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Rutherford scattering

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1: 5.20 Physical Applications
Rutherford Scattering
Veneziano (1968) identifies relationships between particle scattering amplitudes described by the beta function, an important early development in string theory. …
2: 33.22 Particle Scattering and Atomic and Molecular Spectra
§33.22 Particle Scattering and Atomic and Molecular Spectra
Positive-energy functions correspond to processes such as Rutherford scattering and Coulomb excitation of nuclei (Alder et al. (1956)), and atomic photo-ionization and electron-ion collisions (Bethe and Salpeter (1977)). …
§33.22(iv) Klein–Gordon and Dirac Equations
The relativistic motion of spinless particles in a Coulomb field, as encountered in pionic atoms and pion-nucleon scattering (Backenstoss (1970)) is described by a Klein–Gordon equation equivalent to (33.2.1); see Barnett (1981a). …
  • Scattering at complex energies. See for example McDonald and Nuttall (1969).

  • 3: 15.18 Physical Applications
    The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)). More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).
    4: 29.19 Physical Applications
    §29.19(ii) Lamé Polynomials
    Macfadyen and Winternitz (1971) finds expansions for the two-body relativistic scattering amplitudes. …
    5: Mark J. Ablowitz
    for appropriate data they can be linearized by the Inverse Scattering Transform (IST) and they possess solitons as special solutions. …Some of the relationships between IST and Painlevé equations are discussed in two books: Solitons and the Inverse Scattering Transform and Solitons, Nonlinear Evolution Equations and Inverse Scattering. …
    6: 14.31 Other Applications
    §14.31(iii) Miscellaneous
    Many additional physical applications of Legendre polynomials and associated Legendre functions include solution of the Helmholtz equation, as well as the Laplace equation, in spherical coordinates (Temme (1996b)), quantum mechanics (Edmonds (1974)), and high-frequency scattering by a sphere (Nussenzveig (1965)). … Legendre functions P ν ( x ) of complex degree ν appear in the application of complex angular momentum techniques to atomic and molecular scattering (Connor and Mackay (1979)). …
    7: T. Mark Dunster
    He has received a number of National Science Foundation grants, and has published numerous papers in the areas of uniform asymptotic solutions of differential equations, convergent WKB methods, special functions, quantum mechanics, and scattering theory. …
    8: Vadim B. Kuznetsov
    Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics. …
    9: Ian J. Thompson
    Thompson has published papers on special functions, and numerous papers in theoretical nuclear physics, especially in scattering theory. …
    10: 27.17 Other Applications
    Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.