Hyperfine interactions of the nuclear spin with electron systems in the density matrix methods

The matrix elements and expectation values of the operators of the hyperfine electron-nuclear interactions in many-electron systems are presented in an analytical form, which can be applied for numerical calculations in the density matrix methods. The electron-nuclear spin-spin and contact interactions are considered,as well as the interaction between nuclear-spin and electron orbital motions. These interaction which take part in the effective Breit-Pauli Hamiltonian,determine hyperfine structure of the basic effects in the spectroscopy,which can be observed for example in electron spin resonance (ESR) and nuclear magnetic resonance (NMR) experiments