  This paper presents a new method to determine all components of the electric
field gradient tensor and orientation of the hyperfine magnetic field axis in
the absorber Cartesian frame for M\"ossbauer spectroscopy for nuclear
transitions between levels with spin 3/2 and 1/2. The method can be applied for
single-crystal absorbers with well separated absorption lines in their spectra.
Explicit formulas derived from velocity moments are presented. The new method
allows full separation of the electric quadrupolar and magnetic dipolar
hyperfine interactions by using unpolarized radiation.
