Lamb constants 83

Flanged Elliptical Opening The potential flow solution for an elliptical aperture in an infinite wall with a constant potential across the hood face is given by Lamb as... 

FIGURE 7.16 (A) Photocurrents of salamander rod cells following light flashes giving between 10 and 2000 rhodopsin molecule isomerizations. (B) Calculated increments in phosphodiesterase hydrolytic rate constant. (From Lamb, T. D. and Pugh, Jr., E. N., Trends Neurosci., 15, 291-299, 1992. With permission.)... 

One solution that was considered by Rayleigh (Lamb, 1945) for the determination of bubble collapse time, tm, used the model of a bubble with initial size Rm, suddenly subjected to a constant excess liquid pressure pL. Neglecting the surface tension and the gas pressure in the bubble, Eq. (2-29) may be rearranged to... 

Lamb, J. D., Izatt, R. M. Christensen, J. J. (1981). Stability Constants of Cation-Macrocycle Complexes and Their Effect on Facilitated-Transport Rates, Ch 2 in Progress in Macrocyclic Chemistry, Volume 2, ed. R. M. Izatt J. J. Christensen. Wiley-Interscience, New York. 

Gooberman and Lamb [10] used molecular weight distributions to produce rate constants that were independent of any predetermined kinetics scheme. The effect due to degradation of higher species was also ignored to produce Eq. 5.15 where 11 is the number of molecules of length P. ... 

With a monomode CO2 laser, delivering a constant power on any rotational line of either the 10.4 jtx or the 9.4 n band, Bordfe and Henry studied the shape of Lamb dip profiles in CO2 which became asymmetric when two rotational lines were allowed to oscillate simultaneously, since the gains are tightly coupled by rotational thermalization. 

The intervals of gross structure are mainly determined by the Rydberg constant, and the same transition frequencies should be used both for measurement of the Rydberg constant and for measurement of the IS Lamb shift. 

The first task is to obtain an experimental value of the IS Lamb shift which is independent of the precise value of the Rydberg constant. This goal may be achieved by measuring two intervals with different principal quantum numbers. 

For example, measurement of the IS Lamb shift in [34] is disentangled from the measurement of the Rydberg constant by using the experimental data on two different intervals of the hydrogen gross structure [34]... 

Due to the suppression factor the difference of the leading Dirac and recoil contribution of the RHS in (12.10) may be calculated with high accuracy, and practically does not depend on the exact value of the Rydberg constant. Then the precise magnitude of the linear combination of the Lamb shifts on the RHS extracted from the experimentally measured frequencies on the LHS and calculated difference of the leading Dirac and recoil contribution of... 

Determination of the most precise value of the Rydberg constant requires a comprehensive analysis of results of the same experiments used for determination of the 15 Lamb shift [26, 31, 32, 33, 34, 35, 36]. This analysis was performed in [1], and resulted in the value in (12.1) which has relative uncertainty 6 = 6.6 X 10. This uncertainty is limited by the experimental... 

This experimental development was matched by rapid theoretical progress, and the comparison and interplay between theory and experiment has been important in the field of metrology, leading to higher precision in the determination of the fundamental constants. We feel that now is a good time to review modern bound state theory. The theory of hydrogenic bound states is widely described in the literature. The basics of nonrelativistic theory are contained in any textbook on quantum mechanics, and the relativistic Dirac equation and the Lamb shift are discussed in any textbook on quantum electrodynamics and quantum field theory. An excellent source for the early results is the classic book by Bethe and Salpeter [6]. A number of excellent reviews contain more recent theoretical results, and a representative, but far from exhaustive, list of these reviews includes [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. 

Lamb, J. D. and Smith, R. G. (1992) A Comparison of Gradient Capacity Anion Chromatography Using Macrocycles D-2.2.2 and D-2.2.1 in Constant or Variable Temperature Mode, Talanta 39, 923-930. 

The absolute frequency of the fundamental IS — 2S transition in atomic hydrogen has now been measured to 1.8 parts in 1014, an improvement by a factor of 104 in the past twelve years. This improvement was made possible by a revolutionary new approach to optical frequency metrology with the regularly spaced frequency comb of a mode locked femto-second multiple pulsed laser broadened in a non-linear optical fiber. Optical frequency measurement and coherent mixing experiments have now superseded microwave determination of the 2S Lamb shift and have led to improved values of the fundamental constants, tests of the time variation of the fine structure constant, tests of cosmological variability of the electron-to-proton mass ratio and tests of QED by measurement of g — 2 for the electron and muon. 

The aim of this section is to extract from the measurements the values of the Rydberg constant and Lamb shifts. This analysis is detailed in the references [50,61], More details on the theory of atomic hydrogen can be found in several review articles [62,63,34], It is convenient to express the energy levels in hydrogen as the sum of three terms the first is the well known hyperfine interaction. The second, given by the Dirac equation for a particle with the reduced mass and by the first relativistic correction due to the recoil of the proton, is known exactly, apart from the uncertainties in the physical constants involved (mainly the Rydberg constant R0c). The third term is the Lamb shift, which contains all the other corrections, i.e. the QED corrections, the other relativistic corrections due to the proton recoil and the effect of the proton charge distribution. Consequently, to extract i oo from the accurate measurements one needs to know the Lamb shifts. For this analysis, the theoretical values of the Lamb shifts are sufficiently precise, except for those of the 15 and 2S levels. 

Most of the combinations to derive i oo, which scales all atomic energy levels and is used to adjust other constants [61], and the ground state Lamb shift L(1S), which allows one of the best tests of QED, yield a comparable accuracy. Therefore, a general adjustment gives the best answers to date [61,49]. 

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