentum projection. The Woods-Saxon potential and the schematic
separable-type interaction are employed as a microscopic Hamiltonian. As the
first example nuclear wobbling motion was studied in detail in the part~I of
the series. This second part reports on another interesting rotational mode,
chiral doublet bands: two prototype examples, $^{128}$Cs and $^{104}$Rh, are
investigated. It is demonstrated that the doublet bands naturally appear as a
result of the calculation in this fully microscopic framework without any kind
of core, and they have the characteristic properties of the $B(E2)$ and $B(M1)$
transition probabilities, which are expected from the phenomenological triaxial
particle-rotor coupling model.
