  Nowaday, in study of effective interactions, more attention is devoted to
single-particle properties of near-magic nuclei and bulk properties of deformed
ones but quasiparticle states of the latter are rarely used so far because of
theoretical difficulties. In particular, the angular momentum projection
remains too time-consuming for such calculations and the methods, which are
based on the transformation to an intrinsic frame have some unsolved problems
such, e. g., as quantum fluctuations of rotational recoil in the description of
quasiparticle-rotation coupling. To remove a part of these difficulties, the
method of the optimal intrinsic. frame-of-reference is developed. After
applying the Mikhajlov transformation to obtain the nuclear Hamiltonian in the
intrinsic frame, approximate constraints on nucleon's variables are
substantiated, and the quasiparticle structure of the nucleus orientation angle
operators is investigated. That gives possibility to use the variational
principle to derive equations for matrix elements of these operators. An
approximation similar to the cranking model (CM), but with the quantum
rotational recoil, is formulated, which may be considered as a generalization
of the usual self-consistent CM. Simplified model calculations for rotational
bands in $^{163}$Er show that taking into account the recoil operator.
considerably improves the agreement with experimental data
