Level crossing zero field

The first term is characterized by a scalar, 7, and it is the dominant term. Be aware of a convention disagreement in the definition of this term instead of -27, some authors write -7, or 7, or 27, and a mistake in sign definition will turn the whole scheme of spin levels upside down (see below). The second and third term are induced by anisotropic spin-orbit coupling, and their weight is predicted to be of order Ag/ge and (Ag/ge)2, respectively (Moriya 1960), when Ag is the (anisotropic) deviation from the free electron -value. The D in the second term has nothing to do with the familiar axial zero-field splitting parameter D, but it is a vector parameter, and the x means take the cross product (or vector product) an alternative way of writing is the determinant form... 

Pulsed field ionization of an alkali atom differs from the description just given for H because of the finite sized ionic core, or equivalently, the nonzero quantum defects. There are three important effects. First, the zero field levels can only be spherical nim levels, not parabolic levels. Second, in the E > l/3n5 regime there are avoided crossings of states of different n. Third, ionization can occur at lower fields than in H. Specifically, in H blue states have higher ionization fields than red states, but in an alkali atom this is not the case due to nx changing ionization. 

German, K.R., Bergman, T.H., Weinstock, E.M. and Zare, R.N. (1973). Zero-field level crossing and optical radio-frequency double resonance studies of the A2E+ states of OH and OD, J. Chem. Phys., 58, 4304-4318. 

In our picture of microwave ionization the n dependence of the ionization fields comes from the rate limiting step between the bluest n and reddest + 1 Stark states. It would be most desirable to study this two level system in detail, but in Na this pair of Stark levels is almost hopelessly enmeshed in all the other levels. In K, however, there is an analogous pair of levels which is experimentally much more attractive [17,18]. The K energy levels are shown in Fig. 6. All are m = 0 levels, and we are interested in the 18s level and the Stark level labelled (16,3). We label the Stark states as (n, k) where n is the principal quantum number and k is the zero field state to which the Stark state is adiabatically connected. As shown in Fig. 6, the (16, k) Stark states have very nearly linear Stark shifts and the 18s state has only a very small second order Stark shift, which is barely visible on the scale of Fig. 6. The 18s and (16,3) states have an avoided crossing at a field of 753 V/cm due to the coupling produced by the finite size of the K-" core [19]. 

Because of the large distribution of trap levels and difficulties in preparing a homogeneous surface, surface-state trapping is usually studied by characterising the surface recombination velocity. The details of the trapping dynamics can only be qualitatively determined as a product of an effective cross section and surface-state density. These experiments are generally conducted under zero-field conditions (e.g. 

Figure 5.25 Zeeman splitting of an 5 = 2 paramagnet with D = -0.5 cm" and E = 0.01 cm" with the applied field along the molecular z axis. Inset expansion of level anti-crossing between Ms = +2 at zero field...

Another consequence of the interference betweenH2 and Hfield is manifest as an asymmetry in the behavior of rotational levels above and below a zero-field level crossing. Let E — E = A > 0 then the crossings occur at... 

The anticrossings will be much narrower in rotational levels either above (E >E°2) or below ( ° < E ) the zero-field level crossing, depending on the relative signs of H12 and pt 2- The sign of H12H12 is thus an experimental observable and, provided that consistent wavefunction phases are used in computing H12 and H12, should be a priori predictable. 

CIDNP and CIDEP Studies.—Two mechanisms have been proposed to account for the observation of electron spin polarization in radical reactions (CIDEP), the first being termed the radical pair mechanism, in which the polarization results from the mixing of the singlet and triplet states of the radical pair by the magnetic interactions within the radicals, and the second the triplet mechanism, in which the polarization originates in the triplet as a result of spin-selective intersystem crossing from the photoexcited singlet state, as is known to occur in several systems from ODMR measurements (see above). It has recently been pointed out 480 that, for the latter mechanism, unequal population of the triplet sub-levels will depend upon zero-field D and E terms and Zeeman terms, but also... 

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