Proton size contribution

Parametrically the result in (6.13) is of order m Za) m/A), where A is the form factor scale. Hence, this correction is suppressed in comparison with the leading proton size contribution not only by an extra factor Za but also by the extra small factor m/A. This explains the smallness of this contribution, even in comparison with the proton size correction of order (Za) (see below Subsect. 6.3.2), since one factor m/A in (6.13) is traded for a much larger factor Za in that logarithmically enhanced contribution. 

Theoretically, light muonic atoms have two main special features as compared with the ordinary electronic hydrogenlike atoms, both of which are connected with the fact that the muon is about 200 times heavier than the electron First, the role of the radiative corrections generated by the closed electron loops is greatly enhanced, and second, the leading proton size contribution becomes the second largest individual contribution to the energy shifts after the polarization correction. 

Nuclear size and structure corrections for the electronic hydrogen were considered in Chap. 6 and are collected in Table 7.1. Below we will consider what happens with these corrections in muonic hydrogen. The form of the main proton size contribution of order (Za) m (r ) from (6.3) does not change... 

The Zemach correction is essentially a nontrivial weighted integral of the product of electric and magnetic densities, normalized to unity. It cannot be measured directly, like the rms proton charge radius which determines the main proton size correction to the Lamb shift (compare the case of the proton size correction to the Lamb shift of order Za) in (6.13) which depends on the third Zemach moment). This means that the correction in (11.4) may only conditionally be called the proton size contribution. 

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... 

To overcome this limitation will require the measurement of the Lamb shift (the 2S-2P energy difference) in muonic hydrogen. Here the main QED contribution is vacuum polarization, for which calculations are now available at a precision level of 10-6 [11,12,13,14]. Because the effect of the finite proton size contributes as much as 2% to the pp Lamb shift, a precise measurement of the shift will provide an accurate value of the proton radius. The knowledge of the proton radius has intrinsic interest as a fundamental quantity, and is important in other measurements. A measurement of rp at 0.1% precision will permit QED calculations of bound systems to be compared with the ep experiments at a precision level of fewxlO-7 gaining an order of magnitude over the present limits. 

The main part of the nuclear size (Za) contribution which is proportional to the nuclear charge radius squared may also be easily obtained in a simpler way, which clearly demonstrates the source of the logarithmic enhancement of this contribution. We will first discuss in some detail this simple-minded approach, which essentially coincides with the arguments used above to obtain the main contribution to the Lamb shift in (2.4), and the leading proton radius contribution in (6.3). 

The total radiative correction to the proton size effect is given by the sum of contributions in (6.41) and (6.40)... 

The total proton size dependent contribution of order (Za)Ep, which is often called the Zemach correction, has the form... 

The recoil part of the proton size correction of order Za)Ep was first considered in [9, 10]. In these works existence of the nontrivial nuclear form factors was ignored and the proton was considered as a heavy particle without nontrivial momentum dependent form factors but with an anomalous magnetic moment. The result of such a calculation is most conveniently written in terms of the elementary proton Fermi energy Ep which does not include the contribution of the proton anomalous magnetic moment (compare (10.2) in the muonium case). Calculation of this correction coincides almost exactly... 

The last term in the braces is ultraviolet divergent, but it exactly cancels in the sum with the point proton contribution in (11.12). The sum of contributions in (11.12) and (11.13) is the total proton size correction, including the Zemach correction. According to the numerical calculation in [6] this is equal to AE = —33.50 (55) x lO Ep. As was discussed above, the Zemach correction included in this result strongly depends on the precise value of the proton radius, while numerically the much smaller recoil correction is less sensitive to the small momenta behavior of the proton form factor and has smaller uncertainty. For further numerical estimates we will use the estimate AE = 5.22 (1) X 10 Ep of the recoil correction obtained in [6]. 

Which contributes more to an atoms mass electrons or protons Which contributes more to an atom s size ... 

Finally, for hydrogenic systems it has been notedt33] that dominant uncertainty in the nuclear size contribution arises from the normalisation of the electron scattering form factors F(q) which are used to determine the proton and deuteron charge radii. However, if... 

A neutron is characterized by having no electrical charge but has one unit of atomic mass, the same as that of a proton (Figure 46.2). Neutrons, like protons, reside in the atomic nucleus and contribute to the mass of the atom. The chemistry of an atom, like its size, is determined by the electrons in the atom. The mass of the atom is characterized mainly by the total number of neutrons and protons in the nucleus (atomic binding energies are ignored in this discussion). For mass spectrometric purposes of measurement, it is the mass that is important in establishing m/z values. 

The kinetic solvent-isotope effects on these reactions are made up of primary and secondary kinetic isotope effects as well as a medium effect, and for either scheme it is difficult to estimate the size of these individual contributions. This means that the value of the isotope effect does not provide evidence for a choice between the two schemes (Kresge, 1973). The effect of gradual changes in solvent from an aqueous medium to 80% (v/v) Me2SO—H20 on the rate coefficient for hydroxide ion catalysed proton removal from the monoanions of several dicarboxylic acids was interpreted in terms of Scheme 6 (Jensen et al., 1966) but an equally reasonable explanation is provided by Scheme 5. 

The important and stimulating contributions of Kebarle and co-workers 119 14 > provide most of the data on gas-phase solvation. Several kinds of high pressure mass spectrometers have been constructed, using a-particles 121>, proton- 123>, and electron beams 144> or thermionic sources 128> as primary high-pressure ion sources. Once the solute A has been produced in the reaction chamber in the presence of solvent vapor (in the torr region), it starts to react with the solvent molecules to yield clusters of different sizes. The equilibrium concentrations of the clusters are reached within a short time, depending on the kinetic data for the... 

The Haber-Klemensiewicz effect relies on charge accumulation either side of the thin membrane of glass. Usually the proton is the only ion of suitable charge and size that can adsorb to the surface of the glass. The potential measured at the pH electrode is in fact the sum of the charges of all ions adsorbed at the glass solution interface, so if other ions were adsorbed, the potential measured would have additional contributions, i.e. from ions other than the proton. It would be non-selective, as described in Section 3.5.2.2 below. 

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