Hyperfme constant

Assuming for the sake of simplicity an isotropic centre, the effective Bohr radius a can be obtained directly from the hyperfme constant A, since this scales as the third power of the radius ... 

Figure 5. Correlation of the normalized muonium hyperfme constant with electron affinity. (Courtesy of S F J Cox - reference 11.)...

Here the muonium hyperfme constant, relative to the vacuum-state value, is plotted versus electron affinity for a variety of materials, from insulators... 

Combined with a value of r for a electron [60], these angular averages give the following theoretical values for the magnetic hyperfme constants (in cm ) ... 

Safronova, M.S., Johnson, W.R., and Derevianko, A., Relativistic many-body calculations of energy levels, hyperfme constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms, Phys. Rev. A, 60, 4476-4487, 1999. 

It has always been our position to use no more than moderately size d wavefunction expansions. Current limits are about 20,000 symmetry adapted wavefunctions built from fewer than 1 million Slater determinants, and use of two virtuals per /, per shell (n). This allows the physics (systematics) to be more visible and reduces the need for large computational resources that were frequently unavailable in the old days. Development of systematic rules is one of the main goals of our research. Some examples follow (i) determining which correlation effects are most important for a specitic property [14,15], (ii) near conservation of f-value sums for nearly degenerate states [15,16], (iii) similar conservation of g-value sums [16], (iv) similar conservation of magnetic dipole hyperfme constants [17,18]. This approach does mean near maximal use of symmetry, creating extra auxiliary... 

Hence, a measurement of hyperfme coupling constants provides infonnation on spin densities at certain positions in the molecule and thus renders a map of tlie electronic wavefiinction. 

The simplest system exliibiting a nuclear hyperfme interaction is the hydrogen atom with a coupling constant of 1420 MHz. If different isotopes of the same element exhibit hyperfme couplings, their ratio is detemiined by the ratio of the nuclear g-values. Small deviations from this ratio may occur for the Femii contact interaction, since the electron spin probes the inner stmcture of the nucleus if it is in an s orbital. However, this so-called hyperfme anomaly is usually smaller than 1 %. 

The coupling constants of the hyperfme and the electron Zeeman interactions are scalar as long as radicals in isotropic solution are considered, leading to the Hamiltonian... 

As for CIDNP, the polarization pattern is multiplet (E/A or A/E) for each radical if Ag is smaller than the hyperfme coupling constants. In the case where Ag is large compared with the hyperfmes, net polarization (one radical A and the other E or vice versa) is observed. A set of mles similar to those for CIDNP have been developed for both multiplet and net RPM in CIDEP (equation (B1.16.8) and equation (B1.16.9)) [36]. In both expressions, p is postitive for triplet precursors and negative for singlet precursors. J is always negative for neutral RPs, but there is evidence for positive J values in radical ion reactions [37]. In equation (B 1.16.8),... 

Reductant Radical trapped by MNP Hyperfme splitting constant (mT) a N a ... 

Table 6 Hyperfme Splitting Constants of CAN-reductant- PBN Systems [38] ...

Table 3 presents the hyperfme splitting constants of some sulfur-containing aromatic radical anions. The series studied included the monoxides and dioxides of dibenzothio-phene 1, thioxanthene 2, thioxanthone 3, dibenzo[b,/] thiepin 4 and dithienothiophene dioxide 5. 

Dang, M.-Z. Rancourt, D.G. Dutrizac J.E. La-marche, G. Provencher, R. (1998) Interplay of surface conditions, particle size, stoichiometry, cell parameters, and magnetism in synthetic hematite-like materials. Hyperfme Interactions 117 271-319 Daniele, P.G. Rigano, C. Sammartano, S. Zeland,V. (1994) Ionic strength dependence of formation constants - XVIII. The hydrolysis of iron(III) in aqueous KNOj solutions.Ta-lanta41 1577-1582... 

Table 6. Comparison of the Isotropic Hyperfme Coupling Constants for the Flavosemiquinones...

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