Scattering cross section Bound atom

In this chapter we consider the physics of the positronium atom and what is known, both theoretically and experimentally, of its interactions with other atomic and molecular species. The basic properties of positronium have been briefly mentioned in subsection 1.2.2 and will not be repeated here. Similarly, positronium production in the collisions of positrons with gases, and within and at the surface of solids, has been reviewed in section 1.5 and in Chapter 4. Some of the experimental methods, e.g. lifetime spectroscopy and angular correlation studies of the annihilation radiation, which are used to derive information on positronium interactions, have also been described previously. These will be of most relevance to the discussion in sections 7.3-7.5 on annihilation, slowing down and bound states. Techniques for the production of beams of positronium atoms were introduced in section 1.5. We describe here in more detail the method which has allowed measurements of positronium scattering cross sections to be made over a range of kinetic energies, typically from a few eV up to 100-200 eV, and the first such studies are summarized in section 7.6. 

Consider first of all the scattering of neutrons by the nuclei in a monoatomic liquid. This process is characterized by a scattering cross-section, Qq, which, in turn, is related to Z>d, the bound atom scattering length. For slow neutrons. 

The approximation works very well within the limits originally set for its use [1]. However, in the molecular spectroscopy of hydrogenous molecules a further version of the approximation is made. Here the cross section used in the calculation of the observed intensities is the total bound scattering cross section of each atom and the dynamics are always treated as incoherent, irrespective of the momentum transferred. This is discussed further with specific examples in 11.1. 

Abound 2.10 scattering cross section, atom bound bam... 

Table 2 Bound scattering lengths, i>(fm) and cross section for selected isotopes and for selected naturally occurring isotopic mixtures of the elements u(hams, 1 bam = 100 fm ). Z, atomic number A, mass number I, spin of the nuclear groimd state i>coh> bine, coherent and incoherent scattering lengths ffa, ffeCh, coherent and incoherent cross sections ffa, absorption cross section for 2.2 km s neutrons ...

Because our description of differential cross sections for momentum transfer in a reaction initiated by an electron beam depends on our ability to describe both the structure and the reaction mechanism, scattering provides much more information about bound states. This is even more true of ionisation. The information is less accurate than from photon spectroscopy and is obtained only after a thorough understanding of reactions, the subject of this book, is achieved. The understanding of structure and reactions is of course achieved iteratively. A theoretical description of a reaction is completely tested only when we know the structure of the relevant target states with accuracy that is at least commensurate with that of the reaction calculation. The hydrogen atom is the prototype... 

Another important application of all-orders in aZ atomic QED is the theory of the multicharged ions. Nowadays all elements of the Periodic Table up to Uranium (Z=92) can be observed in the laboratory as H-like, He-like etc ions. The recent achievements of the QED theory of the highly charged ions (HCI) are summarized in [11], [12]. In principle, the QED theory of atoms includes the evaluation of the QED corrections to the energy levels and corrections to the hyperfine structure intervals, as well as the QED corrections to the transition probabilities and cross-sections of the different atomic processes photon and electron scattering, photoionization, electron capture etc. QED corrections can be evaluated also to the different atomic properties in the external fields bound electron -factors and polarizabilities. In this review we will concentrate mainly on the corrections to the energy levels which are usually called the Lamb Shift (here the Lamb Shift should be understood in a more broad sense than the 2s, 2p level shift in a hydrogen). 

After their excitation from a bound state within an atom, the photo electrons have to move through the other electron shells of the atom, through the lattice of a solid sample, through the surface barrier into the ultra-high vacuum (UHV) of the instrument and through the environment of the analyzer-detector device. The cross section of scattering processes with any matter is very large for elec-... 

The solid states represent bounded atomic associations and the diffraction intensity is a result of coherently scattered wave interference. The neutron scattering can be coherent elastic or inelastic and incoherent. In coherent total scattering experiment both elastically and inelastically scattered neutrons are detected, thus performing energy integration over the whole range gives a value for The total differential cross-section is,... 

A further difference concerns the bound atom cross sections. The coherent cross section is not isotropic since the scattering processes involve... 

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