Fermi contact interaction term

The hyperfine structure is described by the isotropic Fermi contact interaction term (75), which for the negative ion of naphthalene can be written in the form ... 

From the isotropic coupling constant one may calculate C12, the fractional occupancy of the nitrogen s orbital, which is equal to AUo/Ao. The term Ao is the Fermi contact interaction for an unpaired electron in a pure nitrogen 2s orbital. For NO2 the value of ci2 = 56.5/550 = 0.103. The fraction of the unpaired electron associated with the N nucleus is then... 

Fermi contact interaction. The coupling constant of the Fermi contact term for the nucleus N has the form127 ... 

The hyperfine coupling tensor (A) describes the interaction between the electronic spin density and the nuclear magnetic momentum, and can be split into two terms. The first term, usually referred to as Fermi contact interaction, is an isotropic contribution also known as hyperfine coupling constant (HCC), and is related to the spin density at the corresponding nucleus n by [25]... 

The hyperfine coupling frequency in the hydrogen ground state is given to the leading term by the Fermi contact interaction, yielding... 

The remaining important interactions which can occur for a 2 or3X molecule involve the presence of nuclear spin. Interactions between the electron spin and nuclear spin magnetic moments are called hyperfine interactions, and there are two important ones. The first is called the Fermi contact interaction, and if both nuclei have non-zero spin, each interaction is represented by the Hamiltonian term... 

This is a very important result. The first term in the last line of (4.13) represents the so-called Fermi contact interaction between the electron and nuclear spin magnetic moments, and the second term is the electron-nuclear dipolar coupling, analogous to the electron-electron dipolar coupling derived previously in (3.151). The Fermi contact interaction occurs only when the electron and nucleus occupy the same position in Euclidean space, as required by the Dirac delta function S(-i Rai). This seemingly... 

The magnetic hyperfine interaction is represented by the sum of two terms, representing the Fermi contact interaction, and 3Qiip representing the electron spin-nuclear spin dipolar interaction. They are written as follows ... 

We come now to the magnetic hyperfine interaction terms. Again we make use of the results derived earlier for ortho-H2 in the c 3 nu state. For the Fermi contact interaction, from equation (8.220) ... 

It is instructive to consider in quantitative detail the analysis of a particular hy-perfine transition a simple example would seem to be the F = 2 <+ 1 transition in the level It = 1, N = 0, J = 1, which is observed at a frequency of 20.846 MHz for the v = 0 level. The expressions for the matrix elements of the magnetic and electric hy-perfine terms, (8.258), (8.259) and (8.270), show that for N =0 only the Fermi contact interaction is non-zero and the energies of the hyperfine levels are... 

The next term in the magnetic hyperfine Hamiltonian (8.351) describes the Fermi contact interaction and the calculation of its matrix elements proceeds in a manner similar to that just described for the orbital hyperfine term, as follows ... 

The second part of this term may be regarded as a small correction to the Fermi contact interaction the matrix elements of the first part are diagonal in Q, J and F, with matrix... 

The orbital hyperfine constant a is the same in both (8.509) and (8.510), but the second term in (8.510) describes only the Fermi contact interaction, the constant hp being equal to the first part of b in (8.509). It is clear from a comparison of the two equations that... 

The magnetic hyperfine terms are now familiar, representing the Fermi contact interaction and axial dipolar interaction ... 

The matrix elements were derived in a case (b) basis for each of these terms. For the Fermi contact interaction (8.220) we retain matrix elements off-diagonal in J which can be significant ... 

The fourth and last terms in (11.49) are spin-orbit distortion corrections to the spin-rotation and Fermi contact interactions. The hyperfine and quadrupole terms in this Hamiltonian refer to the 14N nucleus. 

Note that Jefferts used d for y and / for c/. The first two terms contain contributions from both the Fermi contact interaction and the axial component of the electron spin-nuclear spin dipolar interaction, z being along the direction of the internuclear axis. 

We use a basis set ij, A I, 5, G, N, F, M) where // is taken to represent different vibrational levels of the ground electronic state Jefferts measurements involved the v = 4 to 8 levels, these being the ones with the optimum populations and photodissociation cross-sections. The matrix elements of each term in (11.79) are now readily calculated. The Fermi contact interaction is found to be diagonal in the chosen basis ... 

The terms in equation (4) are generally referred to as the orbital-dipolar interaction (o) between the orbital magnetic fields of the electrons and the nuclear spin dipole, the spin-dipolar interaction (D) between the spin magnetic moments of the electrons and nucleus and the Fermi contact interaction (c) between the electron and nuclear spins, respectively. Discussion of the mathematical forms of each of these three terms appears elsewhere. (3-9)... 

A serious drawback to this model is its inability to account for observed Fermi contact interactions. The usual Slater determinant uses the same molecular orbital for spin up as for spin down and will therefore yield a Fermi contact contribution only if the orbital with the unpaired electron contains the s orbital of the atom concerned. Symmetry restrictions, however, prevent the presence of s orbitals in the molecular orbital for aromatic free radicals and many transition metal complexes nevertheless, the large isotropic terms observed in these systems require an extensive contribution from the Fermi contact term. This is explained by assuming the unpaired electrons polarize the inner-filled orbitals having s character to produce a small net unpairing of spin. Very small polarizations will produce large Fermi terms due to the large density of s orbitals in the vicinity of the nucleus. Theoretically, this problem is handled in... 

The first defect is in ignoring or overlooking the fact that orbital effects, discussed under Electron Spin-Nuclear Spin Interaction, can make major contributions to the observed shifts and must be accounted for in order to get the correct Fermi contact contributions. Many researchers have assumed the total isotropic term is from the Fermi contact interaction. 

Coupling constants are usually analysed at present in terms of a MO theory developed by Pople and Santry. They showed that coupling constants involving directly bonded atoms arise almost entirely from the Fermi contact interaction between nuclear moments and electron spins in 5 orbitals. Using the LCAO approximation and retaining only one-centre integrals, they derived the following expression for Ja-b—... 

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