Charge distribution Fourier series

Fourier Series for the Total Electrostatic Energy The Coulombic electronic energy of a continuous charge distribution is defined as... 

For a solid surface with two-dimensional periodicity, such as a defect-free crystalline surface, all the measurable quantities have the same two-dimensional periodicity, for example, the surface charge distribution, the force between a crystalline surface and an inert-gas atom (Steele, 1974 Goodman and Wachman, 1976 Sakai, Cardino, and Hamann, 1986), tunneling current distribution, and STM topographic images (Chen, 1991). These quantities can be expanded into two-dimensional Fourier series. Usually, only the few lowest Fourier components are enough for describing the physical phenomenon, which requires a set of Fourier coefficients. If the surface exhibits an additional symmetry, then the number of independent Fourier coefficients can be further reduced. 

Within the interval r < R the charge distribution is expanded into a Fourier-Bessel series and beyond the cutoff-radius R, the charge distribution is assumed to be zero ... 

Thus, the form factor F q) is the Fourier-Bessel (or Hankel) transform (of order zero) of the charge density distribution p r) [33]. With the short-range series expansion for jo x) one obtains easily the expansion... 

Figure 9.2 Spectra of ESTgenerated cytochrome c ions obtained with (a) an ion trap (IT) and (b) a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. The mass resolving power of the IT is low, so the charge state distribution has to be derived from a series of peaks at different charge states. The mass resolving power of the FT-ICR is high enough to resolve the isotopic pattern of one charge state. The insets display the isotopic patterns of the charge state +/3...

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