Effective Range Approximation Research Articles

Electron-Hydrogen Scattering at Low Energies

The effective range in the singlet electron-hydrogen system has been evaluated as 2.646\ifmmode\pm\else\textpm\fi{}0.004 atomic units by using the asymptotic amplitude of the 202-parameter ${\mathrm{H}}^{\ensuremath{-}}$ wave function of Pekeris. This value of the effective range, together with the value of the electron affinity of ${\mathrm{H}}^{\ensuremath{-}}$, determines the scattering length in the singlet system as 6.167 atomic units. The effective range in the triplet system is calculated to be 1.219 atomic units by a Hartree-Fock approximation. It is shown that the effective-range approximation is very good for all energies at which only elastic scattering is allowed. The photo-ionization of ${\mathrm{H}}^{\ensuremath{-}}$ is briefly discussed on the basis of the effective-range theory.

Note on the Low Energy Electron-Hydrogen Scattering

In a previous paper the low-energy electron-hydrogen scattering was discussed on the effective range approximation. An exa1aination of the energy range of the incident electron to which this method can be applied is presented. An error is corrected in the normalization of the ground state wave function of the negative hydrogen ion. A comparison is made of the results obtained by the variational method with those predicted by the effective rarge theory, (B.O.G.)

Fixed Angle Dispersion Relations for Nucleon-Nucleon Scattering

Dispersion relations in which the scattering angle $\ensuremath{\theta}$ is kept constant are proposed for nucleon-nucleon scattering. These relations are a direct consequence of a general representation proposed by Mandelstam (see reference 4) and can be checked directly up to the fourth-order perturbation theory. An extrapolation procedure based on these dispersion relations is proposed with the purpose of obtaining an independent determination of the pion-nucleon coupling constant and the possibility of discriminating between the different available sets of phase shifts.A first determination of the pion-nucleon coupling constant from these fixed-angle dispersion relations is attempted by means of a more direct extrapolation procedure, closely analogous to the effective range approximation, and a result in good agreement with the currently accepted value is obtained.