About the Project

Rutherford%20scattering

AdvancedHelp

(0.002 seconds)

1—10 of 119 matching pages

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: William P. Reinhardt
    Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions. …
  • In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
    4: 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)).
    5: 10.73 Physical Applications
    See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25). … Bessel functions enter in the study of the scattering of light and other electromagnetic radiation, not only from cylindrical surfaces but also in the statistical analysis involved in scattering from rough surfaces. … …
    §10.73(ii) Spherical Bessel Functions
    Accordingly, the spherical Bessel functions appear in all problems in three dimensions with spherical symmetry involving the scattering of electromagnetic radiation. …
    6: 20 Theta Functions
    Chapter 20 Theta Functions
    7: Bibliography N
  • D. Naylor (1989) On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
  • W. J. Nellis and B. C. Carlson (1966) Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.
  • E. W. Ng and M. Geller (1969) A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
  • H. M. Nussenzveig (1965) High-frequency scattering by an impenetrable sphere. Ann. Physics 34 (1), pp. 23–95.
  • H. M. Nussenzveig (1992) Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.
  • 8: 29.19 Physical Applications
    §29.19(ii) Lamé Polynomials
    Macfadyen and Winternitz (1971) finds expansions for the two-body relativistic scattering amplitudes. …
    9: 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. …
    10: Bibliography V
  • H. C. van de Hulst (1957) Light Scattering by Small Particles. John Wiley and Sons. Inc., New York.
  • H. C. van de Hulst (1980) Multiple Light Scattering. Vol. 1, Academic Press, New York.
  • H. Volkmer (2004a) Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.