Theory of magnetic resonance parameters: Relativistic corrections and moment analysis

Hydrogen‐like relativistic corrections for electric and magnetic hyperfine integrals

“…For that reason the present corrections are, to some extent, obsolete. They may have applications to molecules or solids; reasonable results were obtained for the Knight shifts in metals [9]. Furthermore they allow some insight to the relativistic effects : after all the earlier discussions of quantum defects, screening constants etc., one here finds that the results for a hydrogenic atom having the true nuclear charge are better, a t least for the s I l 2 and p l l z cases.…”

“…The atomic electrons, however, are only slightly influenced by many-electron effects, when they are in the K shell. I n this manner we understand, at least qualitatively, why the Breit correction factor B(n, Z ) , r , = 1.2 x l0-13A-'/3 evaluated for the hydrogen-like atom, is applicable to real atoms to a good approximation [9]. Figure 1 also shows how limitations to our relativistic correction factor arise.…”

“…Pyykko and Pajanne [6] observed that the B(n, 2 ) agreed considerably better with the analogous ratios from relativistic and nonrelativistic Hartree-Fock-Slater calculations, than Equation (12). Pyykko [9] interpreted this success of the hydrogen-like B(n, 2 ) for many-electron atoms by showing, using moment analysis, that the hyperfine interaction arose mainly from distances where the potential is nearly Coulombic. (See Section 3 for a full discussion on this point.…”

“…The change is disregarded in our qualitative discussion in Figure 1.) Second, a typical distance at which the magnetic hyperfine interaction takes place is given by the radius rp, which is defined [9] by…”

“…At distances smaller than rn, the so-called nuclear-volume effects become operative. It was found in Reference [9] that even for the valence electrons of a Hartree-Fock wave function for heavier atoms, the distance r p always lies within the K shell ( r I , < rB for n = 1). At the same time it lies well outside the distances r T , rn and rm provided Z 2 100.…”