Cross Section Dσ Research Articles

Diffusion incohérente de photons de 662 keV par les électrons K de l'or

The differential cross section dσ K/dΩ for the incoherent scattering of 662 keV gamma rays by the K-shell electrons of gold is determined experimentally. This cross section is compared with the Klein-Nishina cross section dσ ι/dΩ for scattering angles function calculated on the basis of certain approximations.

Quantum Mechanical (Phase Shift) Analysis of Differential Elastic Scattering of Molecular Beams

For a spherically symmetrical intermolecular potential V(r)=εf(r/σ) the quantum calculation of the elastic scattering cross section dσ(Θ)/dΩ in the c.m. system is carried out as follows. For a given relative velocity (or deBroglie wavelength) and an assumed V(r), the radial wave equation is integrated for successive values of the angular momentum quantum number l, yielding the phase shifts ηι. Then dσ(Θ)dΩ is computed in terms of the series of ηι's in the standard way. A general computational program (following that of K. Smith) is outlined for the evaluation of the radial wave function and the phase shifts, utilizing an IBM 704 computer. Calculations are presented for the L-J (12, 6) potential function. The results may be concisely represented using the framework provided by the semiclassical treatment of Ford and Wheeler, i.e., in terms of a set of reduced phase constants vs reduced angular momenta at various reduced relative kinetic energies K. Tables and graphs are presented from which the phases may be obtained, to a good approximation, for any given ε, σ and K. Computation of the differential and total cross sections from the phase shifts is then readily accomplished. The results are compared with the classical and semiclassical treatments. The problem of tunneling and orbiting is discussed.

Scattering of Polarized Neutrons by Protons

IN spite of many attempts, it has not been possible so far to develop a theory of nuclear forces which accounts in a satisfactory way for all the properties of even the simplest system, a neutron and a proton. An alternative procedure might, therefore, be attempted, namely, to obtain the interaction potential empirically from the various observed properties like the binding energy, quadrupole moment, magnetic moment of the deuteron and the scattering cross-section. The latter seems particularly useful for this purpose, as there exist general reciprocal quantum mechanical relations between the differential scattering cross-section dσ and the interaction potential; dσ is expressed in terms of certain phase shifts ŋl, (l = 0, 1, 2, . . .), suffered by the partial waves of different orbital angular momentum l due to the interaction between the two particles. For spinless particles, a knowledge of d (as a function of the angle of scattering θ) determines all the phase shifts ŋl and vice versa, and a knowledge of the phase shift ŋl (as a function of energy) for a given l-state determines the interaction potential for that l-state and vice versa. However, the fact that the neutron–proton system splits into the singlet and triplet states (with different interactions) makes the determination of the phase-shifts from a knowledge of dσ (θ) alone impossible.