State-dependent corrections

Some nuclear-structure- and state-dependent corrections were found [23] for arbitrary ns. 

The similar difference has been under investigation also for the Lamb shift and a number of useful auxiliary expressions have been found for calculating the state dependent corrections to the Lamb shift [24]. 

This vanishes in the leading non-relativistic approximation (1) and so it is sensitive to state-dependent corrections to the hyperfine structure. 

The other state-dependent corrections originate from accurate calculations of the Zemach term, which is proportional to the value of the wave function at the origin (i/ (0)). The wave function affected by the Uehling potential leads to a correction... 

Quality in NDT depends upon a number of factors. Qualification of NDT personnel, technical state and correctness of choice of testing equipment, availability of approved working procedures of examination, calibration of NDT equipment have decisive importance among those factors of an NDT laboratory. Assessment of NDT laboratory competence is provided through accreditation in compliance with the EN 45000 series standards. 

Calculation of the state-dependent nonlogarithmic contribution of order a(Za) is a difficult task, and has not been done for an arbitrary principal quantum number n. The first estimate of this contribution was made in [63]. Next the problem was attacked from a different angle [64, 65]. Instead of calculating corrections of order a(Za) an exact numerical calculation of all contributions with one radiative photon, without expansion over Za, was performed for comparatively large values of Z (n = 2), and then the result was extrapolated to Z = 1. In this way an estimate of the sum of the contribution of order a(Za) and higher order contributions a(Za) was obtained (for n = 2 and Z = 1). We will postpone discussion of the results obtained in this... 

The approach does not aim to satisfy the condition Eq. 6.73 exactly. The model functions consist of a sum of three functions whose parameters are related to three -independent and three -dependent terms of the quantum spectral moments, Eqs. 6.31 through 6.34 v is the vibrational quantum number of the final states which differs from v, the initial vibrational state. As a result, the line profile consists of a core which is the same as for rototranslational spectra, and a i/-dependent correction . It converges to the standard solution for potentials that do not depend on the vibrational excitation. The models are six parameter functions which are defined by the lowest three spectral moments [48, 65],... 

Conventionally, the evaluation of bound-state QED corrections is made tractable by including the vacuum fluctuations in several steps. The corrections thus calculated are called radiative corrections, and their evaluation can be made by making two expansions. The first is in powers of (a/7r) and denotes the number of photon propagator loops present. The second is in the number of photon exchanges with the nucleus and is in powers of (Zot), where Z is the nuclear charge. The expression in equation 1 shows the first two terms of the (o/tt) expansion for the case of hydrogenic S-states, i.e. up to two photon loops. In this expression the second expansion has not yet been made and the (Za) dependence is still contained within the functions F and H. 

The product of activity coefficients /and the mole fraction x is often called activity a. It is noteworthy that the chemical equilibrium constant can only be calculated if the acitivity coefficients are known. In the case of reactive distillation, this information is available. It should be mentioned that the equilibrium constant can be calculated from the pure free enthalpies of formation that have to be corrected to the reaction state depending on the model (activity coefficients or fugacity) used. 

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