Protonenrelaxation in Mn2+-Lösungen, Einfluß der Hyperfeinkopplung. I. Theorie
- 1An extension of the usual Redfield relaxation-matrix theory is derived for the case P(τ) ≠ P(−τ). It is shown that the definition of a relaxation-matrix R and a shift-matrix V as introduced by Pfeifer is useful. Equations analogous to the Kronig-Kramers- relations are valid between the spectral densities (ω) (contained in R) and ́ (ω) (contained in V). A general solution of the differential equations is discussed.
- 2If the operator S of the electron spin may be regarded as a lattice operator, expressions for the proton relaxation times in solutions of paramagnetic ions are developed. The influence of the paramagnetic ions on the proton relaxation is described by the relaxation function rq(τ) of the electron spin which may be determined by esr-experiments or by theory.
- 3rq(τ) is calculated for Mn2+-ions in weak fields using a spin-Hamiltonian which includes Zeeman-energy, hyperfine coupling , and zero field splitting. Moreover the calculation is extended to any field for a hypothetical ion (S = K = 1/2) the relaxation mechanism of which is assumed to be caused by a hypothetical stochastic field (Abragam model).
- 4The results show that the influence of hyperfine coupling is generally not negligible. In weak fields the relaxation rates may be only 50% of the values derived from the usual high field equations. In medium fields an anomale frequency dependence may occur.
- 5Similar effects are to be expected for all paramagnetic ions which show a well resolved hyperfine splitting in solution (e. g. V2+-ions).