J P Coleman

The use of second order potentials in the theory of the scattering of charged particles by atoms I. General theory

Equations for approximate wavefunctions describing the scattering of charged particles by atoms are often obtained by using a truncated eigenfunction (or close coupling) expansion. It is shown how allowance can be made for the states omitted in the expansion, by the introduction of suitable second order potentials. The potentials are evaluated in a closure approximation and depend on an effective energy parameter which can be chosen so that the correct long range interaction is obtained in the incident channel. An impact parameter version of the method is introduced and the relationship with the Glauber approximation is discussed.

The use of second order potentials in the theory of scattering of charged particles by atoms. II. Electron and proton scattering by hydrogen atoms

For Pt. I see Ibid Vol.5 No.3 p537. The method of Paper I is applied to collisions of electrons and protons with atomic hydrogen. One-channel and two-channel approximations are used and results are presented for elastic scattering and 1s-2s, 1s-2p and 1s-3p excitation.

The use of second order potentials in the theory of scattering of charged particles by atoms. V. Excitation of helium atoms by fast protons and charge exchange

For pt. IV see abstr. A26590 of 1973. Cross sections are calculated for the excitation by protons of ground state helium to the 21S and 21P levels at incident energies in the interval 25 to 500 keV. Cross sections are also calculated for electron capture by protons from helium at energies above 100 keV, using a distorted wave approximation.

The use of second order potentials in the theory of the scattering of charged particles by atoms. IV. Electron scattering of helium atoms

For pt. III see abstr. A83212 of 1972. The method of paper I (see abstr. A24375 of 1972) is applied to the scattering by helium atoms of electrons between 50 and 1000 eV, and results are presented for elastic scattering and the 21S and 21P excitation. It is found that the inclusion of second order potential terms leads to cross sections which are in significantly better agreement with the experimental data than those of previous calculations.

The use of second order potentials in the theory of the scattering of charged particle by atoms. III. A four-channel approximation for electron and proton scattering by hydrogen atoms

For pt. II see abstr. A28228 of 1972. The method of Bransden and Coleman (1972) is applied to scattering by hydrogen atoms in a four-channel approximation in which the 1s, 2s and 2p states are explicitly included. Results are given for 1s-2s and 1s-2p excitation by electrons and protons.

The use of second order potentials in the theory of scattering of charged particles by atoms. VII. The partial wave formalism and elastic scattering of electrons by hydrogen and helium

The second order potential approximation of Bransden and Coleman (1972) is applied in a partial wave formalism to the elastic scattering of electrons from hydrogen and helium atoms. Differential, integrated, and total cross sections are presented for hydrogen in the energy range 100-200 eV and for helium in the range 50-500 eV. A one-channel approximation is used and the effect of exchange is included to first order in the potential. Conclusions are drawn as to the validity of the impact parameter approximation used in previous applications of the method.

ELECTRON CAPTURE INTO EXCITED STATES IN THE IMPULSE APPROXIMATION.

Impulse approximation cross sections are evaluated for the electron capture processes H+ + H(1s) -> H(2p, 3s or 3p) + H+ He2+ + H(1s) -> He+ (2p or 3s) + H+ The results for capture into the 2p state of atomic hydrogen are in close agreement with the measurements of Stebbings et al. in 1965. Total impulse approximation cross sections for capture by protons and alpha particles are estimated. The proton impact cross sections are practically identical with estimates by Coleman and McDowell based on less reliable data.

Iteration-variation methods and the epsilon algorithm (appl. to atomic scattering problems)

A variety of iteration-variation methods have been used to solve integro-differential equations for atomic scattering problems. These methods are identified as sequence-to-sequence transformations, and relationships are established with Aitkens Delta 2 transformation and the epsilon algorithm. The results give a new insight into the nature of iteration-variation methods and permit a comparison of their various forms. As a practical consequence, the calculations involved in implementing iteration-variation methods are now replaced by some very simple arithmetic.

The impulse approximation for excitation of atomic hydrogen

Cross sections for the process H+ +H(1s) -> H+ +H(2s) have been calculated in the quantal impulse approximation for proton energies in the range 1-500 keV. It is shown that a peaking approximation previously used in the evaluation of impulse approximation matrix elements is invalid and greatly underestimates the true impulse approximation cross section for this process.

The use of second order potentials in the theory of scattering of charged particles by atoms. VI. Elastic scattering of electrons by hydrogen and helium atoms

Angular distributions for the elastic scattering of electrons by hydrogen and helium atoms have been calculated by the second order potential method of Bransden and Coleman (1972), using a partial wave expansion and allowing for exchange, in the energy interval 50 to 200 eV. Good agreement with experimental data is obtained except at large angle scattering, for which the calculated values are up to 25% smaller than those measured.