Journal of Physical Studies 5(3/4), 246–254 (2001)
DOI: https://doi.org/10.30970/jps.05.246

HYPERFINE INTERACTIONS OF THE NUCLEAR SPIN WITH ELECTRON SYSTEMS IN THE DENSITY MATRIX METHODS

R. L. Pavlov^{1}, P. P. Raychev^{1}, M. Dimitrova-Ivanovich^{2}, C. Valdemoro^{3}
^{1}Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,
72 Tsarigradsko Chaussee, BG–1784 Sofia, Bulgaria,
^{2}Institute of Solid State Physics, Bulgarian Academy of Sciences,
72 Tsarigradsko Chaussee, BG–1784 Sofia, Bulgaria,
^{3}Instituto de Matematicas y Fisica Fundamental, CSIC, 123 Serrano, 28006 Madrid, Spain

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 interactions 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. Applying the Wigner-Eckart theorem, using the irreducible tensor-operators technique and the spin-space separation scheme, the matrix elements and expectation values of these relativistic corrections are expressed in a form suitable for direct numeric calculations. The final result is presented as a product (or sums of products) of factors determined by the spin and (or) the angular momentum symmetry, and a spatial part determined by the action of the symmetrized tensor-operators on the normalized matrix or function of the spin distribution or the matrix of the charge distribution. The action of these space tensor operators is the same for a given spin multiplet. This action can be expressed by a standard procedure, well defined in the theory of the irreducible tensor-operators.

PACS number(s): 31.20.Sy, 31.30.Gs, 31.30.Jv