Overlapping series

Table 4.3 Charge states calculated from the electrospray spectrum shown in Figure 4.18, assuming (a) all ions form part of the same series, and (b) the presence of two overlapping series containing these ions...

Usually the number of charges on an ion will not be known, but it can be calculated using a formula based on two different ions appearing in the spectrum. Actually, the molecular mass of a sample can be calculated automatically, or semiautomatically, by the processing software associated with the mass spectrometer. Experimentally, the automatic calculation of molecular mass is very helpful because a complex peptide or protein mixture will display an m/z spectrum with several overlapping series of multiply charged ions. 

Closer inspection of Fig. 10.8 reveals that the first three m series are completely isolated, i.e. the resonances with different m quantum numbers are energetically well separated from each other. But Fig. 10.8 (d) shows that the lowest state of the fifth series intrudes into the fourth series. The higher series are characterized by more and more intruder states. Thus, as conjectured in Section 10.1 on the basis of the simple independent-particle He -f e model, it is the onset of overlapping series with the accompanying intruder states that, on the quantum level, are the source of complicated behaviour in the helium spectrum. 

The helium atom is a classically chaotic system. In Chapter 10 we saw that chaos chooses the way of overlapping resonance series to make its presence felt. The existence of overlapping series in the helium atom was confirmed experimentaUy by Domke et al. (1995). Using synchrotron radiation, helium resonances up to the N = 9 threshold were investigated. At the same time good agreement with theoretical complex rota-... 

Restriction-site mapping in DNA may be performed by end-labelling with polynucleotide kinase as above, and subsequent partial digestion with the restriction enzyme. An overlapping series of polynucleotides with a common labelled terminus is thus formed, and size analysis of these affords a restriction map. Polynucleotide kinase may also be used to assay the number of 5 -phosphorylated termini in DNA generated as the result of the action of restriction endonuclease. In the presence of... 

In the presence of opposite asymmetries (gi and qz of different sign), the intensities of the overlapping series may reflect those of the perturbers, as shown in fig. 8.32. This does not, however, lead to any dramatic changes in the corresponding two-dimensional graph. A good experimental example of this behaviour appears in the 3p-spectrum of Ca [447], where the presence of perturbers from the upper series can be detected through intensity modulations in the lower one. 

The strongest pieces of evidence complex atoms provide in favour of independent electron modes and simple Bohr-Sommerfeld quantisation are (i) the existence of Rydberg series and (ii) the regularity of the periodic table of the elements. As a corollary, we should look for quantum chaos (if it occurs) in atoms for which there is some breakdown in the quality of the shell structure, combined with prolific and heavily perturbed overlapping series of interacting levels. These conditions are most readily met, as will be shown below, in the spectra of the alkaline-earth elements, as a result of d-orbital collapse. 

The problem of determining K independent of measurement of Ho is the principal problem faced in establishing the Ho scale for a series of acidic solutions. What is done is to measure K for some base in aqueous solution where Ho pH. This base can then be used to find the Ho of a somewhat more acidic solution. The K of 3. second, somewhat weaker base is then determined in the more acidic solution. This second base can then be used to measure Ho of a still more acidic solution. By this process of using an overlapping series of bases, the Ho of successively more acidic solutions can be referenced to the original aqueous measurement. The assumption involved in this procedure is that the ratio of the activity coefficients for the series of bases and the series of cation does not change from solvent to solvent, that is,... 

SIMS has not been much used as a tool for studying corrosion. The main reason for this seems to be that SIMS spectra and depth profiles are frequently difficult to interpret in terms of clearly defined diffusion or deposition mechanisms. Spectra from oxides contain a complex (and frequently overlapping) series of molecular ion masses secondary-ion depth profiles are complicated in the oxide and interface region by matrix-effected changes in ion yield... 

The spectra of the atoms of other elements also consist of similar series, although much overlapping makes them less simple in appearance. 

Contig A group of pieces of DNA, derived from a cloning experiment (often a series ( ESTs, see below), that represent overlapping regions of a chromosome... 

It is equivalent, when an ftk spectrometer is used, to re-apodization of the data. Curve fitting is a method of modeling a real absorption band on the assumption that it consists of a series of overlapped peaks having a specific lineshape. Typically the user specifies the number of peaks to attempt to resolve and the type of lineshape. The program then varies the positions, sizes, and widths of the peaks to minimize the difference between the model and the spectmm. The largest difficulty is in knowing the correct number of peaks to resolve. Derivative spectra are often useful in determining the correct number (18,53,54). 

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