  We consider the central spin model in the box approximation taking into
account external magnetic field and anisotropy of the hyperfine interaction.
From the exact Hamiltonian diagonalization we obtain analytical expressions for
the nuclear spin dynamics in the limit of many nuclear spins. We predict the
nuclear spin precession in zero magnetic field for the case of anisotropic
interaction between electron and nuclear spins. We calculate and describe the
nuclear spin noise spectra in the thermodynamic equilibrium. The obtained
results can be used for the analysis of the nuclear spin induced current
fluctuations in organic semiconductors.
