Hyperfine energy

Thus both the (/-factor and the Upvalues affect Tq-S mixing. In general, the two radicals comprising the radical pair will have different gr-values and therefore different Zeeman energies [the first term in equation (12)]. Likewise the upvalues and hyperfine energies [the second term in equation (12)] will differ. The difference between the LPFs for two radicals is then given by equation (13), where gx and are the electronic y-factors... 

Fig. 8.1. Scheme of hyperfine energy levels in the ground state... 

The new value has an experimental error which corresponds to measuring the hyperfine energy splitting at the level of Z z/ea p/(T)t//i) 7 x 10 of the natural linewidth. This is a remarkable experimental achievement. 

The atom exhibits very regular, hyperfine energy-level transitions and it is possible to count these cycles of energy. In 1967 the General Conference accepted 9,192,631,770 cycles of cesium-133 as the measurement of one second, making the atomic clock the true international timekeeper. The cesium clock is maintained in Boulder, Colorado, in the offices of the National Institute of Standards and Technology (formally the National Bureau of Standards). Its accuracy is one part in 1,000,000,000,000 (10 12). It will not gain or lose a second in 6000 years. 

We now combine these results with (8.273) to obtain the total hyperfine energies of the... 

Substituting these values in (8.276) we obtain the following values for the hyperfine energies, and the frequency of the hyperfine transition (all in MHz) ... 

In an electric field of 1475 V cm 1 the Stark energies are +298.119 kHz for Mj = 0, and are —149.064 kHz for Mj = 1. Using these values and the molecular constants given above, we may construct the hyperfine energy level diagram shown in figure 8.38. We label the levels with the basis state labels used in the above... 

Figure 8.38. Hyperfine energy levels and calculated structure for the AM/ = 1 transitions in the. / = 1 level of HF, assuming an electric field of 1475 V cm-1 and the values of the constants given in the text. The predicted structure may he compared with that observed, as shown in figure 8.37. The quantum numbers on the right hand side are the values for MF, MH and Mj (and are only approximate). The total quantum number Mz = Mj + MH + MF is a good one, however.

Figure 11.58. Hyperfine energy levels and magnetic dipole transitions for Hj in the N = 1 rotational level (not to scale). The dashed lines indicate magnetic-dipole allowed transitions which were not observed experimentally (see text).

In some physical situations, namely when the hyperfine energy is small compared to the nuclear Zeeman energy, then the hyperfine splitting is linear in (the projection magnitude of) matrix A for example, see Ref. 131. Then, provided that g is anisotropic (note Ref. 128 on this point), one can detect asymmetry of A directly from EPR line-position measurement see below. 

Fig. 2.19. Breit—Rabi hyperfine energy level diagram for ground-state hydrogen, showing the magnetic energy of the atom A IF normalised to the hyperfine splitting at zero field (5 W).

J.A. Weil, Hydrogen atom in a spherical box. II. Effect on hyperfine energy of excited state admixture, J. Chem. Phys. 71 (7) (1979) 2803-2805. 

For -states the hyperfine energy is the product of the magnetic induction at the origin which arises from the density of the electron-spin magnet there, multiplied by the nuclear magnetic moment. Thus... 

It is hopefully clear by now that even the simplest diatomic molecule-atomic collision partner limit presents us with a number of possible types of contributing collisions to the collision-induced intersystem-crossing rates. It should be emphasized that a truly quantitative treatment would have to even include any hyperfine energies as the mixing angles (3.3c) can be greatly affected by zeroth order hyperfine shifts that are comparable to... 

Since we treat the hyperfine energy contribution by first-order perturbation theory we have a four-component Hamiltonian describing the hyperfine interaction according to... 

At time <2 [Case (2)] therefore, the hyperfine energy is approximately equal to the energy difference between the S and T states and can provide the driving force for T-S mixing. Now the hyperfine constants Uj and Oj are a function of both nuclear and electronic spin states and thus one particular nuclear spin state for Hj and Hj will induce the T-S mixing more readily than the other. Thus nuclear spin selection occurs during the transition between S and T manifolds. However, this would yield no... 

Figure 10.84. Hyperfine energy level diagram and observed transitions (solid lines) for the J = 3/2 - 1/2 rotational transition of NbO in the [237].

One second is defined as 9,192,631,770 times the period of the electromagnetic radiation (see the Physical and Theoreticcd Chemistry chapter for more on electromagnetic radiation) corresponding to the difference in hyperfine energy levels in the ground state of a Cesium-133 atom. 

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