Nuclear size

Elton, L.R.B. Nuclear Sizes. Oxford University Press, Oxford (1961)... 

Bryant You have been showing us preparations in which nuclei have been stained. Are you estimating cell size from nuclear size ... 

Bryant Do you find that the nuclear size is proportional to cell size in all cells ... 

Dehner Neuroblast divisions are asymmetric not just because the cell determinants are distributed asymmetrically, but also the size of the GMC is very different, as is the nuclear size. Is nuclear size difference present from the outset If you look at cells in telophase, are the nuclei the same size ... 

Vande Woude Is it generally understood that nuclear size is regulated by asymmetrical divisions ... 

Bigeleisen, J. Nuclear size and shape effects in chemical reactions. Isotope chemistry of the heavy elements, J. Am. Chem. Soc., 118, 3676 (1996). 

As mentioned, most calculations we have done so far have concerned molecular systems. However, prior to development of the non-BO method for the diatomic systems, we performed some very accurate non-BO calculations of the electron affinities of H, D, and T [43]. The difference in the electron affinities of the three systems is a purely nonadiabatic effect resulting from different reduce masses of the pseudoelectron. The pseudoelectrons are the heaviest in the T/T system and the lightest in the H/H system. The calculated results and their comparison with the experimental results of Lineberger and coworkers [44] are shown in Table 1. The calculated results include the relativistic, relativistic recoil. Lamb shift, and finite nuclear size corrections labeled AEcorr calculated by Drake [45]. The agreement with the experiment for H and D is excellent. The 3.7-cm increase of the electron affinity in going from H to D is very well reproduced by the calculations. No experimental EA value is available for T. 

The term AEcorr contains relativistic, relativistic recoil, Lamb shift, and finite nuclear size... 

Cytoskeleton injury blebbing, shrinkage in apoptosis increased size in mitosis nuclear size contraction with apoptosis and swelling with cell cycle inhibition... 

The main difference between the quoted papers lies in the modeling of the magnetic moment distribution in the nucleus a bulk distribution is assumed in the present paper and in paper [11] and a surface distribution is adopted in ref [22]. A systematic 1% difference is observed, which cannot be explained by the uncertainty in the nuclear radius. However, it is known that variations of the nuclear size within reasonable limits can lead to variations in the value of A of several orders of magnitude [11, 14]. This question will be analysed in a separ-ate paper. 

The last class of corrections contains nonelectromagnetic corrections, effects of weak and strong interactions. The largest correction induced by the strong interaction is connected with the finiteness of the nuclear size. 

In the Breit Hamiltonian in (3.2) we have omitted all terms which depend on spin variables of the heavy particle. As a result the corrections to the energy levels in (3.4) do not depend on the relative orientation of the spins of the heavy and light particles (in other words they do not describe hyperfine splitting). Moreover, almost all contributions in (3.4) are independent not only of the mutual orientation of spins of the heavy and light particles but also of the magnitude of the spin of the heavy particle. The only exception is the small contribution proportional to the term Sio, called the Darwin-Foldy contribution. This term arises in the matrix element of the Breit Hamiltonian only for the spin one-half nucleus and should be omitted for spinless or spin one nuclei. This contribution combines naturally with the nuclear size correction, and we postpone its discussion to Subsect. 6.1.2 dealing with the nuclear size contribution. 

Nuclear Size and Structure Corrections of Order [Zofm, 115... 

Fig. 6.2. Diagrams for elastic nuclear size corrections of order Za) m with one form factor insertion. Empty dot corresponds to factor Gb(—fc ) — 1...

The description of nuclear structure corrections of order Za) m in terms of nuclear size and nuclear polarizability contributions is somewhat artificial. As we have seen above the nuclear size correction of this order depends not on the charge radius of the nucleus but on the third Zemach moment in (6.15). One might expect the inelastic intermediate nuclear states in Fig. 6.4 would... 

The nuclear size and polarizability corrections of order Zaf obtained in Sect. 

Nuclear size corrections of order (Za) may be obtained in a quite straightforward way in the framework of the quantum mechanical third order perturbation theory. In this approach one considers the difference between the electric field generated by the nonlocal charge density described by the nuclear form factor and the field of the pointlike charge as a perturbation operator [16, 17]. 

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). 

In the Schrodinger-Coulomb approximation the expression in (6.33) reduces to the leading nuclear size correction in (6.3). New results arise if we take into account Dirac corrections to the Schrodinger-Coulomb wave functions of relative order (Za). For the nS states the product of the wave functions in (6.33) has the form (see, e.g, [17])... 

This expression nicely illustrates the main qualitative features of the order (Za) nuclear size contribution. First, we observe a logarithmic enhancement connected with the singularity of the Dirac wave function at small distances. Due to the smallness of the nuclear size, the effective logarithm of the ratio of the atomic size and the nuclear size is a rather large number it is equal to about —10 for the IS level in hydrogen and deuterium. The result in (6.35) contains all state-dependent contributions of order (Za) . 

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