  Background: Nuclear self-consistent mean-field approaches are rooted in the
density functional theory and, through the spontaneous symmetry breaking
mechanism, allow for including important correlations, while keeping the
simplicity of the approach. Because real ground states should have all
symmetries of the nuclear Hamiltonian, these methods require subsequent
symmetry restoration.
  Purpose: We implement and study Lipkin method of approximate variation after
projection applied to the restoration of the translational or rotational
symmetries.
  Methods: We use Lipkin operators up to quadratic terms in momenta or angular
momenta with self-consistently determined values of the Peierls-Yoccoz
translational masses or moments of inertia, respectively. Calculations based on
Skyrme energy-density functional are performed for heavy, deformed, and paired
nuclei.
  Results: In deformed nuclei, the Peierls-Yoccoz translational masses along
three different principal-axes directions of the intrinsic system can be
different, which illustrates different widths of the total-momentum
distributions. Numerically, the differences are only of the order of a few per
cent. For the rotational-symmetry restoration, the Lipkin method compares
favorably with the exact angular-momentum projection, which requires much
larger computational effort.
  Conclusions: The Lipkin method of translational and rotational symmetry
restoration is a practical low-cost method of determining the corresponding
correlation energies. It allows for a simultaneous restoration of several
symmetries and can be relatively easily implemented in the standard
self-consistent mean-field calculations, including those required for the
parameter adjustments.
