Hydrogen hyperfine fields

Lepidocrocite is paramagnetic at room temperature. The Neel temperature of 77 K is much lower than that of the other iron oxides and is the result of the layer-like structure of this mineral. The sheets of Fe(0,0H)6 octahedra are linked by weak hydrogen bonds, hence magnetic interactions are relatively weak. The saturation hyperfine field is also lower than for any other iron oxide (Tab. 6.2). In the antiferromagnetic state, the spins are ordered parallel to the c-axis with spins in alternate layers having opposite signs. A decrease of T by 5 K was observed for Al-lepidocrocites with an Al/(Fe-i-Al) ratio of 0.1 (De Grave et al., 1995). 

Secondly, only 4 hours of reduction with hydrogen is necessary to completely reduce these samples. The most easily reduced anion is [FeCClOgNO2-] and for the corresponding Zn2+ and Cu2+ samples, complete reduction is noted in the Mossbauer spectrum. As indicated in Table II, the reported isomer shifts are all close to that of metallic iron and the hyperfine field strength, H, values are all very close to that of alpha iron. It should be noted here that whenever the cation was Fe2+ that reduction was never complete. We now believe that these ion-exchanged Fe2 ions are strongly bonded to the lattice and are not easily reduced. This is also the belief of several other investigators (2-5, 8, 10). 

Experimental support for Breit s suggestion comes not only from hydrogen hyperfine structure, but also from experiments in which atomic magnetic moments are compared directly through their precessional frequencies in the same field. Kusch and Foley [78] compared the moments of gallium in the... 

Fig. 3. Energy levels for the hydrogen atom at constant magnetic field. The allowed transitions having energy = gftB (ha)j2, where a is the hydrogen hyperfine constant.

Future (hydrogen maser) 9 1 420 405 751-786 periods of hydrogen hyperfine oscillation in zero magnetic field... 

Here, /3 and / are constants known as the Bohr magneton and nuclear magneton, respectively g and gn are the electron and nuclear g factors a is the hyperfine coupling constant H is the external magnetic field while I and S are the nuclear and electron spin operators. The electronic g factor and the hyperfine constant are actually tensors, but for the hydrogen atom they may be treated, to a good approximation, as scalar quantities. 

The spin Hamiltonian for the hydrogen atom will be used to determine the energy levels in the presence of an external magnetic field. As indicated in Section II.A, the treatment may be simplified if it is recognized that the g factor and the hyperfine constant are essentially scalar quantities in this particular example. An additional simplification results if the z direction is defined as the direction of the magnetic field. For this case H = Hz and Hx = Hv = 0 hence,... 

In those calculations, the contributions from electronic orbital motion (induced by spin-orbit mixing) were estimated from crystal field theory (for the copper atom) or were neglected (for the nitrogen and hydrogen atoms). Here I discuss for the first time direct calculations of these contributions to the copper and nitrogen hyperfine tensors, as well as to the molecular -tensor. 

For a hydrogen atom in an external field of 10,000 G, draw a figure that shows the effect on the original 1 s energy level of including first the electron Zeeman term, then the nuclear Zeeman term, and finally the hyperfine coupling term in the Hamiltonian. 

Fig. 1. Hyperfine diagram for the ground state of atomic hydrogen. The high field seeking states a and b can be stabilized in a high magnetic field, while the low field seeking states c and d are trapped in the minimum of a magnetic field...

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