Local hyperspherical surface function

ABSTRACT A formulation is presented for the use of hyperspherical coordinates and local hyperspherical surface functions in the electron-hydrogen atom scattering problem. Some representative numerical results of the application of this formulation are given,... 

Although the emphasis of this paper is on the formalism we used in applying the method of hyper spherical coordinates and local hyperspherical surface functions to the e + H elastic and inelastic scattering problem, we present now a sampling of the results obtained. 

We have presented the hyperspherical coordinate formulation for e + T elastic and inelastic scattering using local surface functions and have shown that it is both efficient and accurate. It can in principle be extended to energies above the ionization threshold by including hyperspherical harmonics in the surface function basis set. It also permits a calculation of polarization cross sections. This approach is very promising and should lead to a very complete description of the e H scattering processes. 

In Section 2 we define the symmetrized hyperspherical coordinates for the electron-hydrogen atom system and express the hamiltonian in these coordinates. In Section 3 symmetry is discussed. The appropriate symmetry wave functions are introduced in Section 4, the local surface eigenfunctions and energy eigenvalues in Section 5, and the scattering equations and asymptotic analysis in Section 6. Finally, some representative results are given and discussed in Section 7 and a summary of the conclusions is presented in Section 8. 

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