Fredholm Optical-Potential Calculation of Elastic Electron-Hydrogen-Atom Phase Shifts

A Fredholm technique is used to compute elastic phase shifts for electron-hydrogen-atom scattering using the Feshbach optical potential. The method is noniterative and is computationally highly efficient as it allows computation of the Fredholm determinant $D(E+i\epsilon )$ at a series of energies from a single set of matrix elements of the optical potential. Scattering information is then obtained over a continuous range of energies by interpolation of $D(E+i\epsilon )$; resonance is easily located by inspection of the zeros of $\mathrm{Re}D(E+i\epsilon )$.