High-field limit

Schmidt (1976) has given a classical model for the field dependence of quasi-free electron mobility that predicts p(E) in the high-field limit. At any... 

In the high-field limit (F > 1 atomic unit meaning that it is greater than the binding potential) the smoothed Coulomb potential in Eq. (2) can be treated as a perturbation on the regular, classical motion of a free electron in an oscillating field. So, let us first consider the Hamiltonian for the one-dimensional motion of a free electron in the... 

East and co-workers have dealt with the electron spin relaxation problem for ions with half-filled shells (3c , S = 5/2, such as Mn(II) or Af, S = 7/2, such as Gd(III)) in the high-field limit 120). They allowed for a static ZFS, containing also terms with tensorial rank four and six, along with the rank-two term discussed before. The static ZFS was assumed to be modulated by rotational diffusion. In addition, they included the rank-two transient ZFS,... 

Models for the outer-sphere PRE, allowing for faster rotational motion, have been developed, in analogy with the inner sphere approaches discussed in the Section V.C. The outer-sphere counterpart of the work by Kruk et al. 123) was discussed in the same paper. In the limit of very low magnetic field, the expressions for the outer-sphere PRE for slowly rotating systems 96,144) were found to remain valid for an arbitrary rotational correlation time Tr. New, closed-form expressions were developed for outer-sphere relaxation in the high-field limit. The Redfield description of the electron spin relaxation in terms of spectral densities incorporated into that approach, was valid as long as the conditions A t j 1 and 1 were fulfilled. The validity... 

The sum in the denominator represents the total coupling width of all the low-/ states to the continuum (or continua). The predictions of Bixon and Jortner are in semiquantitative agreement with the MQDT results presented here for example they would predict a mean lifetime of approximately 18 ns for the long-lived states in the region of n = 90 in the high-field limit. 

In the low field limit the ZFS term (the second in the above equation) is dominant, while in the high field limit the Zeeman term (the first in the above equation) is dominant. 

Nuclear transition energies are given by E2 — E and 4 — 3. By referring for simplicity to the high field limit, i.e. when Ze A, we have... 

This exponential relation is appropriate for the intermediate-field limit corresponding to the current given by eqn. (144), as well as for the high-field limit since it does not further reduce whenever qEa/kBT < 1. 

Let us now consider the particle current in the high-field limit for the cases depicted in Fig. 13. Equation (90) is applicable to each of these cases, so that it is possible to examine the predicted effects of the immobile (trapped) space charge on these particle currents. Utilizing our previous conclusion that space charge having the same sign as the surface-charge... 

In the other extreme, / / > 1, the low-temperature or high-field limit, Bs(j) ( )- 1 and Ms = Nog/UBS(J), which is called the saturation moment and is obtained from analysis of data at very low temperatures. These two moments are often confused. 

Here, Ci , is a cofficient which depends on ZFS, B, and the Euler angles relating the molecular and laboratory frames. At a high field limit, all the [ C, , p values become 1/3 for fast tumbling molecules. On the other hand, when the field is not high enough ans/or when the molecule rotation is not so fast, the C,m p values do not necessarily become 1/3. 

The CIDEP due to the T-D quenching occurs at a high field limit from the following procedures ... 

Coulomb Result and the Landau High Field Limit. 71... 

Pfalzner and March [14] have performed numerically the Laplace transform inversion referred to above to obtain the density p( ) from the Slater sum in Eq. (10). Below, we shall rather restrict ourselves to the extreme high field limit of Eq. (10), where analytical progress is again possible. Using units in which the Bohr magneton is put equal to unity, the extreme high field limit amounts to the replacement of the sinh function in Eq. (10) by a single exponential term, to yield... 

The extreme high field limit B tends to infinity is obtained from Eq. (30) by making use of Eq. (28). The result is... 

Ground-State Energy Scaling Properties of Heavy Positive Atomic Ions in Extreme High Field Limit... 

In the extreme high field limit, the scaling properties of the ground-state energy (Z, N, B) can be exposed for positive atomic ions with nuclear charge Ze and with N electrons from the Thomas-Fermi (TF) theory set out above [28]. 

Taking first the high field limit one readily finds from Eq. (B16) B... 

In the high field limit, where the quadrupole interaction acts as a perturbation of the Zeeman states, the terms of this Hamiltonian which commute with L lead to the perturbation of first-order... 

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