Lamb theory

For molecules the Lamb theory is inadequate because it assumes that the electrons are free to move in any direction, whereas in a molecule electronic motion is severely restricted. Ramsey50 used second-order perturbation theory to develop a formula that in principle accounts for the shielding factor in molecules and has long provided a framework for qualitative understanding of the major factors... 

M.D. Levenson, Introduction to Nonlinear Spectroscopy (Academic, New York, 1982) WE. Lamb, Theory of an optical maser. Phys. Rev. A 134, 1429 (1964)... 

W. Lamb, Theory of an optical maser, Phys. Rev. 134A, 1429-1450 (1964). 

Lamb G L Jr 1980 Eiements of Soiiton Theory (New York Wiley)... 

Lagrange Multiplier Method for programming problems, 289 for weapon allocation, 291 Lamb and Rutherford, 641 Lamb shift, 486,641 Lanczos form, 73 Landau, L. D., 726,759, 768 Landau-Lifshitz theory applied to magnetic structure, 762 Large numbers, weak law of, 199 Law of large numbers, weak, 199 Lawson, J. L., 170,176 Le Cone, Y., 726... 

Similarly, self-administration of MDMA in monkeys trained to self-administer amphetamine (Kamien et al. 1986) or in monkeys or baboons trained to self-administer cocaine (Beardsley et al. 1986 Lamb and Griffiths 1987) probably reflects a dopaminergic component to the pharmacology of MDMA. This would be consistent with current theories of dopamine involvement in the mechanism of action of drugs with dependence liability (Wise and Bozarth 1987). 

Letter from G. N. Lewis to Paul Ehrenfest, undated but probably 1925, G. N. Lewis Correspondence, BL.UCB. G. N. Lewis and D. F. Smith promised in their paper, "The Theory of Reaction Rate," JACS 47 (1925) 15081520, to publish a demonstration that a range of frequencies of radiation affecting degrees of freedom in a molecule is responsible for chemical reaction. This paper was the subject of the letter, with anonymous referee s report, from Arthur B. Lamb to G. N. Lewis, 28 February 1925, G. N. Lewis Papers, BL.UCB. The referee said "No real unimolecular reaction has actually been observed they have been shown to be merely catalytic the idea that a unimolecular reaction is due to collision between a quantum and a molecule is not original with Lewis."... 

Lamb and co-workers reviewed techniques of diffusion modeling for air quality with relation to transportation-generated pollution. They discussed the theory and structure of models, presented a series of tabulated comparisons, analyzed the function and design of each model, and offered simple diagrams to illustrate the functions and problems of the various techniques. The report was intended to survey a great deal of unpublished material and therefore was important in bringing the earlier surveys up to date (to about mid-1973). 

The theory behind the method to measure the burning rate was not explicitly presented by Lamb et al. Obviously, the mathematical model must be based on the bed properties, such as packing ratio, loading density, bed height, as well as the trolley speed. No discussion is presented about the limitations and assumptions of the method. 

This situation corresponds to the well-known saturation effect in the emission of most gas laser transitions, where, for the same reason, fewer upper-state molecules can contribute to the gain of the laser transition at the center of the doppler-broadened fluorescence line than nearby. When tuning the laser frequency across the doppler-line profile, the laser intensity therefore shows a dip at the centerfrequen-cy, called the Bennet hole or Lamb dip after W.R. Bennet who discovered and explained this phenomen, and W.E. Lamb 2) who predicted it in his general theory of a laser. 

In the language of control theory, Tr[p(0)P] is a kinematic critical point [87] if Eq. (4.159) holds, since Tr[e p(0)e- P] = Tr[p(0)P] + Tr(7/[p(0),P]) + O(H ) for a small arbitrary system Hamiltonian H. Since we consider p in the interaction picture, Eq. (4.159) means that the score is insensitive (in first order) to a bath-induced unitary evolution (i.e., a generalized Lamb shift) [88]. The purpose of this assumption is only to simplify the expressions, but it is not essential. Physically, one may think of a fast auxiliary unitary transformation that is applied initially in order to diagonalize the initial state in the eigenbasis of P. 

Calculation of the leading logarithmic corrections of order a Za) Ep to HFS parallels the calculation of the leading logarithmic corrections of order a(Za) to the Lamb shift, described above in Subsect. 3.5.1. Again all leading logarithmic contributions may be calculated with the help of second order perturbation theory (see (3.71)). 

The leading nuclear size correction of order Za) m r )EF may easily be calculated in the framework of nonrelativistic perturbation theory if one takes as one of the perturbation potentials the potential corresponding to the main proton size contribution to the Lamb shift in (6.3). The other perturbation potential is the potential in (9.28) responsible for the main Fermi contribution... 

Prom the theoretical point of view the accuracy of calculations is limited by the magnitude of the yet uncalculated contributions to the Lamb shift. Corrections to the P levels are known now with a higher accuracy than the corrections to the S levels, and do not limit the results of the comparison between theory and experiment. 

The Lamb shift theory of P-states is in a better shape than the theory of P-states. Corrections of order a(Za) are now known with uncertainty about 1 Hz for 2P states [10, 11, 12, 13]. 

Many experiments on the precise measurement of the classic Lamb shift were performed since its experimental discovery in 1947. We have collected modern post 1979 experimental results in Table 12.2. Two entries in this Table are changed compared to the original published experimental results [16, 15]. These alterations reflect recent improvements of the theory used for extraction of the Lamb shift value from the raw experimental data. 

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