Form factor, magnetic expansion

Electron spin resonance, nuclear magnetic resonance, and neutron diffraction methods allow a quantitative determination of the degree of covalence. The reasonance methods utilize the hyperfine interaction between the spin of the transferred electrons and the nuclear spin of the ligands (Stevens, 1953), whereas the neutron diffraction methods use the reduction of spin of the metallic ion as well as the expansion of the form factor [Hubbard and Marshall, 1965). The Mossbauer isomer shift which depends on the total electron density of the nucleus (Walker et al., 1961 Danon, 1966) can be used in the case of Fe. It will be particularly influenced by transfer to the empty 4 s orbitals, but transfer to 3 d orbitals will indirectly influence the 1 s, 2 s, and 3 s electron density at the nucleus. 

We have seen above that calculation of the corrections of order a"(Za) m (n > 1) reduces to calculation of higher order corrections to the properties of a free electron and to the photon propagator, namely to calculation of the slope of the electron Dirac form factor and anomalous magnetic moment, and to calculation of the leading term in the low-frequency expansion of the polarization operator. Hence, these contributions to the Lamb shift are independent of any features of the bound state. A nontrivial interplay between radiative corrections and binding effects arises first in calculation of contributions of order a Za) m, and in calculations of higher order terms in the combined expansion over a and Za. 

In some early work, an expansion in powers of sin d has been employed. However, the spherical harmonics form an orthogonal basis and are thus more appropriate. An expansion in Legendre polynomials P (cos 0) has also been frequently used. Although these functions are equivalent to the Y%0,4>)> due account of the scaling factor has not always been included in previous comparisons of anisotropy results. The microscopic anisotropy parameters comprise the terms of various physical origins which enter into the hamiltonian for the system. If the hamiltonian is written in a representation Slf(0,4>) in which the quantization axis is along the magnetization direction, the microscopic and... 

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